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The main camping area from the ferris wheel at the Bonnaroo Music and Arts Festival in Manchester, Tenn., on Thursday, June 7, 2018. (Photo: Shelley Mays / Tennessean.com)
MANCHESTER, Tenn. - A Bonnaroo attendee was found dead Friday morning on the venue's grounds marking the 13th death at the music and arts festival in its 17-year history, officials said.
The Coffee County Sheriff's Office identified the man as Michael Donivan Craddock, Jr., 32 of Mount Juliet, Tenn.
Sheriff's office spokesman Lucky Knott said about 10:30 a.m., the sheriff's office responded to the festival's campground for a medical call. When deputies and investigators arrived at the scene, they found Craddock dead inside a vehicle.
Sheriff Steve Graves said foul play is not suspected in the death.
Graves said Craddock’s body has been sent to the medical examiner office in Nashville, for an autopsy to determine the exact cause of death.
His death is the only known fatality so far at the festival, authorities said.
Bonnaroo 2018 started Thursday and is scheduled to run through Sunday. Festival headliners include Eminem, the Killers, and Muse.
Bonnaroo 2018 day 1: Here's what we saw in the fest’s first hours
So far this year, Knott said dozens of people have been either treated or transported by ambulance to local hospitals to be treated for heat-related issues at the festival.
First responders reminded festival attendees to hydrate and wear hats if possible.
"The temperature is 90 with a heat index of 99," Knott said Friday afternoon. "We can't stress it enough that concert goers to drink a lot of water. Staying hydrated will save your life."
Although he did not give an exact number, Bonnaroo medical director Carl Monzo said transports are "lower than the same time last year."
A high of 94 topped Manchester on Friday and highs in the upper 80s and low 90s are expected during the next three days of the festival.
More: Bonnaroo will now wash your clothes - for free
The last death at Bonnaroo took place in June 2015 after a 47-year-old man died after collapsing in the event's main area — known as Centeroo. His death stemmed from a pre-existing cardiac issue, authorities at the time said.
A year later, on June 11, 2016, festival attendee Casey J. Young, 22, of Louisville, was struck and killed by multiple vehicles outside the festival grounds on Interstate 24.
According to a Davidson County autopsy report, his manner of death was accidental and his cause of death was from multiple blunt force injuries. No drugs or alcohol were found in his system at the time of his death, a toxicology report found.
Arrests, citations and fire calls
Law enforcement overseeing Bonnaroo have cited about 60 people and arrested about 19 people, records as of late afternoon Friday showed.
A majority were for public intoxication, disorderly conduct and illegal possession of a controlled substance, Knott said.
Bonnaroo fire authorities said no major fire calls had been reported.
Glen Aussicker, a firefighter shift leader, said most of the calls stemmed from carbon monoxide alarms triggering in RVs so far this week. Most of the alarms sounded off during the evening hours, he said.
If an RV alarm sounds, firefighters say residents should immediately open all windows to allow the poisonous air to escape, leave the camper and dial 911.
They are also reminding campers carbon monoxide doesn't just affect people inside RVs.
Firefighters are asking festival attendees to remember not to pitch tents next to an RV's exhausts or even car exhausts — especially if someone is in the car cooling off with the AC or charging their phone.
Another safety tip: Crack RV windows when no one is inside.
Read or Share this story: https://usat.ly/2sNt9CQ | – A person has died while attending the Bonnaroo Music and Arts Festival in Tennessee, reports the AP. Coffee County Sheriff Steve Graves confirmed a body was found Friday morning at a festival campground. The sheriff's office has identified the man as 32-year-old Michael Donivan Craddock, of Mount Juliet, Tenn. Coffee County sheriff's spokesman Lucky Knott says officials are investigating the cause of death but foul play is not suspected. Craddock was found dead inside a vehicle, reports USA Today. Graves said dozens of people have been treated for heat-related issues at the festival, which began Thursday in Manchester and runs through Sunday. This is the 13th death at the music and arts festival in its 17-year history, officials said. Festival headliners include Eminem, Muse, and the Killers. |
clinically , osteoarthritis ( oa ) , or degenerative joint disease , is a painful and debilitating condition characterized by a progressive loss of articular cartilage , mild inflammation of the tissues in and around the joints , and sometimes formation of osteophytes and bone cysts .
patients with oa report persistent pain and display increased sensitivity to pressure and noxious stimuli in the arthritic joint . at present
, there is no cure for oa with available therapeutic approaches and analgesics are prescribed to alleviate the pain associated with this condition , with some degree of success .
however , oa pain remains a clinical issue and animal models of oa are being developed to improve our understanding of oa - related pain mechanisms and disclose novel targets for therapy .
however , they involve skillful surgical intervention and are primarily performed in the rat , while destabilization of medial meniscus ( dmm ) is used in the mouse .
spontaneous development of oa occurs in guinea pig and spontaneous joint degeneration has been reported in c57 black mice from 3 to 16 months of age .
spontaneous oa models do not involve any intervention to induce the condition , but they have inherent variability , and as such , incur greater numbers and cost . chemically induced models , on the other hand , require much less invasive procedures than surgical models , and as such , are easier to implement and permit the study of oa lesions at different stages .
these models include single injections in the knee of inflammatory agents , immunotoxins , collagenase , papain , or monoiodoacetate , which can be toxic if they escape the joint space .
of all chemical models of oa , mia is the one most often used , particularly to test the efficacy of pharmacologic agents to treat pain , as this model generates a reproducible , robust , and rapid pain - like phenotype that can be graded by altering mia dosage .
intra - articular injection of mia in rodents reproduces oa - like lesions and functional impairment that can be analyzed and quantified .
mia is an inhibitor of glyceraldehyde-3-phosphatase , disrupting cellular glycolysis and eventually resulting in cell death .
intra - articular injection of mia causes chondrocyte cell death , leading to cartilage degeneration and subsequent subchondral bone alterations such as appearance of bone osteophytes .
as the utility of mia in the rat has been described before , in this paper we focus on the methodology of mia - induced oa in mice as this model is being increasingly used with the availability of knock - out mice .
we describe a procedure for the injection of very small volumes into the knee and methods for measuring sensitivity to noxious and non - noxious stimuli in the hind limbs . the breakdown of the methodology will help to reduce variability , and as such , refine the model and reduce the number of animals needed for study .
procedures involving animal subjects have been approved by the ethical committee at king 's college london and are in accordance with uk home office regulations ( animals scientific procedures act 1986 ) .
house 8 - 10 week - old mice in groups of 5 under a 12 hr light / dark cycle ( lights on at 7:00 am ) with food and water ad libitum .
use body weights as parameters for randomization . on the day of injection , freshly prepare the solution of monoiodoacetate in sterile saline ( 0.9% nacl ) at the desired concentrations . use sterile saline for injections in a separate group of control mice .
therefore , it is recommended that gloves and mask are worn when handling the powder and preparing the solution .
anesthetize mice using an anesthetic trolley by first placing them in a chamber delivering 2% isoflurane in o2 mixture ( flow rate 1.5 l / min ) and then transfer mice to the nose cone section , which also delivers the 2% isoflurane - o2 mixture , and as such , maintains anesthesia during injection .
place vet ointment on the eyes to avoid their drying out while under anesthesia .
confirm anesthesia by checking the animal 's lack of response to a pinch stimulus on the hind paws .
the patellar tendon ( white line bellow the patella ) will become visible . in order to stabilize the injection site ,
keep the knee still , in a bent position , by placing the index finger beneath the knee joint and the thumb above the anterior surface of the ankle joint .
joint preference is not required . to find the precise site of injection , run a 26 g needle attached to a syringe horizontally along the knee ( so as not to pierce the skin with the tip ) until it finds the gap beneath the patella .
apply gentle pressure to mark the area and then lift the needle and syringe vertically for the injection .
insert the needle in the marked area , through the patellar tendon , perpendicular to the tibia .
after injection , massage the knee to ensure even distribution of the solution . discard the needle immediately in the sharps bin.place mice back into a clean home cage on a heated mat and allow them to recover .
keep constant vigilance on the animals until they regain suitable consciousness , which is measured by them regaining sternal recumbency .
note : it is suggested for best practice and training purposes that a dye is used and immediate post - mortem dissection performed to confirm correct localization of injection .
after injection , massage the knee to ensure even distribution of the solution . discard the needle immediately in the sharps bin .
place mice back into a clean home cage on a heated mat and allow them to recover . keep constant vigilance on the animals until they regain suitable consciousness , which is measured by them regaining sternal recumbency .
note : it is suggested for best practice and training purposes that a dye is used and immediate post - mortem dissection performed to confirm correct localization of injection . note : static mechanical withdrawal thresholds are assessed by applying von frey hairs to the plantar surface of the hind paw .
bring mice to the behavioral room and let unrestrained animals acclimatize in acrylic cubicles ( 8 cm x 5 cm x 10 cm ) atop a wire mesh grid .
train mice by handling and 2 hr habituation to the cubicles for two days prior to von frey hair application in order to limit stress and ambulation during application of von frey hairs . on test days , habituate animals to the cubicles for up to 60 min prior to testing .
train mice by handling and 2 hr habituation to the cubicles for two days prior to von frey hair application in order to limit stress and ambulation during application of von frey hairs . on test days , habituate animals
apply calibrated von frey hairs ( flexible nylon fibers of increasing diameter that exert defined levels of force as calibrated by the manufacturing company and expressed as grams ( g ) ) to the plantar surface of the hind paw until the fiber bends .
use 0.008 , 0.02 , 0.04 , 0.07 , 0.16 , 0.4 , 0.6 , and 1.0 g fibers during testing .
hold each hair in place for 3 sec or until the paw is withdrawn , the latter defining a positive response . starting with a stimulus strength of 0.07 g ,
apply hairs according to the " up - down method " : mark as x a withdrawal response and o an absence of response .
apply in ascending order of force , up to 1 g ( cut - off force ) , until a response is detected.re-test the paw by repeating step 2.2.1 , starting with the filament that exerts a force below the one that produced a withdrawal.then , apply the remaining filaments sequentially , by descending force , until no withdrawal occurs .
continue until a sequence of six responses is obtained ( e.g. , oxoxox ) , in order to obtain the ' k ' value by referring to tabular values .express
use the formula ( 10)/10,000 where xr = value of last von frey filament used in the sequence ( in log units ) , k = tabular value , and = mean difference in forces between fibers .
where no response is detected , use the maximal response of 1 g .
hold each hair in place for
3 sec or until the paw is withdrawn , the latter defining a positive response . starting with a stimulus strength of 0.07 g , apply hairs according to the " up - down method " : mark as x a withdrawal response and o an absence of response . apply in ascending order of force , up to 1 g ( cut - off force ) , until a response is detected .
re - test the paw by repeating step 2.2.1 , starting with the filament that exerts a force below the one that produced a withdrawal .
then , apply the remaining filaments sequentially , by descending force , until no withdrawal occurs .
continue until a sequence of six responses is obtained ( e.g. , oxoxox ) , in order to obtain the ' k ' value by referring to tabular values .
use the formula ( 10)/10,000 where xr = value of last von frey filament used in the sequence ( in log units ) , k = tabular value , and = mean difference in forces between fibers .
where no response is detected , use the maximal response of 1 g . following the procedure described above ( 2.2.1 - 2.2.4 ) , assess mechanical thresholds of both hind paws before mia injection as baseline values .
after injection , assess thresholds of the ipsilateral and contralateral paws at regular day intervals for several weeks after mia to ascertain the development of mechanical allodynia .
note : for example , we report thresholds measured 0 , 3 , 5 , 7 , 10 , 14 , 21 , and 28 days after mia injection .
train each mouse to walk into a plexiglass chamber on the apparatus and sit in the holding box . place the mouse in front of the holding box ,
lift the entrance up 45 , and allow the mouse to walk in and close the box .
this training takes at least two days and guarantees that the animal is still and not leaning on either side of the chamber .
calibrate the instrument before use with a 100 g check weight ( or according to equipment instruction ) .
the duration of each measurement takes 1 sec , as per the manufacturer 's instructions .
the duration of each measurement takes 1 sec , as per the manufacturer 's instructions .
collect three measurements of the weight borne on each hind paw from the recording pad for each recording session and use the mean value to calculate the difference in weight borne by ipsilateral and contralateral paws .
then , repeat assessments at regular intervals over several weeks to ascertain the development of gate changes . for example
, we report thresholds measured on 0 , 3 , 5 , 7 , 10 , 14 , 21 , and 28 days after mia injection .
note : a normal weight bearing value of 50% represents an equal weight distribution across ipsilateral and contralateral hindlimb .
measurements of mechanical thresholds and weight bearing deficits can be performed in the same mice , as neither end point affects the other . for pharmacological assessment ,
each group of animals should be tested at set times after dosing in line with the pharmacokinetic profile of the compound used .
house 8 - 10 week - old mice in groups of 5 under a 12 hr light / dark cycle ( lights on at 7:00 am ) with food and water ad libitum .
use body weights as parameters for randomization . on the day of injection , freshly prepare the solution of monoiodoacetate in sterile saline ( 0.9% nacl ) at the desired concentrations . use sterile saline for injections in a separate group of control mice .
the highest recommend dose of mia is 1 mg in 10 l . caution : monoiodoacetate is very toxic .
therefore , it is recommended that gloves and mask are worn when handling the powder and preparing the solution .
anesthetize mice using an anesthetic trolley by first placing them in a chamber delivering 2% isoflurane in o2 mixture ( flow rate 1.5 l / min ) and then transfer mice to the nose cone section , which also delivers the 2% isoflurane - o2 mixture , and as such , maintains anesthesia during injection .
place vet ointment on the eyes to avoid their drying out while under anesthesia .
confirm anesthesia by checking the animal 's lack of response to a pinch stimulus on the hind paws .
the patellar tendon ( white line bellow the patella ) will become visible . in order to stabilize the injection site ,
keep the knee still , in a bent position , by placing the index finger beneath the knee joint and the thumb above the anterior surface of the ankle joint .
joint preference is not required . to find the precise site of injection , run a 26 g needle attached to a syringe horizontally along the knee ( so as not to pierce the skin with the tip ) until it finds the gap beneath the patella .
apply gentle pressure to mark the area and then lift the needle and syringe vertically for the injection . insert the needle in the marked area , through the patellar tendon , perpendicular to the tibia .
after injection , massage the knee to ensure even distribution of the solution . discard the needle immediately in the sharps bin.place mice back into a clean home cage on a heated mat and allow them to recover .
keep constant vigilance on the animals until they regain suitable consciousness , which is measured by them regaining sternal recumbency .
note : it is suggested for best practice and training purposes that a dye is used and immediate post - mortem dissection performed to confirm correct localization of injection .
after injection , massage the knee to ensure even distribution of the solution . discard the needle immediately in the sharps bin .
place mice back into a clean home cage on a heated mat and allow them to recover .
keep constant vigilance on the animals until they regain suitable consciousness , which is measured by them regaining sternal recumbency .
note : it is suggested for best practice and training purposes that a dye is used and immediate post - mortem dissection performed to confirm correct localization of injection .
note : static mechanical withdrawal thresholds are assessed by applying von frey hairs to the plantar surface of the hind paw .
bring mice to the behavioral room and let unrestrained animals acclimatize in acrylic cubicles ( 8 cm x 5 cm x 10 cm ) atop a wire mesh grid .
train mice by handling and 2 hr habituation to the cubicles for two days prior to von frey hair application in order to limit stress and ambulation during application of von frey hairs . on test days ,
train mice by handling and 2 hr habituation to the cubicles for two days prior to von frey hair application in order to limit stress and ambulation during application of von frey hairs . on test days , habituate animals to the cubicles for up to 60
apply calibrated von frey hairs ( flexible nylon fibers of increasing diameter that exert defined levels of force as calibrated by the manufacturing company and expressed as grams ( g ) ) to the plantar surface of the hind paw until the fiber bends .
use 0.008 , 0.02 , 0.04 , 0.07 , 0.16 , 0.4 , 0.6 , and 1.0 g fibers during testing .
hold each hair in place for 3 sec or until the paw is withdrawn , the latter defining a positive response . starting with a stimulus strength of 0.07 g ,
apply hairs according to the " up - down method " : mark as x a withdrawal response and o an absence of response .
apply in ascending order of force , up to 1 g ( cut - off force ) , until a response is detected.re-test the paw by repeating step 2.2.1 , starting with the filament that exerts a force below the one that produced a withdrawal.then , apply the remaining filaments sequentially , by descending force , until no withdrawal occurs .
continue until a sequence of six responses is obtained ( e.g. , oxoxox ) , in order to obtain the ' k ' value by referring to tabular values .express
use the formula ( 10)/10,000 where xr = value of last von frey filament used in the sequence ( in log units ) , k = tabular value , and = mean difference in forces between fibers .
hold each hair in place for 3 sec or until the paw is withdrawn , the latter defining a positive response . starting with a stimulus strength of 0.07 g , apply hairs according to the " up - down method " : mark as x a withdrawal response and o an absence of response . apply in ascending order of force , up to 1 g ( cut - off force ) , until a response is detected .
re - test the paw by repeating step 2.2.1 , starting with the filament that exerts a force below the one that produced a withdrawal .
then , apply the remaining filaments sequentially , by descending force , until no withdrawal occurs .
continue until a sequence of six responses is obtained ( e.g. , oxoxox ) , in order to obtain the ' k ' value by referring to tabular values .
use the formula ( 10)/10,000 where xr = value of last von frey filament used in the sequence ( in log units ) , k = tabular value , and = mean difference in forces between fibers .
where no response is detected , use the maximal response of 1 g . following the procedure described above ( 2.2.1 - 2.2.4 ) ,
after injection , assess thresholds of the ipsilateral and contralateral paws at regular day intervals for several weeks after mia to ascertain the development of mechanical allodynia .
note : for example , we report thresholds measured 0 , 3 , 5 , 7 , 10 , 14 , 21 , and 28 days after mia injection .
train each mouse to walk into a plexiglass chamber on the apparatus and sit in the holding box .
place the mouse in front of the holding box , lift the entrance up 45 , and allow the mouse to walk in and close the box .
this training takes at least two days and guarantees that the animal is still and not leaning on either side of the chamber .
calibrate the instrument before use with a 100 g check weight ( or according to equipment instruction ) .
the duration of each measurement takes 1 sec , as per the manufacturer 's instructions .
the duration of each measurement takes 1 sec , as per the manufacturer 's instructions .
collect three measurements of the weight borne on each hind paw from the recording pad for each recording session and use the mean value to calculate the difference in weight borne by ipsilateral and contralateral paws .
then , repeat assessments at regular intervals over several weeks to ascertain the development of gate changes . for example
, we report thresholds measured on 0 , 3 , 5 , 7 , 10 , 14 , 21 , and 28 days after mia injection .
note : a normal weight bearing value of 50% represents an equal weight distribution across ipsilateral and contralateral hindlimb .
. measurements of mechanical thresholds and weight bearing deficits can be performed in the same mice , as neither end point affects the other . for pharmacological assessment ,
each group of animals should be tested at set times after dosing in line with the pharmacokinetic profile of the compound used .
we have recently reported that the injection of 0.5 - 1 mg mia in the mouse knee joint induces referred mechanical hypersensitivity ( allodynia ) in the ipsilateral hind paw and weight bearing deficits for up to 4 weeks , although onsets are dose - dependent .
the data reported in figure 1 constitute an example of the time course of mia - induced mechanical hypersensitivity in the ipsilateral hind paws following a range of doses injected in the knee .
specifically , the lowest dose of mia ( 0.5 mg / mouse ) induced a 50% decrease of thresholds compared to the injection of saline on day 10 , and thresholds decreased to 70% of those of saline controls by day 28 after injection .
the intermediate dose of 0.75 mg of mia resulted in a gradual decrease in thresholds that were 80% lower than saline control thresholds on day 10 and remained low up to day 28 .
the highest dose of 1 mg mia was associated with a significant drop in threshold on day 5 and a further decrease on day 10 , which was sustained up to day 28 .
the data reported in figure 2 provide examples of weight bearing changes that are associated with mia injection in the knee joints . in this set of experiments , while the 0.5 mg mia dose did not induce significant changes in weight bearing throughout the 28 day duration of the study , the 0.75 mg mia dose resulted in a significant reduction in the weight borne by the ipsilateral paw from day 10 onwards .
notably , weight bearing asymmetry associated with 0.75 mg of mia may produce variable and inconsistent results between studies . instead , the dose of 1 mg mia generally induces reproducible weight bearing asymmetry and the data in figure 2 demonstrate significant reduction of weight borne on the ipsilateral hind paw from day 3 until the end of the observation period . as expected , saline - treated animals showed no weight bearing changes .
paw withdrawal thresholds of the ipsilateral and contralateral hind paws were assessed before and after injection of mia ( 0.5 , 0.75 , and 1mg / mouse ) and saline ( 0.9% nacl ) , n = 8 - 10 mice / group .
