89 research outputs found
The Einstein-Vlasov sytem/Kinetic theory
The main purpose of this article is to guide the reader to theorems on global
properties of solutions to the Einstein-Vlasov system. This system couples
Einstein's equations to a kinetic matter model. Kinetic theory has been an
important field of research during several decades where the main focus has
been on nonrelativistic- and special relativistic physics, e.g. to model the
dynamics of neutral gases, plasmas and Newtonian self-gravitating systems. In
1990 Rendall and Rein initiated a mathematical study of the Einstein-Vlasov
system. Since then many theorems on global properties of solutions to this
system have been established. The Vlasov equation describes matter
phenomenologically and it should be stressed that most of the theorems
presented in this article are not presently known for other such matter models
(e.g. fluid models). The first part of this paper gives an introduction to
kinetic theory in non-curved spacetimes and then the Einstein-Vlasov system is
introduced. We believe that a good understanding of kinetic theory in
non-curved spacetimes is fundamental in order to get a good comprehension of
kinetic theory in general relativity.Comment: 31 pages. This article has been submitted to Living Rev. Relativity
(http://www.livingreviews.org
Global Solution to the Relativistic Enskog Equation With Near-Vacuum Data
We give two hypotheses of the relativistic collision kernal and show the
existence and uniqueness of the global mild solution to the relativistic Enskog
equation with the initial data near the vacuum for a hard sphere gas.Comment: 6 page
The Vlasov limit and its fluctuations for a system of particles which interact by means of a wave field
In two recent publications [Commun. PDE, vol.22, p.307--335 (1997), Commun.
Math. Phys., vol.203, p.1--19 (1999)], A. Komech, M. Kunze and H. Spohn studied
the joint dynamics of a classical point particle and a wave type generalization
of the Newtonian gravity potential, coupled in a regularized way. In the
present paper the many-body dynamics of this model is studied. The Vlasov
continuum limit is obtained in form equivalent to a weak law of large numbers.
We also establish a central limit theorem for the fluctuations around this
limit.Comment: 68 pages. Smaller corrections: two inequalities in sections 3 and two
inequalities in section 4, and definition of a Banach space in appendix A1.
Presentation of LLN and CLT in section 4.3 improved. Notation improve
Global existence of classical solutions to the Vlasov-Poisson system in a three dimensional, cosmological setting
The initial value problem for the Vlasov-Poisson system is by now well
understood in the case of an isolated system where, by definition, the
distribution function of the particles as well as the gravitational potential
vanish at spatial infinity. Here we start with homogeneous solutions, which
have a spatially constant, non-zero mass density and which describe the mass
distribution in a Newtonian model of the universe. These homogeneous states can
be constructed explicitly, and we consider deviations from such homogeneous
states, which then satisfy a modified version of the Vlasov-Poisson system. We
prove global existence and uniqueness of classical solutions to the
corresponding initial value problem for initial data which represent spatially
periodic deviations from homogeneous states.Comment: 23 pages, Latex, report #
Decay and Continuity of Boltzmann Equation in Bounded Domains
Boundaries occur naturally in kinetic equations and boundary effects are
crucial for dynamics of dilute gases governed by the Boltzmann equation. We
develop a mathematical theory to study the time decay and continuity of
Boltzmann solutions for four basic types of boundary conditions: inflow,
bounce-back reflection, specular reflection, and diffuse reflection. We
establish exponential decay in norm for hard potentials for
general classes of smooth domains near an absolute Maxwellian. Moreover, in
convex domains, we also establish continuity for these Boltzmann solutions away
from the grazing set of the velocity at the boundary. Our contribution is based
on a new decay theory and its interplay with delicate
decay analysis for the linearized Boltzmann equation, in the presence of many
repeated interactions with the boundary.Comment: 89 pages
Distributional and classical solutions to the Cauchy Boltzmann problem for soft potentials with integrable angular cross section
This paper focuses on the study of existence and uniqueness of distributional
and classical solutions to the Cauchy Boltzmann problem for the soft potential
case assuming integrability of the angular part of the collision
kernel (Grad cut-off assumption). For this purpose we revisit the
Kaniel--Shinbrot iteration technique to present an elementary proof of
existence and uniqueness results that includes large data near a local
Maxwellian regime with possibly infinite initial mass. We study the propagation
of regularity using a recent estimate for the positive collision operator given
in [3], by E. Carneiro and the authors, that permits to study such propagation
without additional conditions on the collision kernel. Finally, an
-stability result (with ) is presented assuming the
aforementioned condition.Comment: 19 page
A Centre-Stable Manifold for the Focussing Cubic NLS in
Consider the focussing cubic nonlinear Schr\"odinger equation in : It admits special solutions of the form
, where is a Schwartz function and a positive
() solution of The space of
all such solutions, together with those obtained from them by rescaling and
applying phase and Galilean coordinate changes, called standing waves, is the
eight-dimensional manifold that consists of functions of the form . We prove that any solution starting
sufficiently close to a standing wave in the norm and situated on a certain codimension-one local