* p<0.05 , * * p<0.01 , * * * p<0.001 versus saline - treated group ; two - way repeated measurements anova followed by student newman - keuls post hoc test .
changes in body weight distribution between the two hind limbs were calculated as [ ( weight borne on ipsilateral paw / sum of the weight borne on the ipsilateral and contralateral paws)*100 ] were assessed before and after injection of mia ( 0.5 , 0.75 , and 1 mg / mouse ) and saline ( 0.9% nacl ) , n = 8 - 10 mice / group .
* p<0.05 , * * p<0.01 , * * * p<0.001 versus saline - treated group .
two - way repeated measurements anova followed by student newman - keuls post hoc test .
with this methodology , we describe a preferred method for inducing oa - like pain in the mouse by an intra - articular injection of mia in a knee joint and assessment of sensitivity to non - noxious and noxious stimuli in the hind limbs .
mia injection is associated with persistent pain behavior , namely altered hind limb weight bearing and development of referred mechanical hypersensitivity ( allodynia ) .
such static measurements can be complemented by gait analysis on a treadmill or by catwalk analysis in freely moving animals .
mia models are responsive to conventional pain - relieving therapies , indicating that they may be useful for discerning therapeutic approaches . while the injection of mia is not technically difficult , the joint capsule can be pierced during the injection , resulting in leakage of mia outside the capsule , and subsequent failure to induce toxicity of chondrocytes .
indeed , systemic injection of mia can be fatal in rodents and possible effects of mia on tissues and cells other than chondrocytes may confound results , besides being undesirable .
as such , it must be stressed that great care needs to be given to the injection of the mia , as it is a critical component of the model , and confidence needs to be given that the injection occurs into the articular space .
this protocol helps to achieve that . the protocols described here aim to ensure the animals provide consistent pain - like responses throughout the test period
. also , they allow adjustment of disease severity by altering the dose of mia used to induce the pathology .
the rapid induction of both disease state and pain - like behavior allow timely evaluation of pain - modifying compounds .
this is advantageous over existing surgical and spontaneously developing models of oa , which can take a longer period of time to develop hypersensitivity . also , particularly for the spontaneous models , the disease pathology does not manifest in all animals ( approximately 20 - 80% ) , whereas the mia model is associated with significant incidence of responders .
furthermore , spontaneous models are not suitable for measurements of changes in weight bearing , as oa develops in both knees .
when considering behavioral measurements , the animals need to be kept calm and relaxed during the assessments .
this is achieved , as detailed in the protocol , by early training before recording measurements and by repetitive handling , which allows animals to become familiar with the experimenter . a key point to reduce
stress is to use the same experimenter for the behavioral test throughout , as constant changing will induce the issues previously mentioned . like any model , the mia model of oa bears limitations , such as the rapidity of joint disruption , which does not resemble the slow development of oa pathology in patients .
one way to overcome this issue would be to complement this model with a surgical model of oa .
the use of the mia chemical model in compound development allows for the use of preventative and therapeutic protocols over the development and maintenance of oa - like pain .
finally , the mia model would complement studies of phenotypical traits of knock - out mice , helping to further understand the oa disease .
| a major symptom of patients with osteoarthritis ( oa ) is pain that is triggered by peripheral as well as central changes within the pain pathways .
the current treatments for oa pain such as nsaids or opiates are neither sufficiently effective nor devoid of detrimental side effects .
animal models of oa are being developed to improve our understanding of oa - related pain mechanisms and define novel pharmacological targets for therapy .
currently available models of oa in rodents include surgical and chemical interventions into one knee joint .
the monoiodoacetate ( mia ) model has become a standard for modelling joint disruption in oa in both rats and mice .
the model , which is easier to perform in the rat , involves injection of mia into a knee joint that induces rapid pain - like responses in the ipsilateral limb , the level of which can be controlled by injection of different doses .
intra - articular injection of mia disrupts chondrocyte glycolysis by inhibiting glyceraldehyde-3-phosphatase dehydrogenase and results in chondrocyte death , neovascularization , subchondral bone necrosis and collapse , as well as inflammation .
the morphological changes of the articular cartilage and bone disruption are reflective of some aspects of patient pathology . along with joint damage
, mia injection induces referred mechanical sensitivity in the ipsilateral hind paw and weight bearing deficits that are measurable and quantifiable .
these behavioral changes resemble some of the symptoms reported by the patient population , thereby validating the mia injection in the knee as a useful and relevant pre - clinical model of oa pain.the aim of this article is to describe the methodology of intra - articular injections of mia and the behavioral recordings of the associated development of hypersensitivity with a mind to highlight the necessary steps to give consistent and reliable recordings . |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``Independent and Effective Federal
Defenders Act of 2016''.
SEC. 2. REVISION OF SYSTEM TO ENSURE ADEQUATE REPRESENTATION OF FEDERAL
DEFENDANTS.
Section 3006A of title 18, United States Code, is amended to read
as follows:
``Sec. 3006A. Adequate representation of defendants
``(a) Federal Defender Commission.--
``(1) In general.--There is established, as an independent
agency within the executive branch, the Federal Defender
Commission (hereinafter in this section referred to as the
`Commission').
``(2) Composition and appointment by president.--The
Commission shall consist of 12 members, appointed by the
President.
``(3) Director.--The President shall appoint a Director to
serve on the Commission. The Director shall have all of the
qualifications described in paragraph (5) and none of the
disqualifications described in paragraph (6). The term of the
Director shall be 6 years, but a Director may serve after the
expiration of that term until a successor takes office.
``(4) Considerations in appointment.--In appointing members
of the Commission, the President shall ensure that--
``(A) each of the 12 members of the Commission has
primary experience in criminal defense in a circuit in
which no other member of the Commission has such
experience at the time of the appointment; and
``(B) at least a majority of the members of the
Commission are individuals who are former Federal
defenders.
``(5) Qualifications of members.--To be a member of the
Commission, an individual must--
``(A) be a member of the bar of the highest court
of a State; and
``(B) have significant experience in the legal
defense of criminal cases or demonstrated a commitment
to indigent defense representation or juvenile defense
representation.
``(6) Disqualifications of members.--An individual shall
not serve on the Commission who is--
``(A) employed as a Federal defender;
``(B) employed as a prosecutor or law enforcement
official; or
``(C) serving as an active judicial officer of the
United States.
``(7) Term.--
``(A) Except as otherwise provided in this
paragraph, the term of a member of the Commission shall
be 6 years.
``(B) A member may serve after the expiration of
that member's term until a successor takes office.
``(C) Of the 12 members first appointed to the
Commission, 6 shall be initially appointed for 2-year
terms, so that the terms of members of the commission
are staggered.
``(8) Duties of commission.--The Commission shall--
``(A) consult with each United States district
court on a plan operating throughout the district for
furnishing representation to any person financially
unable to obtain representation;
``(B) appoint, taking into consideration the
recommendations of the relevant bar or bars of the
State, law schools in the State, and other
organizations and individuals, a Federal Public
Defender, having the same qualifications for service as
this subsection requires for a member of the Commission
and not having any of the disqualifications described
in this subsection, other than that described in
paragraph (6)(A), for such service, for each district
to carry out the plan for that district; and
``(C) develop for Federal Public Defender offices--
``(i) national guidelines on quality of
representation;
``(ii) program evaluation systems;
``(iii) attorney and staff evaluation
systems to ensure effective management and
representation;
``(iv) training, publications, and
seminars;
``(v) specialty resource centers;
``(vi) research and development pilot
projects;
``(vii) statistical studies; and
``(viii) committees, projects, or working
groups.
``(9) Plan may combine districts.--The plan may include a
combination of districts if such a combined office would be
cost effective, based on the number of appointments each year,
and where the interests of justice of effective representation
require the establishment of such an office. The Commission
shall determine the need for a Federal Public Defender office
and geographic boundaries it serves. However, the Commission
shall ensure that each Federal judicial district has within it
a Federal Public Defender office providing representation.
``(10) Staff.--The Commission may appoint additional
employees as it deems appropriate, to assist the Commission in
carrying out its duties.
``(11) Compensation of members and employees.--Members of
the Commission and employees of the Commission shall be
compensated at rates determined by the Commission, but not in
excess of the rate of level V of the Executive Schedule
specified in section 5316 of title 5.
``(12) Professional responsibility.--The Commission shall
not--
``(A) interfere with any attorney providing
representation under this section in carrying out such
attorney's professional responsibilities to such
attorney's client; or
``(B) abrogate as to attorneys in providing
representation under this section the authority of a
State or other jurisdiction to enforce standards of
professional responsibility generally applicable to
attorneys in such jurisdiction.
``(b) Requirements for Plan.--Each plan for representation under
this section shall include the following:
``(1) Representation provided in all cases.--Representation
shall be provided for any financially eligible person who--
``(A) is charged with a criminal offense;
``(B) is a juvenile alleged to have committed an
act of juvenile delinquency as defined in section 5031;
``(C) is charged with a violation of probation;
``(D) is under arrest, when such representation is
required by law;
``(E) is charged with a violation of supervised
release or faces modification, reduction, or
enlargement of a condition, or extension or revocation
of a term of supervised release;
``(F) is subject to a mental condition hearing
under chapter 313;
``(G) is in custody as a material witness;
``(H) is entitled to appointment of counsel under
the sixth amendment to the Constitution;
``(I) faces loss of liberty in a case, and Federal
law requires the appointment of counsel;
``(J) is entitled to the appointment of counsel
under section 4109;
``(K) is involved in a proceeding in which a
criminal adjudication may result;
``(L) is being considered for, or seeks to obtain,
under subsection (c)(1) or (c)(2) of section 3582, a
modification of a term of imprisonment; or
``(M) is involved in proceedings seeking clemency
or a pardon.
``(2) Representation provided in some cases.--Whenever the
United States magistrate judge or the court determines that the
interests of justice so require, representation may be provided
for any financially eligible person who seeks relief under
section 2241, 2254, or 2255 of title 28.
``(3) Appointment of private attorneys.--Each District
shall develop a panel of private attorneys. A private attorney
shall provide representation under this section when the nature
of the case or ethical considerations so require. Cases shall
be randomly assigned to private panel attorneys on a rotating
basis. The Federal Public Defender in the district shall not be
involved in the selection of private panel attorneys for
individual cases. The panel of private attorneys shall divide
themselves into areas of criminal proceeding expertise.
``(4) Qualifications of private attorneys.--To be a private
attorney on the panel, an individual must have significant
experience in the legal defense of criminal cases.
``(5) Ongoing training and certification of private
attorneys.--Each District shall develop and provide ongoing,
mandatory training programs for private attorneys on the panel.
All attorneys participating on a panel shall have their
performance in representing defendants regularly peer reviewed
by and certified by distinguished members of the local criminal
defense community.
``(6) Use of private attorneys.--Each plan shall provide
that private attorneys be appointed to represent defendants in
a substantial proportion of cases.
``(7) Use of other attorneys.--Each plan may include, in
addition to the provisions for private attorneys, for the use
of attorneys furnished by a bar association or legal aid
society.
``(c) Budget Analyst.--Each District shall have a budget analyst.
The budget analyst shall be hired by the Commission. The budget analyst
shall be operationally independent of the Federal Public Defender and
the judicial branch in such circuit. The budget analyst shall have
significant experience in criminal defense practice. The budget analyst
shall engage in timely, objective, and independent analysis of
reimbursement for costs submitted by the private attorneys. The budget
analyst may mediate any claims for reimbursement payments submitted by
private attorneys. The budget analyst will oversee and approve the use
of investigators and experts for cases.
``(d) Federal Public Defender.--
``(1) Duties and powers.--The Federal Public Defender in
each district shall carry out the plan for representation in
that district. In order to do so, the Federal Public Defender
may appoint such staff, establish salaries for the staff, and
make such contracts as are necessary to carry out the functions
of the office. The salary structure in each office shall be
commensurate with that provided for the lawyers and staff of
the United States Attorney for the relevant district.
``(2) Term.--The term of a Federal Public Defender is 4
years, but a Federal Public Defender may serve after the
expiration of that term until a successor takes office. The
Federal Public Defender may be appointed for more than one
term.
``(3) Removal.--The Commission may, with the concurrence of
three quarters of the members serving at the time of the
removal, remove a Federal Public Defender for cause.
``(4) Vacancy.--The Commission may fill a vacancy of the
office of Federal Public Defender for the remainder of the
term, in the same manner as the original appointment was made.
``(e) Alternative Means of Representation in a District.--
``(1) Generally.--The Commission may create a Community
Defender Organization to carry out the plan for representation
in the District. A Community Defender Organization shall be a
nonprofit defense counsel service established and administered
by any group authorized by the plan to provide representation.
The organization shall be eligible to furnish attorneys and
receive payments from the Commission if its bylaws are set
forth in the plan of the district or districts in which it will
serve.
``(2) Annual report.--Each organization shall submit to the
Commission an annual report setting forth its activities and
financial position and the anticipated caseload and expenses
for the next fiscal year.
``(3) Grants.--Upon application an organization may, to the
extent approved by the Commission--
``(A) receive an initial grant for expenses
necessary to establish the organization; and
``(B) receive periodic sustaining grants to provide
representation and other expenses pursuant to this
section.
``(f) Change of Structure Between That of Federal Public Defender
and That of Community Defender Organization.--Either a Community
Defender Organization or a Federal Public Defender may apply to the
Commission to change its structure to that of the other. The Commission
may allow that change if the Commission determines such a change would
better serve the purposes of this section.
``(g) Duration and Substitution of Appointments.--A person for whom
counsel is appointed shall be represented at every stage of the
proceedings from before being interviewed by pretrial services or a
probation officer through appeal, including ancillary matters
appropriate to the proceedings. If at any time after the appointment of
counsel the United States magistrate judge or the court finds that the
person is financially able to obtain counsel or to make partial payment
for the representation, it may terminate the appointment of counsel or
authorize payment as provided in subsection (f), as the interests of
justice may dictate. If at any stage of the proceedings, including an
appeal, the United States magistrate judge or the court finds that the
person is financially unable to pay counsel whom he had retained, it
may appoint counsel under this section, as the interests of justice may
dictate. The United States magistrate judge or the court may, in the
interests of justice, substitute one appointed counsel for another at
any stage of the proceedings.
``(h) Nonapplicability to Local Courts of the District of
Columbia.--This section does not apply to representation in the
Superior Court of the District of Columbia or the District of Columbia
Court of Appeals.
``(i) Definitions.--In this section the following definitions
apply:
``(1) Circuit.--The term `circuit' means one of the
circuits for which there is a United States court of appeals.
``(2) District court.--The term `district court' means each
district court of the United States created by chapter 5 of
title 28, the District Court of the Virgin Islands, the
District Court for the Northern Mariana Islands, and the
District Court of Guam.
``(3) Representation.--The term `representation' means
representation by legal counsel and also includes
investigative, expert, and other services necessary for
adequate representation.
``(4) State.--The term `State' includes any State or other
similar entity in which a district court is established.''.
SEC. 3. CONTINUATION OF ORGANIZATIONS ESTABLISHED BEFORE ENACTMENT.
A Federal Defender organization established before enactment of
this Act shall continue in operation, and the Federal Public Defender
then in office shall continue to serve the Federal Public Defender's
term in that capacity. A Community Defender Organization, committee,
project, or working group established before enactment of this Act
shall continue in operation.
SEC. 4. GENERAL ACCOUNTABILITY OFFICE STUDY.
Not later than 4 years after the date of the enactment of this Act,
the Comptroller General shall complete a study and report to Congress
on the provision and cost of Federal Defense services. | Independent and Effective Federal Defenders Act of 2016 This bill amends the federal criminal code to revise requirements related to the provision of adequate representation for defendants in federal criminal cases. Under current law, each U.S. district court must operate a plan, in accordance with specified requirements, for furnishing representation to any eligible person who is financially unable to obtain adequate representation. The bill revises these requirements and establishes the Federal Defender Commission as an independent agency tasked with ensuring the provision of adequate representation. |
in this paper , we give further consideration to the 1-d continuum model for adhesion / diffusion of biological cells developed by anguige and schmeiser in @xcite , which took the form of the nonlinear diffusion equation = ( d ( ) ) , [ cont_rho]with quadratic diffusivity d()= 3(-)^2 + 1- , [ d]for the scaled cell density @xmath0 $ ] , and the adhesion coefficient @xmath1 $ ] , the boundary condition being just @xmath2 at @xmath3 .
these equations were obtained as the formal continuum limit of the fundamental biased - random - walk model = ^+_i-1_i-1+^-_i+1_i+1-(^+_i+^-_i)_i , [ walk ] with transitional probabilities ^_i = ( 1-_i1)(1-_i1)/h^2 , [ ti ] on a lattice of points @xmath4 , by taking taylor expansions about @xmath5 , and letting @xmath6 . in the derivation of this equation , @xmath7 was interpreted as a ( microscopic ) measure of cell size .
we recall from @xcite that ( [ cont_rho])-([d ] ) is globally well posed if @xmath8 .
if , on the other hand , @xmath9 then ( [ cont_rho])-([d ] ) is ill - posed iff the initial density profile protrudes into the ` unstable ' interval i_= ( ^ ( ) , ^()):= ( , ) , [ rhointerval ] since in that case @xmath10 is positive iff @xmath11 , and positivity is preserved by the maximum principle .
for completeness , note that in the borderline case @xmath12 , equation ( [ cont_rho ] ) is just the porous - medium equation with quadratic diffusivity and possible change of sign about @xmath13 . for initial data which stays away from @xmath13 (
either above or below ) , ( [ cont_rho ] ) is uniformly parabolic , and global existence of a smooth solution follows as for @xmath8 , while for degenerate initial data one is merely guaranteed a ( unique ) globally existing weak solution @xcite .
the ill - posedness of ( [ cont_rho ] ) for @xmath9 is related to the presence of fine ( wavelength @xmath14 ) spatial oscillations , as well as plateau formation , in solutions of the discrete system ( [ walk ] ) , and the absence of a straightforward existence theory for ( [ cont_rho ] ) leads one to ask just what model should be taken as a reasonable continuum limit of ( [ walk ] ) in the high - adhesion regime .
one approach , and the one we shall adopt in this paper , is to circumvent the problem of ill - posedness by simply declaring that @xmath15-values in @xmath16 are forbidden , and considering solutions to ( [ cont_rho])-([d ] ) which may jump across @xmath16 ( possibly multiple times ) , but which are otherwise smooth .
mathematically , one is then dealing with a kind of ( multi - phase ) stefan problem for the density @xmath17 and the jump locations @xmath18 , such that the @xmath19 are dynamically determined by local conservation of mass , or , in other words , by the rankine - hugoniot condition . in @xcite ,
the analysis of ( [ walk ] ) was aided by considering higher - order modifications of the leading - order equation ( [ cont_rho ] ) .
one such @xmath20-modification takes the form of the fourth - order pde [ mod - equ ] = ( k ( ) + h^2((-1 ) - ( ) ^2 + ) ) , where the cubic @xmath21 is a primitive for @xmath10 .
this equation is rather similar to the viscous cahn - hilliard equation @xcite , and is a regularisation of ( [ cont_rho ] ) in the sense that it is ( at least locally ) well - posed on @xmath22 , for each fixed value of the microscopic parameter @xmath7 , and for all @xmath23 .
presumably , solutions continue to exist globally , as for cahn - hilliard , but a proof is currently lacking .
the steady - state equation for ( [ mod - equ ] ) can , after a change of variables , be written as a hamiltonian dynamical system , and amongst the solutions there is , for each @xmath24 , a unique heteroclinic cycle .
these heteroclinic cycles correspond to ( two - level ) plateau solutions of ( [ mod - equ ] ) , are close ( for small @xmath7 ) to square - wave weak solutions of ( [ cont_rho ] ) , and their critical points , denoted by @xmath25 and @xmath26 , such that @xmath27 and @xmath28 , match very well the numerically - observed long - time plateau values in solutions of ( [ walk ] ) ( see @xcite ) . for these reasons , we demand in our stefan - problem framework that any jumps across @xmath29 should connect @xmath25 to @xmath26 . furthermore , in order to avoid the degeneracies at @xmath30 , we require that the initial data satisfy @xmath31 in low - density phases , and @xmath32 in high - density ones .
we emphasise that @xmath33 and @xmath34 are determined by the particular choice of microscopic model ( [ walk])-([ti ] ) ; other model choices are possible , and these will result in different @xmath15-values .
the paper is organised as follows . in section 2 ,
we develop a partial existence theory and perform a steady - state analysis for the simplest stefan problem , namely , that for which there is only a single discontinuity in the density ; solution behaviour is further clarified with the aid of several numerical simulations . in section 3 , we extend the analysis to the general multi - phase case , which , in particular , allows for the annihilation of phases via coalescence events . finally , in the appendices , we collect a number of results from classical parabolic theory which are used throughout the paper .
we begin the analysis by considering the simplest possible case , in which there are just two phases , connected by a single jump from @xmath33 to @xmath34 ; this situation is depicted in figure 1 . for definiteness , we will assume that the low - density phase lies to the left , and the high - density phase to the right , of the discontinuity ; the converse arrangement can , of course , also be treated .
let the location of the jump discontinuity be denoted by @xmath35 .
the stefan problem for a given @xmath9 then consists of looking for a function @xmath17 on @xmath36\times[0,t]$ ] which satisfies = ( d ( ) ) ; 0<x < s(t),[lphase]g subject to ( 0,t ) = 0,(s^-(t),t ) = _ 1 ( ) , and = ( d ( ) ) ; s(t)<x<1 , subject to ( 1,t ) = 0,(s^+(t),t ) = _ 2().[rphase ] the evolution of @xmath35 is determined by the rankine - hugoniot jump condition = , [ rh ] where the fluxes are given by @xmath37 , this equation being obtained by differentiating the statement of conservation of mass _
0^s(t ) ( x , t ) dx + _ s(t)^1 ( x , t ) dx = m,[mass ] and using ( [ lphase])-([rphase ] ) .
the initial datum for @xmath15 , satisfying the boundary and jump conditions , is chosen to be smooth away from the initial discontinuity , with @xmath31 in the low - density phase and @xmath32 in the high - density phase . by construction , @xmath10 is then initially positive on each phase , and , by virtue of the maximum principle , we can reasonably expect the stefan problem to be well posed . in the sequel
, we will refer to the coupled system ( [ lphase])-([rh ] ) as @xmath38 ; analogous problems @xmath39 , with @xmath40 jumps , will be treated in section 3 .
finally , note that we allow for the possibility that @xmath35 may hit the domain boundary at @xmath41 or @xmath42 in finite time . in this case , provided the gradient remains bounded as the boundary is approached , the solution can be continued via the ordinary neumann problem for ( [ cont_rho ] ) , which we will call @xmath43 . as a convention ,
a solution continued in this way will still be referred to globally as a solution of @xmath38 .
if the total mass @xmath44 satisfies @xmath45 then there is precisely one discontinuous steady - state solution of @xmath38 , given by the step function ^(x ) & = & \ { ccc _ 1 & : & x .
+ s^ & = & , [ s_star ] while if @xmath46 or @xmath47 then no such discontinuous solution exists .
moreover , @xmath38 clearly has the uniform steady - state solution ( x)=m , 0x1 if and only if @xmath48 or @xmath49 . for the two possible kinds of steady state we have the following stability results
: suppose we have a global smooth solution pair , ( @xmath50 ) , for @xmath38 , with initial data @xmath51 , such that @xmath52 . then + + ( i ) if @xmath53 , @xmath17 converges exponentially to @xmath54 in @xmath55-norm , and @xmath35 converges exponentially to @xmath56 , as @xmath57 , + + ( ii ) if @xmath58 ( resp .
@xmath59 ) , and @xmath60 in the low ( high ) phase , the solution is attracted towards @xmath61 as in ( i ) , + + ( iii ) if @xmath62 ( resp .
@xmath63 ) , then @xmath35 hits @xmath64 in finite time , and the continued solution converges to the uniform steady state @xmath65 , exponentially in @xmath55 .
+ + ( iv ) if @xmath66 ( resp .
@xmath67 ) , then @xmath68 @xmath69 as @xmath70 , some @xmath71 , with the possibility that @xmath72 , and @xmath17 approaches @xmath33 ( @xmath34 ) exponentially in @xmath55 in the low ( high ) phase as @xmath70 .
if @xmath71 is finite , the continued solution of np converges to the uniform steady state @xmath65 , exponentially in @xmath55 .
_ to prove ( i ) , first note that , by ( [ mass ] ) and the fact that @xmath15 can not enter @xmath73 , 0<s_mins(t)s_max<1 , t , where s_min(m ) & = & ( ^-m)/^ , + s_max(m ) & = & ( 1-m)/(1-^ ) . next note that , on the subinterval @xmath74 , we have ( -_1 ) = ( d()(-_1 ) ) .
hence , multiplying through by @xmath75 , integrating by parts , and using the mixed boundary conditions gives _ 0^s(t)(-_1)^2 dx = -_0^s(t)d()(_x(-_1))^2 dx , which implies -_1 ^ 2_l^2(0,s ) -_x(-_1)^2_l^2(0,s),[l2 ] where @xmath76 .
since @xmath77 at @xmath78 , we also have the poincar inequality -_1_l^2(0,s)s_x(-_1)_l^2(0,s ) , and hence ( [ l2 ] ) implies -_1 ^ 2_l^2(0,s)(t)-_1 ^ 2_l^2(0,s)(0)e^-t / s^2_max .
an analogous inequality on the subinterval @xmath79 is obtained in exactly the same way .
next , from ( [ mass ] ) we have _ 0^s(t ) ( ( x , t)-_1 ) dx + _ 1s(t ) + _ s(t)^1 ( ( x , t)-_2 ) dx + _ 2(1-s(t ) ) = m , and hence , rearranging and using the @xmath55-decay just shown , substituting the definition of @xmath56 from ( [ s_star ] ) into ( [ s_est1 ] ) gives us to prove ( ii ) , note , for example , that if @xmath58 and @xmath80 for @xmath81 then @xmath65 is a supersolution in the low phase . from this
, it follows once again that @xmath35 remains bounded away from @xmath82 and @xmath42 , by conservation of mass .
convergence to @xmath61 is proved as before .
the same argument goes through for @xmath59 and @xmath83 , @xmath84 . for ( iii ) , if @xmath62 ( resp .
@xmath63 ) then the only candidate for a steady - state solution is given by @xmath65 and @xmath85 , and , by @xmath55-decay in the low ( high ) phase and conservation of mass , @xmath35 is forced to hit the boundary in finite time ; @xmath55-convergence for the subsequent @xmath43 is proved via the usual energy estimate finally , if @xmath66 ( resp .
@xmath34 ) , then the only possible steady state is @xmath77 @xmath86 for @xmath87 . clearly , @xmath35 remains bounded away from @xmath82 ( @xmath42 ) and therefore @xmath88 decays to @xmath33 ( @xmath34 ) , exponentially in @xmath55 on @xmath89 ( @xmath90 ) , as we have already seen .
the @xmath55-decay implies that @xmath68 ( @xmath82 ) as @xmath91 increases , but the convergence may take infinitely long in this exceptional case ; if the convergence takes place in finite time then the subsequent @xmath43 is as in ( iii ) .
this proves part ( iv ) @xmath92 + + we conclude this discussion by noting that , for the cases not covered by theorem 2.1 , namely 1 . @xmath93 for some @xmath94 , 2 .
@xmath95 for some @xmath96 , we have not been able to find a clean analytical criterion for determining which of the two possible steady states will be approached at large times , for given initial data .
however , in the next subsection we show that the discontinuous steady state ( [ s_star ] ) is always linearly stable in a certain sense , whenever it exists , and , moreover , we report on numerical simulations which suggest that @xmath35 can hit the domain boundary in finite time , provided condition 1 or 2 ( directly above ) is satisifed , and the initial density profile is sufficiently far from ( [ s_star ] ) ; in other words , @xmath38 appears to be bistable for some values of the total mass .
we can make a connection between our moving - boundary problem @xmath38 and the traditional two - phase stefan problem for the melting of ice in water by identifying @xmath15 as the specific latent heat , and @xmath97 as the temperature . in the traditional formulation ,
our low - density phase is thought of as the solid , and our high - density phase as the liquid phase . given this ,
one imposes the physically reasonable condition _ 0_1 _ 0_2 , [ class_data ] and then one can write down a favourable weak formulation of the problem , which can be shown to have a unique solution for bounded data ( see appendix c ) . furthermore
, this weak solution turns out to be a global - in - time smooth solution of the original problem ( see , e.g. , @xcite ) . for @xmath38
, however , the restriction on the initial data is just _
0<^ _ 0>^ , [ sp_1_data ] which is weaker than ( [ class_data ] ) . in particular
, this entails that @xmath21 can no longer be assumed monotonically increasing , and , consequently , that there is no nice weak formulation of the problem .
we note that , in the literature , uniqueness of solutions , given ( [ class_data ] ) , is usually proved using the weak formulation @xcite .
moreover , in the basic proof of local existence of smooth solutions as presented in @xcite , for example , it is not so easy to discern whether the restriction ( [ class_data ] ) can be relaxed to ( [ sp_1_data ] ) . for these reasons ,
we now present a concise , reasonably self - contained , classical existence - and - uniqueness theory for @xmath38 , with data subject merely to ( [ sp_1_data ] ) , which employs the standard hlder and sobolev estimates of linear parabolic theory . in order to solve the moving - boundary problem @xmath38 ,
we employ , in each phase , the standard trick of rescaling the spatial variable ( see , for example , @xcite ) , such that ( [ lphase ] ) and ( [ rphase ] ) become a pair of fixed - boundary problems , coupled by the ( rescaled ) rankine - hugoniot condition .
specifically , for @xmath98 we introduce the coordinate transformation ( x , t ) ( , ) : = , = t , while for @xmath99 we take ( x , t ) ( , ) : = , = t . in terms of these new coordinates , and writing @xmath100 for @xmath98 , @xmath101 for @xmath99 , equations ( [ lphase ] ) and ( [ rphase ] ) become , upon dropping hats , = ( d(v ) ) + x,[v ] for @xmath102 , subject to @xmath103 , and , respectively , = ( d(w ) ) + , [ w ] for @xmath102 , subject to @xmath104 , while the jump condition ( [ rh ] ) assumes the form = - ( - ) ( _ 2-_1)^-1,[rescaled_rh ] and we also have the rescaled conservation - of - mass equation s(t ) = .[resc_com ] finally , for the application of classical parabolic theory , the initial data and the dirichlet condition at @xmath105 must satisfy a certain first - order compatibility condition , which is obtained by setting @xmath106 and @xmath107 equal to zero in ( [ v ] ) and ( [ w ] ) , and substituting the initial data , evaluated at the phase boundary , into the right - hand sides of ( [ v ] ) , ( [ w ] ) , and ( [ rescaled_rh ] ) .
the most compact way of writing this compatibility condition is to go back to the original coordinates and introduce the dependent ( temperature ) variable @xmath108 , in terms of which the relevant equations are simply -_x^+(_x^+ - _ x^- ) & = & d(_1)_xx^+ , + -_x^-(_x^+ - _ x^- ) & = & d(_2)_xx^- , where , for example , @xmath109 .
we are able to prove the following : given initial data @xmath110 , such that @xmath111 , @xmath112 , @xmath52 , @xmath113 , @xmath114 , and such that the first - order compatibility condition is satisfied , the system of equations ( [ v ] ) , ( [ w ] ) , ( [ rescaled_rh ] ) ( and hence problem @xmath38 ) has a unique classical solution on some small time interval @xmath115 $ ] .
_ the proof proceeds via an iterative scheme of successive approximations , and to get the required strong - convergence properties , we work in the setting of ` parabolic ' hlder spaces .
first of all , we set @xmath116\times[0,t]$ ] , and , as in @xcite , @xcite , for example , let @xmath117 , @xmath112 non - integer , denote the banach space of functions @xmath118 with continuous derivatives @xmath119 , for @xmath120 , equipped with the norm d^r_td^s_xu^(l-[l])_x , q_t + _ 0<l-2r - s<2d_t^rd_x^su^(l-2r - s)/2_t , q_t , where , for @xmath121 , v^()_x , q_t & = & _ ( x , t),(x,t)q_t\{|v(x , t)-v(x,t)||x - x|^- } , + v^()_t , q_t & = & _ ( x , t),(x , t)q_t\{|v(x , t)-v(x , t)||t - t|^-}. now we describe our iterative scheme for obtaining new approximate solutions of ( [ v ] ) , ( [ w ] ) , ( [ rescaled_rh ] ) from old ones .
suppose we have smooth @xmath122th iterates @xmath123 , with positive diffusivities on @xmath124 , which satisfy the initial and boundary conditions , and suppose that \{|v^i|^(l+1)_q_t , |w^i|^(l+1)_q_t}c,[vw_c_bound ] for some @xmath125 .
next , determine the approximant @xmath126 by solving the nonlinear ode = - ( - ) ( _ 2-_1)^-1,[iterated_rh ] which , for the given datum @xmath127 , has a unique smooth solution on @xmath115 $ ] , provided @xmath128 is chosen small enough ( picard s theorem ) .
clearly , the ordinary hlder norm of @xmath129 is bounded according to ^i_c^l/2([0,t])f(c),[sdot_bound ] for some function @xmath130 .
the functions @xmath131 are now inserted into the right - hand sides of the linearised field equations = ( d(v^i ) ) + x,[newv ] for @xmath102 , subject to @xmath132 , and = ( d(w^i ) ) + ^i,[neww ] for @xmath102 , subject to @xmath133 .
these equations are parabolic , by the choice of @xmath123 , and therefore have unique smooth solutions @xmath134 on @xmath124 , by lemma a.1 ( see appendix a ) , which is a convenient summary of relevant results from classical parabolic theory @xcite ; the updated approximants also have corresponding positive diffusivities , by the maximum principle .
the coefficients of ( [ newv ] ) , ( [ neww ] ) , when expanded into the standard form ( [ linear_para ] ) , are such terms as @xmath135 , @xmath136 , @xmath137 , and analogues for @xmath138 , and are therefore dominated in @xmath139 by @xmath140 and @xmath141 .
thus , by lemma a.1 , @xmath130 is some positive function , @xmath142 , and @xmath143 is the ordinary hlder norm . next , applying lemma b.1 to ( [ vnew_est1 ] ) and ( [ wnew_est1 ] ) results in and |w^i+1|^(l+1)_q_t - k()w_0_c^2 k()t^f(c)(|w_0|^(l+2)_+_2),[wnew_est2 ] where @xmath144 thus , if we choose @xmath145 , and @xmath146 is taken sufficiently small , then ( |v^i+1|^(l+1)_q_t , |w^i+1|^(l+1)_q_t)c .
iteratively , we therefore have that ( [ vw_c_bound ] ) , ( [ sdot_bound ] ) , ( [ vnew_est1 ] ) , and ( [ wnew_est1 ] ) hold uniformly for all @xmath122 .
next , taking the difference of ( [ newv ] ) and the corresponding equation for @xmath147 gives an equation of the form ( v^i+1-v^i ) & = & d_i(x , t)(v^i+1-v^i ) + a_i(x , t)(v^i+1-v^i ) + b_i(x , t)(v^i - v^i-1 ) + & + & c_i(x , t)(v^i - v^i-1 ) + d_i(x , t)(s^i - s^i-1 ) + e_i(x , t)(^i-^i-1),[v_diff_i ] where @xmath148 for all @xmath122 , some @xmath149 , and all the coefficients are bounded in @xmath150 , uniformly in @xmath122 , by the results just obtained .
for the difference @xmath151 , we get , from ( [ rescaled_rh ] ) , ( s^i - s^i-1 ) = p_i(t)(s^i - s^i-1 ) + q_i(t)(v^i_x - v^i-1_x)(1,t ) + r_i(t)(w^i_x - w^i-1_x)(0,t ) , [ sdiff ] where @xmath152 are bounded in @xmath153 , uniformly in @xmath122 , and from this it is easy to deduce that thus , applying ( [ sdiff2 ] ) and lemma a.1 to ( [ v_diff_i ] ) , we get of course , there is also an analogous estimate for @xmath154 , which , together with ( [ vdiff2 ] ) , implies + |w^i - w^i-1|^(l+1)_q_t ) .
finally , an application of lemma b.1 to the right - hand side of this inequality gives , since all iterates have the same initial data , c_1t^(|v^i - v^i-1|^(l+2)_q_t + |w^i - w^i-1|^(l+2)_q_t ) .
( note that @xmath155 stands for various constants in the above ) .
if @xmath71 is chosen so small that @xmath156 , it is easy to see that @xmath147 and @xmath138 are cauchy sequences with respect to @xmath157-norm .
moreover , it follows from ( [ sdiff2 ] ) that @xmath129 is cauchy in @xmath158-norm . by the strong convergence of these sequences , their limits @xmath159
satisfy ( [ v ] ) , ( [ w ] ) , ( [ rescaled_rh ] ) pointwise , and thus constitute a classical solution of @xmath38 . turning to the question of uniqueness ,
suppose we have two smooth solution triples @xmath160 , @xmath161 , satisfying ( [ v ] ) , ( [ w ] ) , ( [ rescaled_rh ] ) , and having the same initial data . subtracting the equation satisfied by @xmath162 from that satisfied by @xmath163 then gives an equation of the form _
t(v-|v ) = d(x , t)_x^2(v-|v ) + a(x , t)_x(v-|v ) + b(x , t)(v-|v ) + c(x , t)(s-|s ) + d(x , t)(-),[v - vbar ] where the coefficients are smooth , and @xmath164 , some @xmath149 .
an analogous equation is obtained for @xmath165 in the same way .
thus , by lemma a.1 , @xmath166 can be bounded by the inhomogeneity in ( [ v - vbar ] ) , according to & & c(|s-|s|^(l)_q_t + |-|^(l)_q_t ) + & & c(|v_x-|v_x|^(l)_q_t + |w_x-|w_x|^(l)_q_t ) + & & c(|v-|v|^(l+1)_q_t + |w-|w|^(l+1)_q_t),[inequality4 ] for various constants @xmath167 , where we used the rankine - hugoniot condition ( [ rescaled_rh ] ) to get the third line . adding the analogous inequality for @xmath165 therefore results in |v-|v|^(l+2)_q_t + |w-|w|^(l+2)_q_t c(|v-|v|^(l+1)_q_t + @xmath168 ,
as required @xmath92 we will prove a global - existence theorem for @xmath38 by showing that , for a local classical solution @xmath169 , the gradient , @xmath170 , and hence also @xmath171 , are _ a priori _ bounded , provided that the one - sided limits @xmath172 satisfy a sign condition .
the proof is rather different from , and somewhat shorter than , that presented in @xcite .
first , with the change of dependent variable @xmath108 , which is smooth and invertible in each phase , the governing pde becomes _ t = ( ) _ xx,[global_sigma ] where @xmath173 , the boundary conditions become _ x(0)=_x(1)=0,(s^-)=k(_1):=_1,(s^+)=k(_2):=_2 , and the rankine - hugoniot condition takes the form = -.[rh_sigma_0 ] next , note that integration by parts gives , for any smooth @xmath174 , and @xmath175 , _
t(_x)^2 m dx = -_0^s(t ) 2m(m-1)_x^2m-2_xx_t dx + _ 0^s(t)[int_by_parts ] .
assuming now that @xmath176 solves @xmath38 , we have @xmath177 , and hence , by differentiation,@xmath178 at @xmath179 , which , with the aid of ( [ int_by_parts ] ) , leads to ( _ x)^m^2_l^2(0,s ) & = & -_0^s 2m(2m-1)(_x)^2m-2_xx_t dx + ( 1 - 2m)(_x)^2m.|_x = s^- + & & ( 1 - 2m)(t)(_x)^2m|_x = s^-,[sig_left ] where we used ( [ global_sigma ] ) to discard the integral term . by a similar calculation , there also follows ( _ x)^m^2_l^2(s,1 ) -(1 - 2m)(t)(_x)^2m|_x = s^+.[sig_right ] if we regard @xmath180 as a function in @xmath181 , then adding ( [ sig_left ] ) and ( [ sig_right ] ) , and using ( [ rh_sigma_0 ] ) , results in ( _ x)^m_2 ^ 2 ( 1 - 2m)((_x)^2m(s^+)-(_x)^2m(s^-)).[sig_decay ] now , if @xmath182 then , inductively , there is a _ positive _ multinomial @xmath183 such that ( a - b)(a^2^n - b^2^n ) = f_n(a , b)(a+b),a , b.[f_n ] using ( [ f_n ] ) in the right - hand side of ( [ sig_decay ] ) with @xmath184 shows that @xmath185 is decreasing for @xmath186 , provided _
x(s^+ ) + _ x(s^-)0t.[grad_sign ] this condition can be guaranteed , for example , by choosing data @xmath187 for @xmath38 satisfying the traditional condition ( [ class_data ] ) , and by appealing to the maximum principle in each phase .