Lipschitz manifold exists globally in time and converges to a point on the
manifold of standing waves. Furthermore, we show that \mc N is invariant
under the Hamiltonian flow, locally in time, and is a centre-stable manifold in
the sense of Bates, Jones. The proof is based on the modulation method
introduced by Soffer and Weinstein for the -subcritical case and adapted
by Schlag to the -supercritical case. An important part of the proof is
the Keel-Tao endpoint Strichartz estimate in for the nonselfadjoint
Schr\"odinger operator obtained by linearizing around a standing wave solution.Comment: 56 page
The Einstein-Vlasov System/Kinetic Theory
The main purpose of this article is to provide a guide to theorems on global
properties of solutions to the Einstein--Vlasov system. This system couples
Einstein's equations to a kinetic matter model. Kinetic theory has been an
important field of research during several decades in which the main focus has
been on non-relativistic and special relativistic physics, i.e., to model the
dynamics of neutral gases, plasmas, and Newtonian self-gravitating systems. In
1990, Rendall and Rein initiated a mathematical study of the Einstein--Vlasov
system. Since then many theorems on global properties of solutions to this
system have been established.Comment: Published version http://www.livingreviews.org/lrr-2011-
What are we measuring? A critique of range of motion methods currently in use for Dupuytren's disease and recommendations for practice
Background: Range of motion is the most frequently reported measure used in practice to evaluate outcomes.
A goniometer is the most reliable tool to assess range of motion yet, the lack of consistency in reporting prevents comparison between studies. The aim of this study is to identify how range of motion is currently assessed and reported in Dupuytrenâs disease literature. Following analysis recommendations for practice will be made to enable consistency in future studies for comparability. This paper highlights the variation in range of motion reporting in Dupuytrenâs disease.
Methods: A Participants, Intervention, Comparison, Outcomes and Study design format was used for the search strategy and search terms. Surgery, needle fasciotomy or collagenase injection for primary or recurrent Dupuytrenâs disease in adults were included if outcomes were monitored using range of motion to record change. A literature search was performed in May 2013 using subject heading and free-text terms to also capture electronic publications ahead of print. In total 638 publications were identified and following screening 90 articles met the inclusion criteria. Data was extracted and entered onto a spreadsheet for analysis. A thematic analysis was carried out to establish any duplication, resulting in the final range of motion measures identified.
Results: Range of motion measurement lacked clarity, with goniometry reportedly used in only 43 of the 90 studies, 16 stated the use of a range of motion protocol. A total of 24 different descriptors were identified describing range of motion in the 90 studies. While some studies reported active range of motion, others reported passive or were unclear. Eight of the 24 categories were identified through thematic analysis as possibly describing the same measure, âlack of joint extensionâ and accounted for the most frequently used. Conclusions: Published studies lacked clarity in reporting range of motion, preventing data comparison and
meta-analysis. Percentage change lacks context and without access to raw data, does not allow direct comparison of baseline characteristics. A clear description of what is being measured within each study was required. It is recommended that range of motion measuring and reporting for Dupuytrenâs disease requires consistency to address issues that fall into 3 main categories:-
Definition of terms
Protocol statement
Outcome reportin
Developing assessments for child exposure to intimate partner violence in Switzerland â A study of medico-legal reports in clinical settings
Purpose: Evidence to inform assessment of needs of children exposed to intimate partner violence (IPV) in health settings is limited. A Swiss hospital-based medico-legal consultation for adult victims of violence also detects childrenâs exposure to IPV and refers cases to the Pediatrics Child Abuse and Neglect Team. Based on a conceptual ecological framework, this study examined the nature and circumstances of childrenâs exposure to IPV described in accounts collected by nurses in consultations with adult IPV victims. Methods: From 2011-2014, 438 parents (88% female) of 668 children aged 0 to 18 sought medico-legal care from the Violence Medical Unit in Lausanne Switzerland, following assaults by intimate partners (85% male). As part of the consultation, nurses completed a semi-structured questionnaire with victimized parents, recording their answers in the patient file. Victimsâ statements about the abuse, their personal, family and social contexts, and their childrenâs exposure to IPV were analyzed. Descriptive statistics and qualitative thematic content analyses were conducted to identify, from the victimized parentsâ accounts, elements useful to understand the nature and circumstances of childrenâs exposure and involvement during violent events. Results: Parent statements on specific violent events described children being present in 75% of the cases. Children were said to be exposed to, and responded to, severe physical violence, serious threats and insults, in the context of repeated assaults and coercive control. Families, especially mothers, were often coping with additional socio-economic vulnerabilities. Conclusions: Implications for further developing assessments of children living with IPV, especially in health settings were identified
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