thus , assuming ( [ grad_sign ] ) holds , we have _ x_l^2^n(t ) _
x_l^2^n(0 ) _
x_(0 ) , for @xmath188 , and therefore , by theorem 2.8 of @xcite , _
x_(t)_x_(0 ) . in 1-d , such an _ a priori _ bound on @xmath189 , which of course also gives a pointwise bound on the corresponding @xmath190 and on @xmath171 , is actually enough to continue the local solution of @xmath38 obtained in sect.2.3 , by standard theory . indeed , if @xmath163 and @xmath191 are as in ( [ v])-([w ] ) , then combining the estimates of appendix a gives , for @xmath192 , and a constant @xmath167 which is controlled by @xmath193 , |v|^(2-)_q_tc(v_c^2((0,1))+_1 ) , and an analogous estimate for @xmath191 .
thus , for some @xmath194 , the @xmath195-norm of @xmath163 and @xmath191 is controlled by @xmath193 and the @xmath196-norm of the initial data . given this ,
lemma a.1 implies in turn that the @xmath197-norm of @xmath163 and @xmath191 is controlled by @xmath193 and the @xmath198-norm of the initial data .
thus , the local classical solution can always be extended onto to a larger time interval , provided , of course , @xmath35 stays away from the domain boundary .
we have already seen ( theorem 2.1 ) that if the total mass @xmath44 lies outside the interval @xmath199 , it can not be ruled out that @xmath35 will hit the domain boundary in finite time ; should this occur , the solution can be continued via the neumann problem on @xmath200 , as mentioned above .
note that , on a disappearing phase , the solution ( in terms of the original variable @xmath15 ) merely approaches @xmath33 or @xmath34 , as appropriate , by the boundedness of the gradient .
since we have already extended our definition of @xmath38 to cover such eventualities , we have therefore proved given phase - wise smooth initial data @xmath51 satisfying ( [ class_data ] ) and the first - order compatibility condition , problem @xmath38 has a unique smooth , global - in - time solution @xmath169 , such that the corresponding @xmath201 is monotonically decreasing for all @xmath91 .
in general , it is not clear whether a corresponding global - existence result can be obtained in the situation where ( [ class_data ] ) is not satisfied .
an exception to this is the special case of 1-phase problems , to which we now turn our attention .
if the initial density is constant for either @xmath94 or @xmath96 , then we refer to the corresponding evolution problem @xmath38 as a one - phase problem . as a consequence of the neumann condition at the domain boundary
, it then turns out that there is a change of the spatial variable , different from a simple rescaling , which transforms the one - phase @xmath38 into a regular quasilinear parabolic problem on a fixed domain .
this allows us to prove a global - existence theorem , using standard parabolic theory , regardless of the direction of the gradient at the phase boundary . without loss of generality ,
let us assume that @xmath15 is constant ( @xmath202 ) in the high - density phase , and variable in the low - density phase , and let us again make the change of dependent variable @xmath108 on @xmath98 .
since we are assuming @xmath31 in the low - density phase , this change of variable is invertible there , with inverse denoted by @xmath203 . in terms of @xmath174 , the governing equation ( [ cont_rho ] ) becomes = , [ b_sigma ] subject to @xmath204 at @xmath41 , and @xmath205 at @xmath206 , while the rankine - hugoniot condition takes the form = ( s^-)/(_2-_1 ) .
next , we transform ( [ b_sigma ] ) by introducing so - called mass lagrange coordinates @xcite , @xmath207 , which are defined by = t , y=_x^s(t ) d. since , by construction , @xmath208 , this coordinate change is good , and , introducing @xmath209 , ( [ b_sigma ] ) now takes the form = , [ b_v ] which is a regular quasilinear parabolic equation for @xmath163 . clearly , the moving boundary @xmath206 gets mapped to @xmath210 , and , as a consequence of conservation of mass , the domain boundary @xmath41 gets mapped to y_0:=_0^s(0 ) dx=. thus , ( [ b_v ] ) is to be solved on a fixed spatial domain subject to the boundary conditions @xmath211 at @xmath212 , and @xmath213 at @xmath210 . it is well known that this problem has a unique , global classical solution @xmath214 , given @xmath215 initial data compatible with the dirichlet condition at @xmath210 @xcite .
the corresponding jump location @xmath35 , which can be reconstructed from @xmath214 by integrating , for each @xmath216 , the equation = b(v(y , ) ) from the point @xmath217 until @xmath218 hits zero , could conceivably hit @xmath219 in finite time ( see the numerics in the next subsection ) .
if this occurs , the solution of ( [ b_v ] ) should be stopped , and then continued for all time via np for ( [ cont_rho ] ) on @xmath142 .
we thus arrive at given smooth , one - phase initial data which satisfies the first - order compatibility condition , problem @xmath38 has a unique smooth , global - in - time solution @xmath169 .
the use of rescaled coordinates , as introduced early on in this subsection , allows us to investigate linear stability of the unique discontinuous steady state ( [ s_star ] ) of @xmath38 , which exists as long as @xmath45 .
linearising ( [ v ] ) and ( [ w ] ) around @xmath220 and @xmath221 , respectively , and using hats to denote differentials , we get the pair of heat equations _
t & = & d(_1)_xx , + _ t & = & d(_2)_xx , which are to be solved subject to @xmath222 , @xmath223 , @xmath224 , @xmath225 , while linearising ( [ resc_com ] ) around @xmath226 gives = ( _ 1-_2)^-2\{-(_1-_2)_0 ^ 1
dx + ( _ 2-m)_0 ^ 1(- ) dx}. for a solution @xmath227 of the linearisation , it is therefore clear that , say , @xmath228 and @xmath229 as @xmath57 , and also that @xmath230 as @xmath57 . in this sense , then , the unique discontinuous steady state of @xmath38 is always linearly stable , whenever it exists . as well as facilitating mathematical analysis , the rescaled
, fixed - boundary representation of @xmath38 , ( [ v ] ) , ( [ w ] ) , ( [ rescaled_rh ] ) , also comes in useful for numerical simulations .
specifically , we use a method - of - lines approach in which the diffusion terms in ( [ v ] ) and ( [ w ] ) are discretised using the random - walk model ( [ walk ] ) , while the advection terms are discretised by means of a standard , explicit upwinding scheme . a simulation
in which the global - existence criterion ( [ class_data ] ) is satisfied is shown in figure 2 , and one in which it is violated is shown in figure 3 . in each case
, the solution approaches the appropriate discontinuous steady state at large times .
several other simulations have been carried out in the case where ( [ class_data ] ) is violated , and no singularities have been observed to develop . turning to the question of bistability for cetain values of the mass @xmath44 , we next show in figure 4 a close - up of a solution with @xmath231 and @xmath232 , for which the phase boundary hits the domain boundary in finite time .
this should be compared with the simulation shown in figure 5 , in which the solution has the same mass and adhesion coefficient , but this time evolves to the unique discontinuous steady state as @xmath57 .
it is perhaps worth noting that such bistability can not occur if the traditional restriction ( [ class_data ] ) is imposed on the initial data , by theorem 2.1 .
we now consider the general case of our stefan - problem set - up , in which the initial density profile jumps @xmath40 times across the the unstable region @xmath16 .
this initial / boundary - value problem will be denoted by @xmath39 .
the problem @xmath39 consists of looking for a piecewise - smooth @xmath15 which satisfies the diffusion equation ( [ cont_rho ] ) away from @xmath40 discontinuities @xmath18 , with @xmath233 , such that @xmath15 always jumps between @xmath33 and @xmath34 at the @xmath19 , which evolve according to the rankine - hugoniot condition = , [ rh_i ] where @xmath234 , and @xmath235=(\rho(s_i^+,t)-\rho(s_i^-,t))$ ] ( @xmath236 ) , and the neumann condition is again imposed at the domain boundary @xmath237 ; a schematic for @xmath39 is given in figure 6 .
we also allow for the possibility that @xmath238 or @xmath239 may hit the domain boundary in finite time , or that neighbouring discontinuities could collide , leading to the annihilation of a phase .
should any of these events occur , the solution can be continued via @xmath240 or @xmath241 , as appropriate , and so on . a solution continued in this way
will still be referred to globally as a solution of @xmath39 .
the steady - state picture for @xmath39 , given @xmath242 is more complicated than that for @xmath38 .
first of all , for a given mass @xmath44 satisfying @xmath45 , there is a continuum of two - valued , @xmath40-jump steady states , each of which is given by a choice of the @xmath19 which merely has to be compatible with @xmath44 .
moreover , discontinuous steady states with fewer than @xmath40 jumps can also be considered permissible - these could be approached dynamically by ( multiple ) coalescence events , and/or by ( successive ) collisions of phase boundaries with the domain boundary . each steady state with more than one discontinuity is expected to be merely neutrally stable , since the total mass is invariant under small translations of an internal phase ( i.e. , one which does _ not _ touch the domain boundary ) .
if the stronger condition @xmath53 holds , then there is no possible continuous steady state , and thus , for a global solution of @xmath39 , at least one discontinuity must remain as @xmath57 . if , instead , @xmath58 or @xmath59 , then the uniform steady state exists alongside the discontinuous family already discussed . in this regard , note that figures 4 and 5 could be considered as simulations of one half of a reflection - symmetric @xmath243 , with @xmath244 , in which the central high - density phase is either annihilated in finite time ( figure 4 ) or preserved as @xmath57 ( figure 5 ) , depending on the proximity of the initial data to the ( unique ) discontinuous , symmetric steady state . in general
, it is difficult to say anything analytical about the stability of steady states of @xmath39 , although in each phase the solution will still decay to @xmath33 or @xmath34 , as appropriate , exponentially in @xmath55 , by essentially the same calculation as in section 2.2 , as long as the relevant phase boundaries stay away from the domain boundary .
finally , note that if @xmath47 or @xmath46 , then there is only one possible steady state , namely the uniform one , and , by @xmath55-decay , phase boundaries for a global solution must disappear in finite time ( or possibly infinite time in the exceptional cases @xmath245 ) via coalescence events , or by merging with the domain boundary .
for the subsequent @xmath43 , exponential @xmath55-convergence to the uniform steady state @xmath65 follows as before .
the multi - phase problem , @xmath39 , is solved , locally in time , in the same way as @xmath38 ; in each phase the spatial variable is rescaled in order to fix the moving boundary ( or boundaries ) , and the same estimates go through as before . to be explicit ,
on the interval @xmath246 $ ] we make the coordinate transformation ( x , t ) ( , ) : = , = t , such that , writing @xmath247 , the governing pde ( [ cont_rho ] ) becomes , upon dropping hats = ( s_i+1-s_i)^-2(d(v_i ) ) + , [ v_i ] on @xmath36\times[0,t]$ ] , for @xmath248 , where we adopt the conventions @xmath249 and @xmath250 . on an internal phase ,
this equation is to be solved subject to the appropriate dirichlet conditions at @xmath237 , while on an extremal phase the mixed neumann / dirichlet conditions are used , as in the two - phase case ( see figure 6 ) .
the rescaled family of rankine - hugoniot conditions takes the form = -(-)(_2-_1)^-1,[rescaled_rh_i ] for @xmath251 .
equations ( [ v_i ] ) , ( [ rescaled_rh_i ] ) are solved by the same kind of iteration employed for @xmath38 ; the required hlder estimates are obtained via linear parabolic theory and picard s theorem for systems of odes .
the upshot of all this is given initial data @xmath252 , @xmath251 , for which the @xmath253 and @xmath254 belong to the hlder space @xmath255 , @xmath112 , and such that the first - order compatibility conditions are satisfied , the system of equations ( [ v_i ] ) , ( [ rescaled_rh_i ] ) , and hence problem @xmath39 , has a unique classical solution on some small time interval @xmath115 $ ] . with the same notation as in sect .
2.4 , and by a similar calculation , it is straightforward to see that the gradient of a local solution of @xmath39 satisfies , for @xmath175 , the _ a priori _ estimate ( _ x)^m^2_l^2((0,1))()_i[]_i(_x(s_i^+)-_x(s_i^-))(_x^2m(s_i^+)-_x^2m(s_i^- ) ) .
thus , @xmath201 , and hence also the @xmath256 and @xmath257 , are bounded for all time , provided [ ] _ i(_x(s_i^+)+_x(s_i^-))0,i .
this condition holds if , for example , _ 0_1,_0_2,[grad_cond2 ] which is the multi - phase analogue of ( [ class_data ] ) . inequalities ( [ grad_cond2 ] ) therefore guarantee global existence of the corresponding solution to @xmath39 , modulo coalescence events , and the possibility that an extremal discontinuity might hit the boundary in finite time . in order to continue a solution of @xmath39 after the coalescence of two phases ,
it is necessary to extend our existence theory ( which has thus far required the initial data to lie in @xmath255 ) to the case where the initial density profile may have a ` corner ' in one of the phases .
this can be seen by considering the situation illustrated in figure 7 , in which two high - density phases coalesce , thus annihilating a low - density phase .
if we make the assumption that condition ( [ grad_cond2 ] ) holds , then , in fact , the required extension for such phase - wise @xmath215 data follows from theorem 14 , sect.v of @xcite , and hence , putting together the results of this section , we therefore arrive at given @xmath40 initial jump locations @xmath258 , and a phase - wise smooth initial density profile @xmath259 satisfying the first - order compatibility conditions at phase boundaries , along with the gradient condition ( [ grad_cond2 ] ) , the multi - phase stefan problem @xmath39 has a unique , global classical solution , on the understanding that phases may in time be annihilated via coalescence events , or that an extremal discontinuity may hit the domain boundary in finite time .
moreover , @xmath201 is monotonically decreasing for all time .
we end by noting that it is not clear whether even a local existence theorem for @xmath39 can be proved for merely @xmath215-data if ( [ grad_cond2 ] ) is not satisfied ; one can , for example , proceed by approximating @xmath215 data with smooth data , but it seems that the _ a priori _ bound on @xmath180 implied by ( [ grad_cond2 ] ) is required to get the necessary convergence .
the results of this paper can be interpreted as saying that cell - cell adhesion is enough to stabilise sharp - edged aggregations of diffusing cells if there is enough mass present in the biological domain , and that diffusion homogenises the cell density in each given high- or low - density phase . for low masses ,
however , narrow high - density regions can become annihilated even if the adhesion is very strong - that is to say , diffusion in the low - density regions wins , leading to a globally uniform cell density at large times . in the case of intermediate masses , bistability becomes possible - either adhesion or diffusion can win out , depending on the profile of the initial data .
next , while being motivated by the adhesion - diffusion equations ( [ cont_rho ] ) and ( [ mod - equ ] ) , it should be clear that the analysis carried out in this paper does not require that the diffusivity @xmath10 have the special form ( [ d ] ) ; indeed , all arguments go through for _ any _ equation of the form @xmath260 , provided the @xmath196 function @xmath261 is increasing outside an unstable interval of @xmath15 values , and provided @xmath262_i=0 $ ] at jump locations @xmath19 .
finally , one rather obvious biologically - relevant extension of the work described here would be to carry out a similar analysis with a chemotactic term factored into the right - hand side of ( [ cont_rho ] ) .
in that situation , one could imagine beginning with a low - density initial datum , evolving the solution until , through chemotactic aggregation , @xmath15 hits the unstable region @xmath16 at some point @xmath263 , and then continuing the solution via a stefan problem with an initial spike at @xmath263 which jumps from @xmath33 to @xmath34 .
the transition from well - posed neumann problem to stefan problem is somewhat singular in that case , and is the subject of ongoing analytical investigation .
the author wishes to thank christian schmeiser for suggesting this problem , and for several helpful discussions along the way .
first of all , we have * lemma a.1 * _ the equation _ = d(x , t ) + a(x , t ) + b(x , t)u + f(x , t),[linear_para ] d(x,0 ) + a(x,0 ) + b(x,0)u_0 + f(x,0 ) = 0 , + for the proof , see @xcite , ch.4 , thms .
5.2 - 5.4 . next , let @xmath264 denote the usual second - order @xmath55-type sobolev space on the unit interval , let @xmath265 , @xmath266 , be the sobolev space with norm u_1,q = u_l^q((0,1 ) ) + u_x_l^q((0,1 ) ) , and let @xmath267 denote the fractional - order sobolev space with norm u_2-,q = u_1,q + \ { _ _ dxdy}^,[frac_norm ] where @xmath142 , @xmath268 .
then it is elementary to prove + + * lemma a.2 * @xmath269 , _ for @xmath270_. + + finally , let @xmath271 be the @xmath272-type parabolic sobolev space with norm u^(2)_q , q_t = u_q(q_t)+u_x_q(q_t)+u_xx_q(q_t)+u_t_q(q_t ) .
then , by the fractional - order case of @xcite , ch .
iv , thm . 9.1 , we have + + * lemma a.3 * if @xmath118 is the solution of the mixed dirichlet / neumann problem for ( [ linear_para ] ) , and if @xmath273 is _ a priori _ bounded , then we have u^(2)_q , q_tc(u(,0)_2-,q ( ) + |u_1|).[w(2)_q_est ] finally , by @xcite , ch .
iv , top of p.343 , we have + + * lemma a.4 * for @xmath274 , and @xmath275 , there holds the imbedding inequality |u|^(2-)_q_tc u^(2)_q , q_t .
* lemma b.1 * _ for a function @xmath276 , @xmath277 , such that @xmath278 $ ] , @xmath279 , we have _ _ proof . _ the parabolic hlder norms in question are , when written out in full , & + & u^(l+1)/2_t,_t + u_x^l/2_t,_t , + & & + & + & u_x^l_x,_t + u_xx^l_x,_t + u_t^l_x,_t + & + & u_t^l/2_t,_t + u_x^(l+1)/2_t,_t + u_xx^l/2_t,_t .
we proceed to estimate each of the terms appearing in @xmath280 . first , u_c(_t)tu_t_c(_t ) + u(,0)_c ( ) .
second , u_x_c(_t ) & & _ x , t|u_x(x , t)-u_x(x,0)| + _ x|u_x(x,0)| + & & t^(l+1)/2u_x^(l+1)/2_t,_t + u_x(,0)_c(_t ) . third , u_x^l_x,_t & = & _ x , x,t + & = & _ x , x,t + & & _ x , x|x - x|^1-lu_xx_c(_t ) + & = & c(,l)u_xx_c(_t ) + & & c_x , t(|u_xx(x , t)-u_xx(x,0)| + |u_xx(x,0)| ) + & & ct^l/2u_xx^l/2_t,_t + u_xx(,0)_c ( ) .
fourth , u^(l+1)/2_t,_t & = & _ x , t , t + & & u_t_c(_t)t^(1-l)/2 .
fifth , u_x^l/2_t,_t & = & _ x , t , t + & & t^u_x^(l+1)/2_t , . putting these estimates together
gives the desired result @xmath92
subject to a restriction on the initial data , a weak formulation of @xmath39 can be written down in such a way that the rankine - hugoniot condition becomes ` hidden ' , thus aiding mathematical analysis .
essentially the same kind of formulation was written down many years ago by ladyenskaya _
@xcite , and , for example , their uniqueness proof goes through without change . to obtain the correct weak formulation on @xmath286\times[0,t]$ ] , first note that for a smooth test function @xmath287 such that @xmath288 , we have , for classical solutions of @xmath39 , and with @xmath289 , _ 0^t_0 ^ 1 dxdt = _ 0^t_0 ^ 1 dxdt - _ 0^t_i=1^n(s_i , t)[_x]_i dt - _ 0^t_i=1^n _ x(s_i , t)[]_i dt . thus , using ( [ rh_sigma ] ) , and noting that @xmath174 is continuous at @xmath19 by construction , we arrive at _ 0^t_0 ^ 1 ( b()_t+ ) dxdt + _ 0 ^ 1 b()|_t=0 dx = 0[weak ] for all smooth @xmath287 such that @xmath288 , as the weak formulation of @xmath39 .
this is identical to the problem considered in chapter v.9 of @xcite , and existence and uniqueness of solutions follows by exactly the same argument used there , since one merely requires that @xmath291 be piecewise smooth and monotonically increasing .
we record this result as + + * lemma c.1 * _ for a given bounded , continuous initial datum @xmath292 , equation ( [ weak ] ) has a unique bounded solution @xmath293 . _
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oxford science publications ( 2007 ) . | we consider a family of multi - phase stefan problems for a certain 1-d model of cell - to - cell adhesion and diffusion , which takes the form of a nonlinear forward - backward parabolic equation . in each material
phase the cell density stays either high or low , and phases are connected by jumps across an ` unstable ' interval .
we develop an existence theory for such problems which allows for the annihilation of phases and the subsequent continuation of solutions .
stability results for the long - time behaviour of solutions are also obtained , and , where necessary , the analysis is complemented by numerical simulations . |
a pseudoaneurysm is an extra - luminal collection of blood with turbulent flow that communicates with the parent vessel through a defect in the arterial wall .
the development of an arterial pseudoaneurysm is a rare but reported complication of pelvic surgery , vascular trauma during c - section or after uterine curettage .
after hematoma formation , there is central liquefaction that leaves a cavity with turbulent blood flow , as a result of persistent communication between the parent artery and the hematoma .
the absence of a 3-layer arterial wall lining the pseudoaneurysm differentiates it from a true aneurysm , which is less common than a pseudoaneurysm .
pseudoaneurysm of the uterine artery is an uncommon cause of delayed postpartum hemorrhage following caesarean or vaginal delivery and is potentially life threatening .
typically , the lesions are discovered because the patients have symptoms related to delayed rupture of the pseudoaneurysm , causing hemorrhage .
a pseudoaneurysm may be asymptomatic , may thrombose , or may lead to distal painful embolization .
transcatheter uterine artery embolization ( uae ) has emerged as a highly effective technique for controlling obstetric and gynaecologic hemorrhage , including that from pseudoaneurysms .
we report a case of uterine artery pseudoaneurysm presenting with secondary postpartum hemorrhage 3 weeks after c - section delivery and managed successfully with coil embolization .
a 28-year - old gravida 2 , para 1 was transferred to our institution 19 days post operation with symptoms of excessive bleeding per vaginum .
she later developed excessive bleeding per vaginum , high grade fever , and was readmitted .
on abdominal examination , the c - section scar was found to be healthy and no abnormality was detected .
she was stabilized with crystalloids , five units packed red blood cells , and started on broad spectrum antibiotics .
there was no evidence of residual placental tissue in the uterine cavity and endometrial thickness was 7 mm .
a hypoechoic lesion measuring 2 cm 1.5 cm [ figure 1a ] was detected in the isthmic region of uterus and power doppler revealed blood flow within it [ figure 1b ] .
color flow doppler sonography showed yin and yang blood flow pattern within the body of pseudoaneurysm .
( a ) gray - scale ultrasound of the pelvis shows a hypoechoic lesion in the anterior wall of uterus .
( b ) power doppler evaluation of the uterus demonstrates blood flow within this hypoechoic lesion .
computed tomography angiogram was done with non - ionic contrast showed early contrast filling of the lesion within the uterus [ figure 2a , b ]
. maximum intensity projection ( mip ) and volume rendered ( vr ) images nicely demonstrated the pseudoaneurysm in relation to the uterine artery [ figure 2c , d ] .
( a ) axial and ( b ) sagittal mpr ct angiogram images show contrast filling the pseudoaneurysm ( arrow ) within the uterus .
( c ) mip and ( d ) vr images show a pseudoaneurysm in relation to the left uterine artery . to preserve the fertility in this young patient , a transcatheter arterial embolization of this pseudoaneurysm was planned .
arteriography revealed a pseudoaneurysm from the terminal part of the left uterine artery , in addition the left uterine artery was tortuous and was hypertrophied [ figure 3a , b ] .
left uterine artery was selectively embolized with mixture of gelfoam and contrast media followed by 2 stainless steel coils 4 mm in diameter [ figure 4a ] .
the right uterine artery was also tortuous and hypertrophied and was embolized with gel foam .
a post embolization angiographic study was performed to ensure the complete occlusion of the vessels [ figure 4b ] .
follow - up color doppler us showed aneurysmal cavity filled with echogenic content with no evidence of blood flow [ figure 4c ] , except for pain in the abdomen that was managed with analgesics .
selective left internal iliac angiogram : ( a ) early and ( b ) late phase shows the pseudoaneurysm ( arrows ) , arising from the left uterine artery ( arrowhead ) in addition the hypertrophy of the left uterine artery can also be appreciated .
( b ) selective left internal iliac angiogram ( postembolization ) using gelfoam and embolization coils show complete obliteration of the pseudoaneurysm .
( c ) follow up color doppler sonography shows no evidence of blood flow within the pseudoaneurysm .
secondary postpartum hemorrhage is defined as excessive bleeding starting any time from 24 hours after delivery up to 6 weeks postpartum and most commonly occurring between 8 and 14 days postpartum .
common causes include retained products of conception , subinvolution of the placental bed , and endometritis .
rare causes include pseudoaneurysm of uterine artery , arteriovenous malformations , and choriocarcinoma . when the more common causes have been excluded , pelvic angiography may be performed .
brown et al . , reported the first case of selective arterial embolization used successfully to treat an extrauterine pelvic hematoma after three failed surgical attempts to control the bleeding .
since then , arterial embolization has been used successfully to control postpartum bleeding from uterine atony , placenta accreta , and vulvar and vaginal hematomas .
the efficacy and safety of selective arterial embolization of uterine arteries was evaluated by pelage et al .
, in women with delayed secondary postpartum hemorrhage . in their series of 14 women , pseudoaneurysms of the uterine artery were found in 2 women . immediate resolution of external bleeding was observed after embolization . in this series ,
a true aneurysm has all three layers of arterial wall , whereas pseudoaneurysm does not have all the three layers of arterial wall .
the differential diagnosis of pseudoaneurysm includes acquired arteriovenous malformations ( avms ) , arteriovenous fistulas , and direct vessel rupture .
avms are characterized by multiple communications of varying sizes between arteries and veins , which can be congenital or acquired .
congenital uterine avms are due to abnormality in the embryologic development of primitive vascular structures , whereas acquired avm 's consist of multiple small arteriovenous fistulas between intramural arterial branches and the myometrial venous plexus . acquired avm 's occur more commonly following d and c , uterine surgery , or trauma to the uterus .
color flow doppler demonstrates to - and - fro sign in the neck of the pseudoaneurysm and yin - yang sign in the body of the pseudoaneurysm .
avm 's are characterized by marked aliasing on color flow doppler and arterialized venous flow on spectral doppler evaluation . in a small series of women , who underwent embolotherapy for obstetric hemorrhage , all 3 women who attempted conception after embolization were successful .
treatment was by angiographic embolization of uterine arteries with gelfoam and embolization coils . in a series of women , rosenthal et al . , observed angiographic arterial embolization was shown to be the most useful clinical tool in the management of post operative vaginal hemorrhage .
angiographic embolization has the advantages of decreased morbidity , ability to localize the bleeding site and provide a more distal occlusion than surgical ligation , and preservation of future fertility compared to hysterectomy .
burchell demonstrated that bilateral internal iliac artery ligation was more effective in reducing the pulse pressure than unilateral ligation .
it is possible that the redistribution and redirection of blood or hypoxia - induced neovascularization allows bleeding to occur from the contralateral side after unilateral embolization .
inadequate embolization of a pseudoaneurysm due to extrauterine feeding arteries , such as the internal pudendal artery , ovarian artery , inferior epigastric artery , or contralateral uterine artery leading to embolization failure can occur .
we conclude that in a woman with unexplained vaginal bleeding after c - section delivery , pseudoaneurysm is a potentially life - threatening complication and should be considered in the differential diagnosis of secondary postpartum hemorrhage .
although data are scant , bilateral uterine artery embolization for obstetric hemorrhage appears to have no increased deleterious effect on future fertility and is more effective when compared to unilateral embolization . | uterine artery pseudoaneurysm is a rare cause of secondary postpartum hemorrhage but is potentially life - threatening and can occur after caesarean section ( c - section ) or a hysterectomy .
a 28-year - old woman who developed secondary postpartum hemorrhage after c - section was diagnosed to have pseudoaneurysm from the left uterine artery on ultrasound ( us ) and computed tomography ( ct ) scan .
she was treated with coiling of the pseudoaneurysm with stainless steel coil via selective catheterization of the uterine artery .
the procedure was uneventful and the pseudoaneurysm was successfully obliterated .
angiographic embolization is a safe and effective method for treating postpartum hemorrhage due to pseudoaneurysm in hemodynamically stable patients .
therefore , it should be considered as a treatment option before resorting to surgery , in appropriately selected cases . |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``Boosting Equity for the American
Middle Class Act of 2016'' or as the ``BEAM Act of 2016''.
SEC. 2. REFUNDABLE CREDIT FOR EARLY PRINCIPAL PAYMENTS ON CERTAIN HOME
MORTGAGES.
(a) In General.--Subpart C of part IV of subchapter A of chapter 1
of the Internal Revenue Code of 1986 is amended by inserting after
section 36B the following new section:
``SEC. 36C. EARLY PRINCIPAL PAYMENTS ON CERTAIN HOME MORTGAGES.
``(a) In General.--In the case of an individual, there shall be
allowed as a credit against the tax imposed by this subtitle for the
taxable year an amount equal to 50 percent of the excess home mortgage
principal payments made by the taxpayer during such taxable year.
``(b) Annual Dollar Limitation.--The credit allowed under
subsection (a) with respect to any taxpayer for any taxable year shall
not exceed $500.
``(c) Lifetime Limitation.--No credit shall be allowed under
subsection (a) to any taxpayer for any taxable year if credit was
allowed under subsection (a) to such taxpayer for any 10 preceding
taxable years.
``(d) Limitation Based on Modified Adjusted Gross Income.--
``(1) In general.--The amount which would (but for this
paragraph and after the application of subsection (b)) be
allowable as a credit under subsection (a) shall be reduced
(but not below zero) by the amount which bears the same ratio
to the amount which would be so allowable as--
``(A) the excess of--
``(i) the taxpayer's modified adjusted
gross income for the taxable year, over
``(ii) $125,000 (twice such amount in the
case of a joint return), bears to
``(B) $10,000 (twice such amount in the case of a
joint return).
``(2) Modified adjusted gross income.--The term `modified
adjusted gross income' means adjusted gross income increased by
any amount excluded from gross income under section 911, 931,
or 933.
``(e) Excess Home Mortgage Principal Payments.--For purposes of
this subsection--
``(1) In general.--The term `excess home mortgage principal
payments' means, with respect to qualified home mortgage
indebtedness for any taxable year, the excess of--
``(A) the aggregate amount of principal paid by the
taxpayer with respect to such indebtedness during such
taxable year, over
``(B) the aggregate amount of principal which would
have been paid by the taxpayer with respect to such
indebtedness during such taxable year if the taxpayer
had timely made each required payment under the terms
of the indebtedness during such taxable year (and no
other payments).
``(2) Qualified home mortgage indebtedness.--
``(A) In general.--The term `qualified home
mortgage indebtedness' means any acquisition
indebtedness (as defined in section 163(h)(3)(B)) if--
``(i) the residence with respect to such
acquisition indebtedness is the primary
residence (within the meaning of section 121)
of the taxpayer, and
``(ii) such indebtedness constitutes a
traditional mortgage.
``(B) Traditional mortgage.--For purposes of this
paragraph, the term `traditional mortgage' means
indebtedness--
``(i) the term of which is not less than 15
years and not more than 30 years, and
``(ii) the required payments under which
are each the same amount and made in equal
intervals during the term of the indebtedness
(or if any payment is required at a different
interval, the amount of such payment is
adjusted in the same proportion as the change
in interval).
``(f) Rules Related to Joint Returns.--
``(1) No credit for married individuals filing
separately.--In the case of a married individual, no credit
shall be allowed under this section for any taxable year unless
such individual files a joint return with such individual's
spouse for such taxable year.
``(2) Application of lifetime limitation with respect to
joint returns.--If the credit under subsection (a) is allowed
with respect to a joint return for any taxable year, such
credit shall be treated for purposes of applying subsection (c)
as allowed to both spouses for such taxable year. For purposes
of applying subsection (c) with respect to a joint return for
any taxable year, the taxpayer shall be treated as having been
allowed the credit under subsection (a) for 10 or more
preceding taxable years only if both spouses have been so
allowed such credits.''.
(b) Reporting of Excess Home Mortgage Principal Payments.--Section
6050H(b)(2) of such Code is amended by striking ``and'' at the end of
subparagraph (C), by redesignating subparagraph (D) as subparagraph
(E), and by inserting after subparagraph (C) the following new
subparagraph:
``(D) the amount of excess home mortgage principal
payments (as defined in section 36C(e)) received with
respect to such mortgage during the calendar year,
and''.
(c) Conforming Amendments.--
(1) Section 6211(b)(4)(A) of such Code is amended by
inserting ``36C,'' after ``36B,''.
(2) Section 1324(b)(2) of title 31, United States Code, is
amended by inserting ``36C,'' after ``36B,''.
(3) The table of sections for subpart C of part IV of
subchapter A of chapter 1 of the Internal Revenue Code of 1986
is amended by inserting after the item relating to section 36B
the following new item:
``Sec. 36C. Early principal payments on certain home mortgages.''.
(d) Effective Date.--The amendments made by this section shall
apply to taxable years ending after the date of the enactment of this
Act. | Boosting Equity for the American Middle Class Act of 2016 or the BEAM Act of 2016 This bill amends the Internal Revenue Code to allow a refundable tax credit equal to 50% of the excess home mortgage principal payments made by a taxpayer during the year. The credit is limited to $500 per year and to taxpayers who have not received the credit for any of the 10 preceding years. The bill reduces the amount of the credit for taxpayers with modified adjusted gross incomes above specified levels. An "excess home mortgage principal payment" is the excess of: (1) the amount of principal paid by the taxpayer with respect to a mortgage during the year, over (2) the amount of principal the taxpayer would have paid by making each required payment on a timely basis under the terms of the mortgage (and no other payments). The mortgage must: (1) be for a primary residence, (2) for a term between 15 and 30 years, and (3) require payments that are each the same amount and made in equal intervals during the term of the mortgage (or if any payment is required at a different interval, the amount of the payment is adjusted in the same proportion as the change in interval). Married individuals must file a joint tax return to claim the credit. Persons engaged in a trade or business (e.g., lenders, mortgage companies, or banks) who are required to report mortgage interest payments from individuals of $600 or more must also report the amount of excess home mortgage principal payments received during the year. |
in recent years a lot of effort has been
undertaken in order to
prepare and investigate ordered structures of -conjugated organic
molecules on nanoscopic and mesoscopic scales .
the interest of both
fundamental and applied science was mainly driven by the goal to understand
and improve the properties of materials used for organic electronics
( e.g. , light emitting diodes , field effect transistors and solar cells ) and to establish novel systems
for optical applications ( e.g. , waveguiding and lasing ) . frequently small rodlike molecules like oligothiophenes ,
oligoacenes
and oligophenylenes have been selected as model systems . in the group
of oligothiophenes sexithiophene ( 6 t )
has shown interesting high quality
properties like a charge carrier mobility of up to 0.1 cm/(v s ) .
consequently there has been an interest
in understanding the growth mechanism of such molecules on well - defined
model substrates like single crystalline cu , sheet silicates or patterned sio2 .
the study in this paper
aims at providing a conclusive picture
of the formation of 6 t nanostructures by an in - depth analysis of the
growth on an alkali - halide single crystal , namely potassium chloride
( kcl ) .
kcl exhibits a face centered
cubic crystal structure with a lattice constant of 6.36 .
the unit cell of the ( 100 ) surface can be described
by the 2d - space group p4 mm as shown
in figure 1 .
importantly , this high symmetry
surface exhibits rotation centers of order 2 and 4 as well as mirror
and gliding planes .
it is expected that the symmetry of the substrate
will be reflected in the multiplicity of epitaxial alignments of the
deposited molecules .
( a ) the ( 100 ) surface
of the kcl crystal , with the white rectangle
illustrating the surface unit cell .
( b ) the p4 mm symmetry of the surface unit cell including
the respective symmetry elements .
the hot wall epitaxy ( hwe ) technique
was applied for the deposition of the organic material , which allows
the growth process to be performed close to thermodynamic equilibrium ,
and in further consequence relatively high vapor pressure of the organic
deposit in the substrate region can be achieved .
therefore the requirements
concerning vacuum conditions are reduced as compared to , e.g. , molecular
beam epitaxy .
the source material 6 t
was purified twice by thermal sublimation before filling it into the
quartz tube of the hwe reactor .
kcl substrates were transferred into
the deposition chamber via a load lock and subsequently preheated
at the deposition temperature ( 60135 c ) for 30 min to
clean the surface from adsorbed species and to ensure a stable temperature
during the whole deposition process .
the deposition was performed
thereafter under a base pressure of 9 10 mbar at a nominal deposition rate of 0.4 nm / min .
x - ray diffraction ( xrd ) measurements
were carried out on a philips xpert x - ray diffractometer using
cr k radiation ( = 2.29 ) and a secondary graphite
monochromator .
brentano
configuration by varying the z - component of the scattering
vector q. consequently it is possible to detect lattice
planes which are parallel to the sample surface .
pole figures are acquired by measuring at a
constant length of q and only varying its direction .
based on both
the observed bragg peaks of the specular scan and the direction of
the poles ( net - plane normals ) within the pole figures , the involved
crystallographic phases as well as the azimuthal alignment of the
crystallites with respect to the substrate can be identified .
optical microscope images
have been acquired by a nikon labophot 2a microscope in combination
with a nikon type 115 digital camera .
scanning force microscopy
( sfm ) studies of the deposited organic films were performed using
a digital instruments dimension 3100 in the tapping mode .
the images
have been acquired at scan speeds of 46 m / s using sic
tips exhibiting a cone angle of 40. nominal values for resonance
frequency and tip radius are 325 khz and 10 nm respectively .
in this paper we reported
on epitaxial growth of 6 t on kcl ( 100 ) ,
which was examined by crystallographic and morphological investigations . by means of sfm analysis different morphologies
furthermore , it was
found that the area covered by islands is declining with increasing
substrate temperature , whereas the sample area covered by needles
is constant over the investigated temperature range ( 60135
c ) .
consequently we can draw the conclusion that needle - like
structures are energetically more stable as compared to flat islands
formed of standing 6 t molecules on kcl ( 100 ) .
additionally , different
activation energies for the growth of nanoneedles in height and width
have been deduced from sfm analysis , namely , 0.26 0.02 ev and
0.15 0.04 ev , respectively . by means of xrd specular
scans it was possible to determine the
contact planes of the structures on the surface .
needles with { 010 }
and { 411 } and islands with the { 100 } facet parallel to the
substrate surface have been detected . utilizing xrd pole figures and
fft analysis of optical microscope images we observed that there is
a well - defined azimuthal alignment of the structures on the surface
in addition to the stacking in growth direction . notably structures
with { 100 } and
{ 411 } contact planes are in perfect azimuthal
alignment to each other , which is explained by ledge directed epitaxy
of the islands on the sidewalls of already existing needles .
the orientation of the crystallographic structures which are present
on the substrate surface fulfills the growth model for rodlike molecules
on sheet silicate substrates developed by simbrunner et al .
therein it is explained that the adsorption
of a single molecule dominates in a first step and the nucleation
of organic crystallites which follows thereafter only leads to a slight
reorientation of the lmas .
in particular rotational and mirror symmetries
have to be reflected by the formed needle orientations .
the latter
considerations are substantiated by the results presented in this
paper . the 4-fold rotational symmetry and the mirror symmetry of the
kcl ( 100 ) substrate surface leads to eight distinct growth directions
of each crystal type .
moreover two different crystal contact planes ,
namely , { 010 } and { 411 } , are characterized by an analogous
lma orientation as similarly observed for p - hexaphenyl
on kcl ( 100 ) .
this hints that the adsorption
geometry of single molecules seems to be decisive for the organic
crystal nucleation as expected by the growth model .
the fact that
one adsorption geometry can lead to different crystal contact planes
may be explained by polymorphs of the first monolayer , that are both
based on the same azimuthal orientation of the lma on the substrate
surface .
the argument is supported by the fact that monolayer polymorphs
of 6 t have already been reported on ag ( 001 ) and ag ( 110 ) . concluding the
latter discussion it can be stated that the azimuthal
alignment of the organic crystals and molecules is basically determined
by a two step process .
the initial phase is dominated by the adsorption
of single molecules in their energetically preferred adsorption geometry
on the substrate surface .
this adsorption process is mainly determined
by an interplay between substrate geometry , molecular geometry and
importantly symmetry properties . in the second step , where the organic
crystal nucleation takes place ,
only a slight azimuthal realignment
of the molecules can be caused in order to optimize the lattice match
at the interface . | the morphology and structure of sexithiophene deposited
on kcl
( 100 ) substrates was investigated by scanning force microscopy and
specular x - ray diffraction measurements .
two different needle - like
structures with { 010 } and { 411 } contact planes have been observed
as well as islands of almost upright standing sexithiophene molecules
with a { 100 } contact plane .
furthermore an azimuthal alignment of
all three crystal orientations was observed by x - ray diffraction pole
figure measurements , and the growth directions reflect the 4-fold
rotational symmetry of the substrate surface .
in addition the analysis
of crystals with { 411 } and { 100 } contact planes unveiled that
they share a common crystallographic direction which is explained
by ledge directed epitaxy . |
ly@xmath0 nebulae , or `` blobs , '' are extended sources at @xmath9 @xmath6 26 with typical ly@xmath0 sizes of @xmath105 ( @xmath1050kpc ) and line luminosities of @xmath11 ergs@xmath4 . their number density and its large variance suggests that blobs lie in massive ( @xmath12 @xmath6 @xmath13@xmath14 ) dark matter halos , which will evolve into those typical of rich clusters today @xcite .
galaxies embedded within blobs are likely to become brightest cluster galaxies .
therefore , blobs are important sites for studying the early interaction of galaxies with the surrounding intergalactic medium ( igm ) . this interaction is probably tied on some scale to the source of the blobs extended ly@xmath0 emission , but the mechanism is poorly understood .
for example , the blob may represent emission from galactic - scale outflows generated by star formation , intense radiative feedback from agns , or even cooling radiation from accreting gas .
there are generally two ways to unravel the nature of the blobs .
the first approach is to study what powers the ly@xmath0 emitting gas , counting all ionizing sources within or around the extended ly@xmath0 emission and comparing that energy budget with the observed ly@xmath0 luminosity .
sometimes , one can identify possible energy sources , e.g. , powerful agns detected in x - rays @xcite .
some potential sources may even lie outside a blob @xcite .
if no such source is found , the remaining ly@xmath0 luminosity may be attributable to cooling radiation .
an alternative path is to observe spectroscopically the kinematics of the extended ly@xmath0-emitting gas .
even addressing whether the gas is falling into an embedded galaxy or outflowing into the igm would be a significant step forward , providing evidence for either gas accretion by forming galaxies or for agn / starburst - driven galactic winds , respectively .
combining the two approaches by considering the blob s energetics and kinematics simultaneously is ideal , a test of whether the bulk motions of the gas are in fact coupled to the source of its illumination .
for example , gas infall is possible even in the presence of an agn ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) .
cases in which blob gas is both outflowing on small scales due to galactic processes and infalling on larger scales from the extended igm are not unlikely .
unfortunately , the kinematic approach has been stymied by the limitations of the ly@xmath0 line , which , although bright compared with other lines , is hard to interpret .
the ambiguity arises because ly@xmath0 is a resonant line and typically optically thick in the surrounding intergalactic medium . as a result
, studies even of the same blob s kinematics can disagree .
on one hand , @xcite argue that ifu spectra from a certain blob are consistent with a simple model where the ly@xmath0 emission is absorbed by a foreground slab of neutral gas swept out by a galactic scale outflow . on the other
, @xcite claim that the same data can be explained by the infall of the surrounding intergalactic medium .
worse , @xcite comment that the same ly@xmath0 profiles are most consistent with static surrounding gas . to distinguish among such possibilities
requires a comparison of the ly@xmath0 line center with the center of an optically - thin line like h@xmath0@xmath16563 ( see also * ? ? ?
h@xmath0 is a better measure of the blob s systemic velocity , i.e. , of the precise redshift , because it is not seriously altered by radiative transfer effects and is more concentrated about the galaxies in the blob s core . despite the complexity of various blob models ,
infall models predict that the peak of the optically thick ly@xmath0 emission line must be blueshifted with respect to h@xmath0 , whereas outflows will redshift the ly@xmath0line @xcite .
this diagnostic has been applied both to local starburst galaxies @xcite and to lyman break galaxies ( lbgs ) at @xmath9 = 1.52.5 @xcite and has provided evidence for outflows driven by strong stellar winds .
an analysis in a similar spirit , but using the 21 cm absorption line to mark the systemic redshift of a high-@xmath9 radio galaxy , finds that the ly@xmath0line is blueshifted and thus that extended gas is inflowing to the agn @xcite .
previous spectroscopic observations of ly@xmath0 blobs ( e.g. , at @xmath15 ; * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
* ) include only ly@xmath0 , precluding a direct comparison with a cleaner line s center and muddling the interpretation of the kinematics . to overcome this challenge , @xcite conduct blind surveys for ly@xmath0 blobs at @xmath2 , a redshift at which important rest - frame optical diagnostic lines ( e.g. , [ ] @xmath13727 , [ ] @xmath15007 , h@xmath16@xmath14868 , h@xmath0@xmath16563 ) fall in nir windows and avoid bright oh sky lines ( or atmospheric absorption ) .
in this paper , we present optical and nir spectroscopy of the two brightest blobs , cdfs - lab01 and cdfs - lab02 , of the 25 in the @xcite sample . for each
, we compare the ly@xmath0line profile with the center of the h@xmath0 line and use existing radiative transfer models @xcite to test whether the detected gas is infalling or outflowing .
in addition to the blob s systemic velocity , nir spectroscopy can constrain ( 1 ) the velocity dispersion and any ordered motion like disk rotation of the brightest embedded galaxies , ( 2 ) the presence of agns with rest - frame optical nebular line diagnostics ( e.g. , [ ] /h@xmath0 ) , ( 3 ) the gas - phase metallicity , and ( 4 ) the star formation rate ( sfr ) directly from the h@xmath0 flux , allowing a comparison with that derived from the rest - frame uv . before now , none of these measurements has been available for ly@xmath0 blobs . in this paper , we focus on the kinematics of the gas in the blob and in the embedded galaxies , deferring discussions of the agn line diagnostics , gas - phase metallicity , and sfrs to a future paper ( y. yang et al .
2011 , in preparation ) . in [ sec : observation ] , we review how we selected blobs from our narrowband imaging surveys @xcite and then describe the optical / nir spectroscopy of the first two blobs . in [ sec : result ] , we present the first results from the spectroscopic campaign .
we confirm spectroscopically the blob redshift and discover multiple h@xmath0 sources within each blob ( [ sec : confirmation ] ) .
we compare the ly@xmath0 profiles with the h@xmath0 line centers to discriminate between simple infall and outflow scenarios ( [ sec : shift ] ) . in
[ sec : absorption ] , we describe the interstellar absorption lines detected in lab02 and compare the low ionization lines with h@xmath0 .
we estimate the velocity dispersions of three of the embedded galaxies in [ sec : dynamical_mass ] . in [ sec : discussion ] , we compare the ly@xmath0 profiles and ly@xmath0@xmath17h@xmath0 offsets with existing radiative transfer models .
we also discuss our results in the context of the clumpy circum - galactic gas model proposed by @xcite .
[ sec : conclusion ] summarizes our conclusions . throughout this paper ,
we adopt cosmological parameters : @xmath18 = 70@xmath19 , @xmath20 , and @xmath21 .
we observe the two brightest ly@xmath0 blobs from the @xcite sample , which consists of 25 blobs discovered in four different survey fields .
these two blobs lie in the extended chandra deep field south ( e - cdfs ) and were found via deep imaging with the ctio-4 m mosaic ii camera and a custom narrowband filter ( _ nb_403 ) .
this filter has a central wavelength of @xmath22 , designed for selecting ly@xmath0-emitting sources at @xmath23 , and a band - width of @xmath24 , providing a line of sight ( hereafter los ) depth of @xmath25 that corresponds to 46.8 comoving mpc .
the blob selection criteria are : ew@xmath26 @xmath27 100 and isophotal area @xmath28 @xmath27 10 above the surface brightness threshold of 5.5 @xmath29 10@xmath30 ergs@xmath4@xmath31arcsec@xmath32 .
we show the images of the two blobs ( cdfs - lab01 and cdfs - lab02 ) in figure [ fig : image ] .
we refer readers to @xcite for details of the sample selection .
we obtained high resolution optical spectra of the two ly@xmath0 blobs using the magellan echellette spectrograph ( mage ; * ? ? ?
* ) on the magellan clay 6.5 m telescope .
mage provides a spectral resolution of @xmath33 @xmath6 4100 for a 1 slit over a wide wavelength range of 3000 10000 . while the slit length is small ( 10 ) compared to typical longslits , the excellent blue sensitivity around 4000 is ideal for obtaining the ly@xmath0 line profile .
observations were carried out on ut 2008 july 26 and october 1 , and 2009 february 17 .
for lab01 , we first acquired a low resolution spectrum in 2008 july 26 to spectroscopically confirm the redshift prior to the nir spectroscopic run . later , we obtained the @xmath34 spectrum with a slit orientation of p.a.=42 as shown in figure [ fig : image ] ( ly@xmath0 panel ) . for lab02 , we used a 2 slit and a p.a.=0 to obtain a @xmath33 @xmath6 2000 spectrum .
the sky condition was clear , and the seeing ranged from 0.9 to 1.3 .
the individual exposure times varied from 20 to 40min , depending on the variability of the seeing .
total exposure times were 2.5 and 2.0 hrs for lab01 and lab02 , respectively . for accurate wavelength calibration , we took thar lamp frames right before and after the science exposures and at the same telescope pointing to eliminate systematic errors introduced by instrument flexure .
we reduce the mage data using the daniel kelson s carnegie - python package @xcite .
the frames are overscan - corrected , bias - subtracted , and flat - fielded with xenon - flash and quartz ( incandescent ) lamps . using night sky lines and thar lamp spectra
, we estimate the uncertainties in the wavelength solution to be @xmath60.03(0.1 pixel ) .
the sky background is then subtracted in 2d using the method described in @xcite , and the frames are corrected for spatial distortions .
we combine the rectified 2d spectra and extract the 1d spectra using idl routines .
we also re - reduce the data with the mage spectral extractor package ( mase ; * ? ? ? * ) and confirm that the results are consistent .
the spectra are flux - calibrated with 23 standard stars each night . due to the limited spatial coverage of the slit and the relatively short exposure times ,
our spectra are dominated by the brightest spots within the blobs , which coincide with the galaxies detected in the _ hst _ rest - frame uv images .
future ifu observations should be helpful in constraining how the ly@xmath0 profiles vary over the blobs .
we carried out nir integral field unit ( ifu ) spectroscopy of the two ly@xmath0blobs using sinfoni @xcite on the vlt ut4 telescope in visitor mode between ut 2009 january 30 and february 4 . to measure the redshifted h@xmath0 ( @xmath35 @xmath6 2.175 ) line
, we used the _
k_-band grating , which covers 1.95 2.45 with a spectral resolution of @xmath33 @xmath36 4000 ( @xmath5 @xmath36 75kms@xmath4 ) and dispersion of 2.5pixel@xmath4 . because the blobs are spatially extended over 510 and include multiple sources , we employed the seeing - limited mode ( i.e. , no adaptive optics ) , which provided the largest fov ( 8@xmath298 ) and a plate scale of 025pixel@xmath4 for the spatial resolution elements ( spaxels ) . in each observing block , we observed reference stars , which we used to blind offset to the blobs as well as to monitor the telescope pointing accuracy and the seeing variations .
the _ k_-band seeing ranged from 03 to 12 , and the sky condition was clear . to maximize the on - source integration time , we adopted an `` on - source dithering '' strategy in which the science targets were always kept within the fov but at different detector positions .
for lab01 , we used a three - point dithering scheme that moves among the pointings by @xmath64 to south or west , providing a usable fov of two 4@xmath294 squares ( see the sinfoni panel in figure [ fig : image ] ) .
for lab02 , we employed a two - point dither pattern in the north - south direction , resulting in a 8@xmath294 effective fov ( dot - dashed line in figure [ fig : image ] ) .
the total integration times for lab01 and lab02 are 6 hrs and 0.5 hrs , respectively , which consist of 5 or 10 min individual exposures depending on the sky condition . for the telluric correction and flux calibration ,
we observed four b or g stars every night before or after the science targets with wide range of airmass .
we reduce the sinfoni data using the eso pipeline .
dark current and sky background are removed from each science frame by subtracting the pseudo - sky frame , which is constructed from the average of the two science frames bracketing each science frame .
then , we flat - field the data and correct for bad pixels . because we will compare the velocity centers of the ly@xmath0 and h@xmath0 lines ,
accurate wavelength calibration is critical .
we compare the wavelength solution obtained from the oh sky lines in the science frames to that from the daytime arc lamps .
the arc lamp wavelength calibration error arising from instrument flexure can be as large as 1.5 , depending on the airmass ( which ranges up to @xmath62.0 ) .
therefore , we adopt the oh sky line wavelength calibration , whose error is typically @xmath6 0.1(0.04 pixel ) for each science frame . using this wavelength solution
, we constructed 3d data cubes from the 2d spectra after correcting spatial distortion . because it is not possible to identify / centroid the sources in individual exposures , we align them according to the dither offsets within each observing block ( ob ) .
the spatial offsets between obs are calculated from the psf calibration frames and are typically small ( @xmath6 01 ) .
when combining the data cubes , we adopt an iterative @xmath37-clipping algorithm to reject possible outliers and produce the `` sigma cubes '' that represent the standard deviation of the adopted pixels . because no stellar continuum is detected , we subtract the median sky values from each wavelength plane to avoid the strong variation of global sky background . finally , we flux - calibrate the cubes using the broad - band magnitudes of standard stars .
atmospheric absorption is minimal at h@xmath0 due to our choice of survey redshift , so we do not apply a telluric correction .
we spectroscopically confirm the redshifts ( @xmath9 @xmath36 2.31 2.32 ) of the two ly@xmath0 blobs using both the ly@xmath0 and h@xmath0 emission lines .
figure [ fig : image ] shows the two ly@xmath0 blobs at various wavelengths : _ u _ , continuum - subtracted ly@xmath0 line , _ b _ , _ k _ , _ spitzer _ irac 3.6 , and _ hst _
f606w images overlain with the ly@xmath0contours ( left six panels ) . the archival ground - based images ( _ u , b _ , and _
k _ ) , the _ spitzer _
irac images , and the _ hst _ images are obtained from the multiwavelength survey by yale - chile ( musyc ; * ? ? ?
* ) , the spitzer irac / musyc public legacy in e - cdfs survey ( simple ; * ? ? ?
* ) , and the galaxy evolution from morphology and seds ( gems ; * ? ? ?
* ) survey , respectively . in the right panels
, we show the enlarged _ hst _ images and sinfoni h@xmath0 intensity maps that are collapsed in the wavelength direction centered at @xmath1 @xmath36 2.1746 ( @xmath38 @xmath36 66 ) and 2.1788 ( @xmath38 @xmath36 42 ) for the two blobs , respectively . for the sinfoni image of lab01
, we show only data taken in the best seeing ( @xmath6 03 ) to be comparable with the _ hst _ resolution .
interestingly , in the _ hst _ rest - frame _ uv _ images , both ly@xmath0blobs include multiple galaxies and/or fragments , some of which appear to be interacting ( see also * ? ? ?
a few are also detected in h@xmath0 , indicating that they lie at the same redshift . in @xcite
, we found that the number density and the field - to - field variance of ly@xmath0 blobs are consistent with their occupying massive dark matter halos ( @xmath6 @xmath13@xmath14 ) that probably evolve into those of typical galaxy clusters today .
thus , while some clumps / fragments could be part of a one large galaxy ( e.g. , * ? ? ?
* ; * ? ? ?
* ) , we speculate that others may merge and evolve into present - day brightest cluster galaxies .
figure [ fig : spec1d ] shows the 1d ly@xmath0 spectra extracted from 1@xmath2924 and 2@xmath2924 mage slits for lab01 and lab02 , respectively .
in addition to strong ly@xmath0 emission , lab01 also has @xmath11549 and @xmath11640 emission lines , implying the presence of hard ionizing sources ( e.g , * ? ? ? * ; * ? ? ? * ) . we defer analysis of these lines and their relative strengths to a future paper ( y. yang et al .
2011 , in preparation ) , which focuses on the multi - wavelength properties of the full blob survey and the implications for the sources of blob emission .
lab02 has several interstellar absorption lines that we use in [ sec : absorption ] to help constrain the kinematics of gas around the embedded galaxies .
in contrast to the optically thick and spatially extended ly@xmath0 emission , we can use the optically thin , more spatially concentrated h@xmath0 emission to make an independent determination of the blob redshift from the galaxies embedded in the centers of the blobs .
we extract the h@xmath0 spectra from a 2@xmath292 aperture in the sinfoni cubes . figure [ fig : linefit ] shows the resulting spatially integrated h@xmath0 profiles within the blobs .
the lab01 h@xmath0 spectrum includes all 6hr exposures combined to obtain higher s / n and total flux .
note that whenever we show individual ly@xmath0 or h@xmath0 spectra ( figures [ fig : spec1d ] and [ fig : linefit ] ) , we adopt different aperture sizes that maximize the s / n
. on the other hand , we use the same aperture when comparing the ly@xmath0 and h@xmath0 lines directly ( [ sec : shift ] ) . for lab01
, we focus on the brighter sw component of the blob . the excellent seeing of our sinfoni observation ( @xmath6 0.3 ) allows us to spatially resolve two embedded galaxies ( a and b ) in the sw part of the blob ( hereafter lab01a and lab01b ; fig . [ fig : image])5kpc and the velocity offset is @xmath6440kms@xmath4 . ] .
these two galaxies are also kinematically separated as shown in the sinfoni h@xmath0 channel map ( figure [ fig : channel ] ) , a series of h@xmath0 intensity maps constructed by stepping through the 3d sinfoni data cubes in increments of 70kms@xmath4 .
galaxy b shows an apparent velocity shear of @xmath6 250 kms@xmath4 , suggesting disk rotation , while galaxy a has no obvious velocity structure . in their spatially integrated h@xmath0 spectra
, these two galaxies have the nearly same redshift , @xmath39 = 2.31421 @xmath40 0.0001 and @xmath41 = 2.30928 @xmath40 0.0001 , a separation of @xmath42 = 0.0049 or @xmath5(a b ) = 440kms@xmath4 .
this relative velocity is a poor estimate of the velocity dispersion @xmath37 of the halo in which these galaxies are embedded .
nevertheless , it is consistent with the @xmath37 expected for a massive , @xmath6@xmath13@xmath14 halo .
lab02 also contains several continuum sources in the _ hst _ uv images ( labeled as a
at least one of the brightest sources ( lab02a ) is detected in the sinfoni h@xmath0 image .
with sinfoni , we marginally detect the two sources ( b+c ) blended in the _ hst _ image .
it is also possible that galaxy d is blended with the much brighter galaxy a in the ifu data .
we are not able to reliably extract h@xmath0 profiles from galaxies ( b+c ) and d because of the shallow exposure ( 30 min ) and insufficient spatial resolution .
the integrated spectrum of lab02 is dominated by the brightest galaxy a , for which we measure the @xmath43 = 2.31928 @xmath40 0.0001 .
we summarize the properties of h@xmath0 lines in table [ tab : line_properties ] .
while it is possible that the h@xmath0 detections include some extended gas , the centers of the emission coincide with the galaxies resolved in the _ hst _ image and are likely to originate there .
therefore , in the following section , we compare the ly@xmath0 and h@xmath0 profiles along the los toward these embedded galaxies .
there are small astrometry offsets ( @xmath60.2 ) between _ hst _ uv images and sinfoni h@xmath0 maps ( right panels in figure [ fig : image ] ) . while it is likely that this mismatch arises from the astrometric calibrations of sinfoni , which rely entirely on blind offsets , we extract the ly@xmath0 and h@xmath0 spectra from the same aperture , accepting the current astrometric solution .
changing the relative position of extraction aperture ( green boxes ) for ly@xmath0and h@xmath0 does not affect any of the conclusions in this paper .
we show the selected extraction apertures ( small green boxes ) in figure [ fig : image ] . in lab01
, we extract the spectra along the los toward galaxy a , because the peak of ly@xmath0 map coincides with galaxy a. while galaxies a and b are well - resolved in the h@xmath0 image , the spectrum extracted from the sight - line to lab01a ( green box in fig .
[ fig : image ] ) is slightly contaminated with light from galaxy b. therefore , we simultaneously fit the profile with a total of six components ( three for each galaxy ) and remove the galaxy b components when comparing the h@xmath0 and ly@xmath0 line centers in the following section .
the ly@xmath0 profile emerging from the blob should be complicated , a mixture of the bulk motions of the gas and geometry . for the details of ly@xmath0 radiative transfer
, we refer readers to the literature ( e.g. , * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
in this section , we compare the ly@xmath0 and h@xmath0 lines to constrain the gas kinematics within the blobs .
more specifically , we measure the velocity shift of the ly@xmath0 line relative to the h@xmath0 line center to distinguish between any infall and outflow of the igm relative to the blob s systemic velocity . once we measure this first - order kinematic diagnostic ( i.e. , any blueshift or redshift of the ly@xmath0 line ) , we discuss the detailed ly@xmath0 and h@xmath0 profiles in [ sec : discussion ] , comparing them with radiative transfer calculations to determine the velocity of the dominant bulk motion . to illustrate what we expect from this experiment , we first consider the simplest geometric case : a galaxy surrounded by a spherically symmetric gas cloud that is static , collapsing , or expanding @xcite . here
we assume that the h@xmath0 line arises from the embedded galaxy , as we do not detect extended h@xmath0 emission , and that the ly@xmath0 line originates either in the same region of the galaxy before eventually escaping the surrounding cloud or in the cloud itself .
thus this blob will be observed as a point source in h@xmath0 , but as an extended source in ly@xmath0 .
note that the ly@xmath0 and h@xmath0 spectroscopy is along the los toward the central galaxy .
while h@xmath0 from the galaxy can escape the surrounding gas without suffering absorption , ly@xmath0photons from the galaxy and from gas along the los will be resonantly scattered many times until their frequencies are right for escaping the cloud , a condition dependent on the bulk motions of gas along the los .
because the cloud is optically thick to the ly@xmath0 line , ly@xmath0 photons on the doppler wings should escape the cloud through random scatterings in the frequency domain .
if the surrounding gas is static , the ly@xmath0line will have a double - peaked profile , while the optically thin h@xmath0 photons will escape without any radiative transfer effects .
if the cloud is collapsing , ly@xmath0 photons within the cloud on the red side of double - peaked profile will see higher optical depth due to the los infalling gas , and the red peak will be depressed
. if the gas is outflowing , the blue side of the profile will be more diminished .
therefore , if there is gas infall , the ly@xmath0 profile will be asymmetric and blueshifted against the h@xmath0 line due to radiative transfer in the optically thick medium , but the corresponding h@xmath0 line profile should be symmetric . for outflowing gas , the ly@xmath0 will be redshifted against the symmetric h@xmath0 line .
the amount of shift depends on various parameters such as infall / outflow velocity and optical depth .
note that one can not determine whether the ly@xmath0 line is redshifted or blueshifted against the background velocity field unless there is a optically thin reference line , i.e. , h@xmath0 .
the actual geometry of the system is likely to be more complicated ( [ sec : discussion ] ) . yet
the blue- or redshift of the ly@xmath0photons relative to the systemic velocity will occur as they make their way out of the system , as long as they encounter optically - thick gas that is infalling or outflowing along the los @xcite .
in other words , we are studying the bulk motion of gas along the pencil beam toward the embedded galaxies when we compare the ly@xmath0 and h@xmath0 profiles extracted from this sight - line . in principle , it is even possible to compare the velocity offsets between extended ly@xmath0 and _ extended _ h@xmath0 lines in two dimensions ( i.e. , h@xmath0 and ly@xmath0 screens ) with much deeper h@xmath0 spectroscopy and optical ifu data . in summary ,
the basic assumptions for our simple test using the velocity offset between the ly@xmath0 and h@xmath0 lines are : 1 . ly@xmath0 should go through an optically thick column of gas ( either infalling or outflowing ) to escape .
2 . h@xmath0 represents the systemic velocity of the entire system , and gas is moving ( infalling or outflowing ) relative to this center . with these assumptions in mind
, we now consider the ly@xmath0 and h@xmath0 line profiles for our two ly@xmath0 blobs .
we then examine these assumptions further and discuss how to overcome their limitations in [ sec : discussion ] .
we show the ly@xmath0 and h@xmath0 profiles for the two ly@xmath0 blobs in figure [ fig : line_comparison ] .
we shift each blob s ly@xmath0 profile into its h@xmath0 frame using @xmath44 = @xmath45 @xmath29 @xmath46 .
we place both blobs in the same velocity frame using the redshifts obtained from h@xmath0 .
note that all the optical and nir wavelengths are converted to vacuum wavelengths and corrected to the heliocentric frame . in both blobs , the ly@xmath0 line is broader than the h@xmath0 line and has a more complicated structure ( i.e. , an asymmetric profile or multiple peaks ) , implying that the ly@xmath0 lines do experience resonant scattering .
lab01 has a ly@xmath0 line width of @xmath47 = 520@xmath4040kms@xmath4 whose peak coincides with that of the h@xmath0 line .
while the blue side of the ly@xmath0 profile ( @xmath48kms@xmath4 ) agrees well with that of the h@xmath0 line , it has an extended red wing up to at least @xmath49 @xmath6 + 600kms@xmath4 .
it is not clear whether this red wing arises from the several poorly - resolved red peaks .
lab02 shows a double peaked ly@xmath0 profile with a stronger red peak , which is often observed in high-@xmath9 ly@xmath0 galaxies @xcite .
lab02 s ly@xmath0 profile is broad , extending from @xmath6@xmath50kms@xmath4 to @xmath6@xmath511000kms@xmath4 .
the stronger red peak itself has a line width of @xmath47 @xmath6 420kms@xmath4 .
lab02 s ly@xmath0 profile also has a sharp absorption feature ( or lack of emission ) at @xmath52kms@xmath4that coincides with its h@xmath0 line center . to quantitatively measure the velocity offset between the ly@xmath0 and h@xmath0 lines
, we must first determine each line s center .
for the asymmetric ly@xmath0 line , we measure the wavelength at the peak flux , which is consistent with the methodology of @xcite . because the ly@xmath0 profile is noisy , we smooth the spectrum with a boxcar filter of 3 spectral pixels ( @xmath5 @xmath36 40kms@xmath4 ) and measure the wavelength of the brightest flux . for the symmetric h@xmath0 profiles in both blobs
, we fit the spectrum with a gaussian profile including the neighboring [ ] lines .
we fit three gaussian components with the same velocity width , but different intensities , centered at 6563 ( h@xmath0 ) , 6549 , and 6583 ( [ ] ) . as mentioned earlier , due to the slight contamination of lab01a s spectrum with light from lab01b , we simultaneously fit the observed h@xmath0 profile for both galaxies and show only the spectrum of galaxy a in figure [ fig : line_comparison ] .
ccccccc cdfs - lab01 & a & 2.31421 @xmath40 0.0001 & 1.16 @xmath40 0.06 & 184 @xmath40 9&@xmath510 @xmath40 20 + & b & 2.30928 @xmath40 0.0001 & 0.78 @xmath40 0.05 & 134 @xmath40 8 & ... + cdfs - lab02 & a & 2.31928 @xmath40 0.0001 & 2.42 @xmath40 0.11 & 152 @xmath40 5 & @xmath51230 @xmath40 30 [ tab : line_properties ] the velocity offset , @xmath7 is defined as the difference between the h@xmath0 line center and the ly@xmath0 peak wavelength .
we find a negligible offset between ly@xmath0 and h@xmath0 ( @xmath7 @xmath36 @xmath53@xmath4020kms@xmath4 ) for lab01a , and an offset , @xmath7 @xmath36 @xmath54@xmath4030kms@xmath4 , for lab02a . these @xmath7 are smaller than those of lbgs , which range from + 150kms@xmath4 up to + 900kms@xmath4 with an average of + 450kms@xmath4@xcite . among this lbg sample ,
only 12% of galaxies have @xmath7 smaller than 225kms@xmath4 , thus the probability of finding @xmath7@xmath55 230kms@xmath4 for two ly@xmath0 blobs by chance is rather small ( @xmath61.5% ) if our ly@xmath0h@xmath0 offsets are drawn from the same @xmath7 distribution in @xcite is representative of all lbgs given its sharp break around 300kms@xmath4 . ] . for our two blobs
, @xmath7 is either consistent with zero ( lab01 ) or somewhat redshifted ( lab02 ) .
therefore , according to the simplest picture , we find no evidence for a blueshift and thus for gas infall in either blob .
the absence of a redshifted @xmath7 in lab01 does not necessarily exclude an outflow , because lab01a s ly@xmath0 profile has an extended red wing and/or multiple red peaks , which can be outflow signatures .
if we interpret the observed @xmath7 as a proxy for outflow velocity , then , at face value , any outflows in lab01 and lab02 are weaker than those typical of lbgs . in [ sec : discussion ] , we further consider the implications of our @xmath7 results using radiative transfer calculations .
in addition to the ly@xmath0 emission line , the optical spectrum of lab02 shows several absorption lines ( figure [ fig : spec1d ] ) .
these absorption lines provide an opportunity to constrain the kinematics of cold gas on the near side of the galaxy , i.e. , between the galaxy and observer , and thus to verify the detection of the modest @xmath7 outflow signature in the previous section .
note that the systemic velocity from h@xmath0 spectroscopy is again critical . because the s / n of the continuum in the lab02 spectrum is very low , we first re - bin the spectrum by four spectral pixels , which worsens the resolution of the final velocity bins to @xmath690 kms@xmath4 .
figure [ fig : absorption ] shows the velocity profiles of six absorption lines whose peaks were detected at the @xmath10 3@xmath37 level in the rebinned spectrum .
we show the absorption profiles of three low - ionization interstellar lines ( @xmath11260.42 , @xmath11334.53 , and @xmath11526.72 ) and three high - ionization lines ( @xmath561393.76 , 1402.77 and @xmath11548.20 ) . for comparison
, we also plot the composite lbg spectrum ( @xmath57 ) from @xcite and the individual spectrum of ms1512-cb58 ( @xmath58 ) which is one of the apparently brightest lbg whose light is amplified due to the gravitational lensing @xcite .
although the s / n is low , the velocity ranges spanned by lab02 s absorption lines roughly agree with these two templates .
we find that all interstellar absorption lines are blueshifted against the systemic velocity , indicating that the intervening gas is outflowing , which is consistent with the observed @xmath7 outflow signature discussed in the last section . to estimate the velocity of the outflowing material , we measure how much the centroids of these velocity profiles are offset from the h@xmath0 line : @xmath59 . while the high - ionization lines ( @xmath561393 , 1402 and @xmath11548 ) have the highest s / n , they are known to be contaminated with broader absorption features arising from stellar winds from massive stars @xcite .
therefore , we measure the centroid velocities ( @xmath59 ) using the three low - ionization lines .
two low - ionization lines ( @xmath11334 and @xmath11526 ) have @xmath59 @xmath6 @xmath17100kms@xmath4 to @xmath17200kms@xmath4 .
( it is difficult to reliably measure the centroid of the @xmath11260 line . )
the absorption profile of @xmath11334 might extend up to @xmath60 @xmath6 600kms@xmath4 blueward , although its low s / n precludes a reliable measurement . if we adopt its centroid velocity as an outflow velocity , then it is similar to that of lbgs , which average @xmath61 = @xmath62kms@xmath4 , but can be as large as @xmath17500kms@xmath4 @xcite . by fitting gaussian profiles to the integrated h@xmath0 profiles ( figure [ fig : linefit ] ) , we obtain the velocity dispersions , @xmath63 = 184@xmath409kms@xmath4 and 134@xmath408kms@xmath4 for the lab01a and lab01b , respectively . for lab02a , @xmath64 = 152@xmath405kms@xmath4 .
these velocity dispersions are corrected for the instrumental resolution ( @xmath65 @xmath6 32kms@xmath4 ) .
the internal velocity dispersions of the embedded galaxies ( @xmath66 = 130 190kms@xmath4 ) are high compared to those of star - forming galaxies at @xmath67 .
@xcite find that lbgs at @xmath67 have an average of @xmath68 = 108kms@xmath4 with a standard deviation of 41kms@xmath4 , excluding galaxies with agns .
our lowest @xmath69kms@xmath4 corresponds to the upper @xmath630% percentile of their distribution . in particular , there is only one galaxy in the @xcite sample that has higher @xmath37 than lab01a does ( @xmath64 = 190kms@xmath4 ) .
in this section , we compare the observed ly@xmath0 profiles and their offsets from the h@xmath0 lines with the predictions of ly@xmath0radiative transfer ( rt ) calculations ( * ? ? ? * ; * ? ? ? * ; * ? ? ?
* hereafter d06 , v06 and v08 , respectively ) .
to test the scenario in which gas in the surrounding cloud cools and flows toward the blob center , we compare our data with the spherical collapse model in d06 . for the picture in which gas outflows from the embedded galaxies in the blob s core , we employ the expanding shell model investigated by v06 . note that these rt calculations assume that infall and outflow occur in spherical symmetry , in a collapsing sphere for the inflow model and in an expanding shell for the outflow model . as we argued previously
, even such simple models should reproduce the general behavior of the ly@xmath0profile as long as the basic assumptions listed in [ sec : shift ] are valid . in [ sec : future ] , we examine those assumptions in detail and discuss the future work required to overcome these limitations . in [ sec : shift ] , we found that the ly@xmath0 lines of the two blobs are not blueshifted relative to the h@xmath0 line centers within the measurement uncertainties .
the absence of a blueshift rules out the simplest infall model where a spherical gas cloud is collapsing onto a central ly@xmath0 source or where the collapsing cloud itself is emitting ly@xmath0 photons . in this model , @xcite and @xcite study ly@xmath0radiative transfer , which depends on various parameters such as the location of the ly@xmath0 source , the infall velocity field , the column density of neutral hydrogen ( @xmath70 ) , and the doppler parameter @xmath71 representing the thermal and turbulent motion of the gas ( see fig . 4 and 7 in d06 or fig .
57 in v06 ) .
the key prediction of these rt calculations is that the ly@xmath0 spectrum is double peaked with an enhanced blue peak , producing an effective blueshift of the ly@xmath0 profile . while the blue peak might be suppressed by the intervening igm after the ly@xmath0 photons
escape the collapsing cloud @xcite , this effect is unlikely to be significant here because the mean transmission blueward of ly@xmath0 should be relatively high at @xmath2 : @xmath72 @xmath6 0.8 @xcite , where @xmath73 represents ly@xmath0 optical depth .
the blueshift of ly@xmath0 photons against the systemic velocity should arise as long as 1 ) there are infall motions along the los and 2 ) ly@xmath0photons on their way out of the system encounter optically thick gas with a velocity opposite to their propagation direction @xcite .
one possible way to hide a blueshift in this simple infall model would be if the infalling gas is made optically thin by an ionizing source or has low enough column density so that the ly@xmath0 photons do not suffer resonant scattering ( see fig . 11 in d06 or fig .
6 in v06 ) . in this case
, we should still see nearly symmetric ly@xmath0 profiles or extended blue wings , neither of which is observed in our ly@xmath0 profiles .
therefore , we rule out this simple gas infall scenario for our two ly@xmath0 blobs .
in contrast to this simple model , the actual situation is likely to be more complex and the bulk motion of gas may not be spherically symmetric .
for example , the h@xmath0 detections suggest that the galaxies embedded in the blobs are forming stars , which could generate mechanical feedback into the surrounding gas cloud .
there is also ample evidence for galactic scale outflows in star - forming galaxies at @xmath9 = 23 ( e.g. , * ? ? ?
thus , one could imagine that even if gas infall takes place over larger radii ( up to @xmath650 kpc ) , the innermost part of the gas cloud , close to the galaxies , could be strongly affected by outflows similar to those observed in other star - forming galaxies at @xmath74 . in this case , the emerging ly@xmath0 profile will be more sensitive to the core of the blob , presumably the densest part of the igm , than to the gas infall . as a result
, it might be difficult to detect the infalling gas by measuring the ly@xmath0 line shift .
more simulations are required to test whether generic galactic scale outflows could affect gas infall and whether infall and outflows can coexist .
this kind of more realistic model has not been considered yet in rt calculations , so its spectral signatures ( if any ) are unknown .
the other caveat is that the inflow might occur along filamentary streams @xcite and their covering factor could be small such that we might completely miss the infall signatures in a particular los .
we will further discuss this caveat in [ sec : misalignment ] . in [ sec :
shift ] , we found that the offset of the ly@xmath0 line relative to h@xmath0 was either consistent with zero ( lab01 ) or redshifted ( lab02 ) .
the existence of a modest outflow in lab02 was further supported by the low - ionization absorption line shifts discussed in section [ sec : absorption ] .
the absence of a redshifted @xmath7 in lab01 does not necessarily exclude an outflow because of its extended ly@xmath0 profile toward the red .
here we compare the ly@xmath0 profiles of our blobs with the rt outflow models of @xcite to interpret the velocity offset @xmath7 in a more sophisticated manner . in these radiative transfer calculations ,
the ly@xmath0h@xmath0 velocity offset is modulated entirely by the radiative transfer of ly@xmath0 photons through a continuous medium within the shell .
another possibility , which we discuss in section [ sec : clumpycgm ] , is that the gas around the galaxy is clumpy and that the bulk motions of these clumps primarily modulate the emerging ly@xmath0 profile @xcite . in the following section , we constrain the outflow velocity or `` wind velocity '' from the embedded galaxies using the rt calculations .
it is then possible to ask whether such an outflow is energetic enough ( i.e. , the expansion velocity @xmath75 is large ) to expel / launch gas out to larger radii , thus creating the extended ly@xmath0 emission observed as a blob with a typical size of @xmath10 50kpc . to connect @xmath7 with an outflow velocity
, we compare each blob s ly@xmath0profile with a model with an expanding shell geometry . such a geometry would arise in the simple `` superwind '' or `` hyperwind '' model for ly@xmath0blobs proposed by and @xcite . in this scenario ,
supernova explosions or stellar winds following an intense starburst in galaxies develop into a so - called superbubble .
if the kinetic energy deposited into the surrounding gas overcomes the gravitational potential energy of the galaxy , the gas clouds are blown out into intergalactic space as a superwind ( e.g. , heckman et al .
the gas blown out from the galaxies forms a shell , and the ly@xmath0photons are scattered from this expanding shell ( with @xmath75 ) , escaping preferentially by the scattering from the backside .
in contrast , the h@xmath0 lines provide the systemic velocity of the star forming region .
v06 and v08 demonstrate that the radiative transfer of ly@xmath0 in this simple shell geometry is able to explain a wide range of observed ly@xmath0profiles .
v08 classified ly@xmath0 profiles into three categories : ( 1 ) single - peaked asymmetric profile with an extended red wing , ( 2 ) profile with double peaks separated by sharp absorption at @xmath52kms@xmath4 , and ( 3 ) asymmetric profile with bluer bump(s ) . thanks to the h@xmath0 line , which provides the velocity center , we can determine that lab01 and lab02 correspond to ( 1 ) and ( 2 ) without ambiguity .
we start with lab01 , which has an asymmetric ly@xmath0 profile without any obvious blue peaks , but with an extended red wing and/or multiple red peaks ( i.e. , category 1 above ) .
v06 show that a blue peak ( @xmath49 @xmath76 0kms@xmath4 ) is strongly suppressed with increasing ( @xmath77 ) ratio , i.e. , when the bulk outflow motion becomes more important than the thermal and turbulent motion of the shell gas .
the resonant scattering in the expanding shell produces mainly two red peaks depending on the paths of the emergent photons : one peak near the line center ( @xmath49 @xmath6 0kms@xmath4 ) and another at @xmath78 , corresponding to photons that experience zero or one back - scattering from the receding shell , respectively .
here , the back - scattering of a photon means that it travels across the empty interior before re - entering the shell at a different location .
thus the location of the second red peak is a useful diagnostic for the outflow velocity .
because of the degeneracy between many model parameters ( @xmath75 , @xmath71 , @xmath70 , @xmath79 ) , constraining the outflow velocity well requires fitting the spectra directly to the rt calculations .
we do not have the means to do that here , so we estimate @xmath75 for lab01 from how much its red ly@xmath0 peaks are redshifted against its h@xmath0 line center .
if @xmath70 is sufficiently large ( @xmath70@xmath10 @xmath80cm@xmath4 ) , the second red peak becomes larger and merges with the first red peak , so that the stronger red peak measures 2@xmath75 ( see fig . 1 of v08 ) .
if this case applies here , our @xmath7@xmath6 0kms@xmath4 implies @xmath75@xmath6 0kms@xmath4 , i.e. , that the shell is static . on the other hand , decreasing @xmath70 , increasing dust extinction ( @xmath82 ) , and decreasing @xmath77 tends to strengthen the first red peak , so that the brighter peak is located at 0 @xmath83 @xmath75 and does not carry any @xmath75 information . in this case
, the location of the weaker second peak provides an estimate of @xmath75 . as discussed in [ sec : confirmation ] , the lab01 profile s extended red wing could be interpreted as multiple components ( see figure [ fig : line_comparison ] ) . if we adopt the small bump at @xmath49 @xmath6 300kms@xmath4 as the second peak , the expansion velocity of the shell is @xmath75 @xmath6 150kms@xmath4 . considering both cases ,
the outflow velocity in lab01 could range from 0kms@xmath4 to @xmath6150kms@xmath4 .
the ly@xmath0 profile of lab02 is most consistent with the double - peaked profile ( i.e , category 2 above ) of @xcite , who claim that such profiles arise when the shell is almost static ( @xmath75 @xmath6 0kms@xmath4 ) . due to the h@xmath0 measurement
, there is no ambiguity about the location of the velocity center .
even if we consider only the red side of the profile and classify it as a single asymmetric profile like lab01 , we would obtain an outflow velocity only as high as @xmath6 @xmath7/2 = 115kms@xmath4 .
the blueshifted centroids of the low - ionization absorption lines in lab02 are also consistent with this inferred outflow velocity . therefore , if the expanding shell geometry is applicable to our two ly@xmath0 blobs , we conclude that any outflows from the embedded galaxies are not strong ( @xmath75 @xmath55 150kms@xmath4 ) compared to the values required by the extreme `` superwind '' or `` hyperwind '' scenarios to explain the large size ( @xmath84kpc ) and broad ly@xmath0 linewidth ( fwhm @xmath6 1000kms@xmath4 ) of blobs .
the simple shell geometry assumed here has some physical motivation and has been explored by extensive rt calculations ( e.g. , v06 and v08 ) .
however , this model implies that the outflows are intermittent with a small duty cycle , contrary to the observation that outflows are seen in most star forming galaxies at high redshift .
we note that if there is a continuous stream of outflowing material , it might lead to a different interpretation of kinematic signatures discussed above .
one other claim of an outflow in a blob was reported by @xcite using ifu observations of the ly@xmath0 line in steidel s blob 2 .
using an expanding shell model , they found that the central wavelength , i.e. , velocity , of absorption systems on top of the underlying broad ly@xmath0 profiles is coherent across the whole blob with a blueshift of @xmath6250 kms@xmath4 . because the systemic velocity of the blob gas is unknown in their case ,
there are other possible interpretations of their data , even including an inflow @xcite . @xcite and @xcite found that steidel s blob 1 has an extremely complicated velocity structure , including velocity shears around the embedded galaxies that can be interpreted as either outflow or rotation .
it is interesting that all investigations of blob kinematics to date ( in our cdfs - lab01 and cdfs - lab02 , steidel s blobs 1 and 2 ) suggest relatively small outflow velocities .
therefore , the large wind speeds required by super / hyper - wind models to explain the extended ly@xmath0emission are excluded .
one way to reconcile the small outflows with the `` superwind '' model is to assume that the outflow was once more energetic and that the expanding shell has been broken up or slowed by contact with the surrounding igm @xcite . clearly , constraining the kinematics of more ly@xmath0 blobs is needed to address whether these small outflows are representative .
we conclude that the gas motion around the galaxies embedded in these ly@xmath0 blobs is not consistent with models like the simple superwind picture that assume a spherical shell geometry and a shell velocity exceeding @xmath6500 kms@xmath4 . yet
galactic scale outflows from star - forming galaxies at @xmath74 appear to be common .
the outflow properties have been extensively studied by comparing the ly@xmath0 velocity center with those of optically - thin nebular lines and/or interstellar absorption lines ( e.g. , * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
recently , @xcite show that ly@xmath0 lines from lbgs are redshifted against h@xmath0 lines up to several hundreds kms@xmath4 with an average of @xmath85 = + 445kms@xmath4 , while the interstellar absorption lines are blueshifted against the nebular lines by @xmath86 = @xmath62kms@xmath4 .
while these @xmath7 and @xmath59 offsets are interpreted as an outflow signature , it is not clear how the absorbing material is distributed around galaxies .
_ were the gas blown out in a spherical shell _ , as in the superwind picture discussed above , we could directly compare the observed @xmath7of blobs and lbgs as a proxy for @xmath75 .
the velocity offsets of our two ly@xmath0 blobs , @xmath7
@xmath6 0kms@xmath4 and 230kms@xmath4 , are small in relation to lbgs @xcite ; of 41 lbgs at @xmath9 = 2 2.6 with both ly@xmath0and h@xmath0 spectroscopy , @xmath688% have @xmath7 @xmath27 225kms@xmath4 .
therefore , any wind arising from galactic star formation has a lower expansion velocity in these two labs than is typical of lbgs .
we have adopted two basic assumptions in our analysis : that there is inflowing or outflowing gas in the los to the blob and that the h@xmath0 line marks the kinematic center of the blob gas . here
we examine how these assumptions may affect our conclusions and comment on the recent model suggested by @xcite to explain the circum - galactic kinematics of lbgs .
we have assumed that there is gas inflowing or outflowing along the los to the embedded galaxies that lie in our spectroscopic slit . in this case , the observed ly@xmath0 photons resonantly scatter in this optically thick infalling / outflowing material until escaping into the los of the observer .
however , we do not know how the blob gas is distributed around the embedded galaxies nor whether it is clumpy or smooth .
for example , the gas flow may not be isotropic .
as in bipolar outflows , a galactic - scale outflow may occur in the direction of minimum ism pressure , which is typically perpendicular to the stellar disk . or , the covering factor of the outflow material , the fraction of emission intercepted by the absorbers , could be rather high , at least 0.5 or up to unity as observed in nearby agns @xcite .
if gas accretion is taking place instead @xcite , numerical simulations suggest that the infall may occur preferentially along filamentary streams @xcite . if the bulk motion of gas ( either infalling or outflowing ) happens to be mis - aligned with our los , we may underestimate or even fail to detect the relative velocity shifts .
therefore , it is critical to expand the ly@xmath0h@xmath0 comparison to a larger sample to average over any geometric effects and obtain better constraints on the incidence , direction , speed , and isotropy of bulk gas motions in blobs .
if no large values of @xmath75 are measured , even for a larger sample , outflows are unlikely to push the blob gas to larger radii , where it can be illuminated . on the other hand
, an absence of blueshifted ly@xmath0 lines would argue that infall is not dominant , at least not near the galaxies .
recent cosmological simulations including radiative transfer are now able to examine the statistics of blobs whose extended ly@xmath0 emission arises from cooling radiation .
these models can predict the range of gas accretion covering factors , surface brightness profiles and ratio of blue - to - redshifted ly@xmath0 lines for blobs . a larger sample of blobs with measured ly@xmath0 and h@xmath0 kinematics would provide a new test of these blob emission models .
our second key assumption is that the h@xmath0 line marks the kinematic center of the surrounding gas , i.e. , the terminus of any infall or the origin of any outflow . for an outflow ,
this assumption is reasonable because all possible causes of the outflow ( e.g. , stellar winds , sne , or agns ) lie in or about galaxies , as does the h@xmath0 line itself . for similar reasons , this assumption is likely to be valid for gas accretion ( infall ) into an embedded galaxy .
however , it is possible that the accreting gas responds to the overall dm potential rather than to individual galaxies .
thus one could expect that detecting gas infall is more difficult than finding outflows using the technique presented in this paper . to overcome this issue
, it is critical to increase the sample size and measure how each blob s ly@xmath0 profile varies spatially .
this experiment should be conducted along multiple sightlines using using different h@xmath0 sources found in the same blob . in principle , it is possible to compare the offsets between the extended ly@xmath0 and and the _ extended _
h@xmath0 lines in two dimensions , i.e. , between the h@xmath0 and ly@xmath0 screens .
unfortunately , the h@xmath0 surface brightness is expected to be @xmath63%
10% of ly@xmath0 depending on the energy source .
thus , it will be challenging to obtain 2d h@xmath0 ifu measurements in the near future .
currently , our ly@xmath0h@xmath0 comparison includes only a handful of ly@xmath0blobs because of the limited redshift range where nir spectroscopy of the optically - thin nebular lines ( e.g. , h@xmath0 and the [ ] @xmath15007 line ) is allowed .
however , future co observations with alma will also provide the systemic velocity of the embedded galaxies , permitting this test to be expanded to a larger sample of ly@xmath0 blobs . as we were writing this paper
, @xcite proposed a model for lbgs in which cool gas is distributed around the galaxy and accelerates radially outward with increasing galactocentric distance .
they suggest that this blown - out material extends to @xmath680kpc , comparable to the typical size of ly@xmath0 blobs , and that all lbgs would be classified as blobs if narrowband images were sensitive to surface brightness thresholds 10 times lower than typical of blob / emitter surveys ( i.e. , @xmath6@xmath87ergs@xmath4@xmath31arcsec@xmath32 ) .
is this `` clumpy circum - galactic medium ( cgm ) model '' consistent with the properties of our ly@xmath0 blobs ? unlike in the rt models that we considered earlier , the gas in this model is composed of small clumps . a critical part of the @xcite analysis involves stacking spectra of apparent galaxy - galaxy pairs at @xmath88 to obtain a high s / n interstellar absorption profile arising from the gas surrounding the foreground galaxies .
sightlines to the background galaxies provide information on the spatial distribution of circum - galactic gas as a function of the galactocentric distances .
there are no background galaxies behind our two blobs , and even constraining the absorption profile in lab02a was challenging .
we do not detect a stellar continuum in lab01a or lab01b . as a result
, we are unable to test whether the @xcite lbg model could explain the kinematics of either of our ly@xmath0 blobs . nevertheless , we add a few qualitative comments here .
in the @xcite model , ly@xmath0 photons from the central galaxy are scattered off the _ surface _ of these discrete clumps ; thus photons acquire a doppler shift corresponding to the velocity of each clump .
ly@xmath0 photons can escape the system when they achieve velocity offsets large enough to take the photons off - resonance for any material between the last scattering clump and the observer .
therefore , the ly@xmath0 line shift is due to bulk motions of the clumpy material rather than to radiative transfer effects where ly@xmath0 photons experience numerous resonant scatterings before escaping the cloud ( section [ sec : outflow ] ) .
the profiles of ly@xmath0 and the low - ionization interstellar absorption lines are determined by the velocity field and covering fraction of these gas clumps .
the apparent peak of ly@xmath0 emission is modulated primarily by the clumps with @xmath52 : ly@xmath0 emission is more redshifted and weaker for a wider velocity range spanned by the interstellar absorption .
the velocity of the clumpy medium continually increases outward , unlike in the radiative transfer models discussed earlier , where the outflowing shell had one velocity . in the @xcite model ,
the velocity range spanned by the absorption lines reflects that of the surrounding gas distribution , and the ly@xmath0h@xmath0 offset does _ not _ represent the outflow velocity .
if this clumpy cgm model is applicable to blobs , then our observations of a small ly@xmath0h@xmath0 offset could indicate an absence of neutral gas at @xmath52 rather than the weak gas outflow suggested by the rt models .
one test would be to constrain the interstellar absorption line profile , which should extend to larger blueward velocities , but lack a component around @xmath89kms@xmath4 , if the clumpy model is accurate .
clearly , higher s / n spectra to reliably measure these weak absorption lines are required .
the most notable outcome of the large spatial extent of a clumpy cgm around star - forming galaxies is diffuse ly@xmath0-emitting halos .
extended ly@xmath0 emission has been detected in stacked narrowband images of lbgs by @xcite .
more recently , by stacking deeper narrowband ly@xmath0 images of lbgs , @xcite show that all classes of star - forming galaxies exhibit diffuse ly@xmath0 halos out to projected radii of @xmath680kpc , regardless of their spectroscopic properties ( i.e. , either absorption or emission in ly@xmath0 within a spectroscopic slit ) , although these halos are 10@xmath29 lower surface brightness than typical blobs .
the ly@xmath0surface brightness profiles of the stacked images are similar among lbg subclasses , with only different intensity scalings .
thus , ly@xmath0 blobs may represent the most extreme example of galaxies with diffuse ly@xmath0 halos .
the key difference of the clumpy cgm model is that the diffuse ly@xmath0 halo originates from ly@xmath0 photons scattered from the galaxy s region(s ) rather than from external mechanisms such as photoionization by agn , photoionzation by metagalactic uv background radiation , or via cooling radiation . at this time
, the applicability of the clumpy model to ly@xmath0 blobs is unclear .
any comprehensive model must explain the differences between our blobs and lbgs : 1 ) a comparison of their number density and clustering properties suggests that blobs could occupy higher density environments ( e.g. , * ? ? ?
* ) , 2 ) the extended emission of blobs is typically 10 times brighter , 3 ) the ly@xmath0h@xmath0 offset of our blobs is lower .
the first and second differences could arise if the blobs host more massive galaxies and higher star formation rates than typical of star - forming galaxies at high-@xmath9 .
it remains to be tested whether star formation in the galaxies embedded in blobs can produce enough ly@xmath0 photons to explain the higher luminosity and surface brightness of ly@xmath0 halos .
the ly@xmath0h@xmath0 offset is clearly tied in some way to the extended ly@xmath0 emission of our blobs , as it is unusually low for both blobs compared to the offset distribution for lbgs ( see also * ? ? ? * for compact ly@xmath0 emitters ) . it would interesting to check whether the lbg subclasses in @xcite with brighter extended emission have smaller ly@xmath0h@xmath0 offsets and weaker is absorption at @xmath89kms@xmath4 than the others . for now
, we note that the rt outflow model discussed in section [ sec : discussion ] adequately explains the sense and magnitude of both the ly@xmath0h@xmath0 and the h@xmath0-interstellar absorption line offsets in lab02 , whereas the @xcite model would require this agreement of the offsets to be a coincidence . of course
, we are only able to perform this test using one blob at present . as stressed earlier , a larger sample of ly@xmath0h@xmath0 offsets is required to test whether smaller ly@xmath0h@xmath0 offsets are generic properties of ly@xmath0 blobs .
determining the source of ly@xmath0 emission in extended nebulae at high redshift requires that we measure their gas kinematics with an optically - thin line such as h@xmath0 @xmath16563 , which , unlike the optically - thick ly@xmath0 emission , is not much altered by radiative transfer effects and is more concentrated about the blob s core .
the comparison of the ly@xmath0and h@xmath0 line centers then constrains any infall or outflow of the ly@xmath0-emitting gas relative to the systemic velocity of the blob defined by h@xmath0 .
we obtain optical and nir spectra of the two brightest ly@xmath0 blobs ( cdfs - lab01 and cdfs - lab02 ) from the @xcite sample using the magellan / mage optical and vlt / sinfoni nir spectrographs . both the ly@xmath0 and h@xmath0 lines confirm that these blobs lie at the survey redshift , @xmath90 ( @xmath22 ) .
the blobs contain several h@xmath0 sources , which roughly coincide with galaxies in _ hst _ rest - frame uv images .
the h@xmath0 detections of these embedded galaxies reveal large internal velocity dispersions ( @xmath3kms@xmath4 ) .
furthermore , in the one system ( lab01 ) where we can reliably extract profiles for two different h@xmath0 sources , their velocity difference is @xmath5 @xmath6 440kms@xmath4 .
the presence of multiple galaxies within the blobs , and those galaxies large velocity dispersions and large relative motion , supports the result of @xcite that ly@xmath0 blobs inhabit massive dark matter halos that will evolve into rich clusters today .
the embedded galaxies may represent the precursors of brightest cluster galaxies . to determine whether the gas near the embedded galaxies is predominantly infalling or outflowing
, we compare the ly@xmath0 and h@xmath0 line centers .
ly@xmath0 is not offset ( @xmath7 = + 0kms@xmath4 ) in lab01 and redshifted by only + 230kms@xmath4 in lab02 .
these offsets are small compared to those of lyman break galaxies , which average + 450kms@xmath4 and extend to about + 700kms@xmath4 @xcite . by comparing the observed ly@xmath0 profiles with simple radiative transfer models , we constrain the outflow velocity from the embedded galaxies to be @xmath60 150kms@xmath4 in the two blobs . in lab02 , we detect low - ionization , interstellar absorption lines , including @xmath11334 and @xmath11526 , whose blueward shifts of @xmath8kms@xmath4 are consistent with the small outflow implied by the redward shift of ly@xmath0 . models with simple infall geometries or that require outflow velocities exceeding @xmath6500kms@xmath4 are ruled out . because of the unknown geometry of the gas distribution and the possibility of multiple sources of ly@xmath0 emission embedded in the blobs , a larger sample and more sophisticated models are required to test other infall and outflow scenarios .
we thank anonymous referee for his / her helpful comments .
we thank christy tremonti , dusan kere and mark dijkstra for useful discussions .
we also thank max pettini for providing the spectrum of ms1512-cb58 .
thanks the max - planck - institut fr astronomie and the center for cosmology and particle physics at new york university for their hospitality and support during her stays there .
y.y . and a.i.z.acknowledge support from the nsf astronomy and astrophysics research program through grant ast-0908280 and from the nasa astrophysics data analysis program through grant nnx10ad47 g .
is supported through the emmy noether programme of the german science foundation ( dfg ) .
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, the ly@xmath0 line must be compared with an optically - thin line like h@xmath0 @xmath16563 , which is not much altered by radiative transfer effects and is more concentrated about the galaxies embedded in the nebula s core .
we obtain optical and near - infrared ( nir ) spectra of the two brightest ly@xmath0 blobs ( cdfs - lab01 and cdfs - lab02 ) from the @xcite sample using the magellan / mage optical and vlt / sinfoni nir spectrographs . both the ly@xmath0 and h@xmath0 lines confirm that these blobs lie at the survey redshift , @xmath2 . within each blob ,
we detect several h@xmath0 sources , which roughly correspond to galaxies seen in _
hst _ rest - frame uv images .
the h@xmath0 detections show that these galaxies have large internal velocity dispersions ( @xmath3kms@xmath4 ) and that , in the one system ( lab01 ) , where we can reliably extract profiles for two h@xmath0 sources , their velocity difference is @xmath5 @xmath6 440kms@xmath4 .
the presence of multiple galaxies within the blobs , and those galaxies large velocity dispersions and large relative motion , is consistent with our previous finding that ly@xmath0 blobs inhabit massive dark matter halos that will evolve into those typical of rich clusters today and that the embedded galaxies may eventually become brightest cluster galaxies @xcite . to determine whether the gas near the embedded galaxies is predominantly infalling or outflowing
, we compare the ly@xmath0 and h@xmath0 line centers , finding that ly@xmath0 is not offset ( @xmath7 = + 0kms@xmath4 ) in lab01 and redshifted by only + 230kms@xmath4 in lab02 .
these offsets are small compared to those of lyman break galaxies , which average + 450kms@xmath4and extend to about + 700kms@xmath4 . in lab02
, we detect @xmath11334 and @xmath11526 absorption lines , whose blueward shifts of @xmath8kms@xmath4 are consistent with the small outflow implied by the redward shift of ly@xmath0
. we test and rule out the simplest infall models and those outflow models with super / hyper - winds , which require large outflow velocities . because of the unknown geometry of the gas distribution and the possibility of multiple sources of ly@xmath0emission embedded in the blobs , a larger sample and more sophisticated models are required to test more complex or a wider range of infall and outflow scenarios . |
"Facts & Summary of Findings \n \n · Arkansas produces 11% of the nation’s broiler chickens. \n \(...TRUNCATED) | "– No one's more thankful for Thanksgiving than the workers who toil away in turkey plants in the (...TRUNCATED) |
"superconductivity is one of the most well studied phenomena in condensed matter physics .\nsupercon(...TRUNCATED) | " using the non - linear ginzburg - landau ( gl ) eqs . \n type i superconducting disks of finite ra(...TRUNCATED) |
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Dataset Name: Long-Form Article Summarization Dataset
Description: The Long-Form Article Summarization Dataset is meticulously curated for the purpose of fine-tuning Natural Language Processing (NLP) models specifically tailored for summarization tasks. It is a rich collection of long-form articles that have been carefully condensed and summarized. The dataset provides a diverse range of topics and writing styles, making it an invaluable resource for researchers and practitioners working on summarization algorithms and applications.
Data Sources:
- Billsum: This dataset includes summaries of U.S. congressional and state bills, providing insights into legislative documents.
- Scientific Papers: A collection of scientific papers covering various disciplines, enabling a deep dive into research-oriented content.
- Multi_news: This dataset incorporates news articles, offering a blend of current events and journalistic writing styles.
- CCDV/Pubmed-Summarization: Focused on biomedical literature, this dataset contains summaries from Pubmed articles, offering specialized content related to the field of medicine and life sciences.
Data Combination: The Long-Form Article Summarization Dataset is an amalgamation of the above-mentioned datasets. By combining these diverse sources, the dataset achieves a comprehensive coverage of topics, styles, and domains. This fusion enhances the dataset's versatility and applicability across a wide array of domains, making it a valuable asset for NLP research and development.
Data Preprocessing: To ensure equal representation of unique domains and to manage the scale of the dataset, large datasets were down-sampled. This meticulous preprocessing step guarantees that each domain is adequately represented, promoting a balanced and unbiased training environment for NLP models.
Intended Use: This dataset is specifically designed for fine-tuning NLP models focused on summarization tasks. Researchers and developers can utilize this dataset to train and evaluate their algorithms for generating concise and informative summaries from long-form articles. The dataset's diverse origins and careful preprocessing make it an ideal choice for enhancing the summarization capabilities of NLP models.
Access: The Long-Form Article Summarization Dataset is available for research purposes and can be accessed through authorized channels. Researchers and developers interested in using this dataset are encouraged to adhere to ethical guidelines and data usage policies governing the respective sources.
Citation: Researchers and practitioners are expected to cite the original sources of the datasets used in this amalgamation, namely "Billsum," "Scientific Papers," "Multi_news," and "CCDV/Pubmed-Summarization," in addition to acknowledging the creation of the Long-Form Article Summarization Dataset in their publications and research outputs.
This dataset card provides an overview of the Long-Form Article Summarization Dataset, outlining its sources, preprocessing methods, intended use, and access guidelines, ensuring transparent and responsible utilization of the valuable data it encapsulates.
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