The Newtonian limit of the relativistic Boltzmann equation

The relativistic Boltzmann equation for a constant differential cross section and with periodic boundary conditions is considered. The speed of light appears as a parameter $c>c_0$ for a properly large and positive $c_0$. A local existence and uniqueness theorem is proved in an interval of time independent of $c>c_0$ and conditions are given such that in the limit $c\to +\infty$ the solutions converge, in a suitable norm, to the solutions of the non-relativistic Boltzmann equation for hard spheres.Comment: 12 page

Animal welfare impact following the 4 September 2010 Canterbury (Darfield) earthquake

At 4.35am on Saturday 4 September 2010, a magnitude 7.1 earthquake struck near the township of Darfield in Canterbury leading to widespread damage in Christchurch and the wider central Canterbury region. Though it was reported no lives were lost, that was not entirely correct. Over 3,000 animals perished as a result of the earthquake and 99% of these deaths would have been avoidable if appropriate mitigation measures had been in place. Deaths were predominantly due to zoological vulnerability of birds in captive production farms. Other problems included lack of provision of animal welfare at evacuation centres, issues associated with multiple lost and found pet services, evacuation failure due to pet separation and stress impact on dairy herds and associated milk production. The Canterbury Earthquake has highlighted concerns over a lack of animal emergency welfare planning and capacity in New Zealand, an issue that is being progressed by the National Animal Welfare Emergency Management Group. As animal emergency management becomes better understood by emergency management and veterinary professionals, it is more likely that both sectors will have greater demands placed upon them by national guidelines and community expectations to ensure provisions are made to afford protection of animals in times of disaster. A subsequent and more devastating earthquake struck the region on Monday 22 February 2011; this article however is primarily focused on the events pertaining to the September 4 event

Multipole radiation in a collisonless gas coupled to electromagnetism or scalar gravitation

We consider the relativistic Vlasov-Maxwell and Vlasov-Nordstr\"om systems which describe large particle ensembles interacting by either electromagnetic fields or a relativistic scalar gravity model. For both systems we derive a radiation formula analogous to the Einstein quadrupole formula in general relativity.Comment: 21 page

Momentum Regularity and Stability of the Relativistic Vlasov-Maxwell-Boltzmann System

In the study of solutions to the relativistic Boltzmann equation, their regularity with respect to the momentum variables has been an outstanding question, even local in time, due to the initially unexpected growth in the post-collisional momentum variables which was discovered in 1991 by Glassey & Strauss \cite{MR1105532}. We establish momentum regularity within energy spaces via a new splitting technique and interplay between the Glassey-Strauss frame and the center of mass frame of the relativistic collision operator. In a periodic box, these new momentum regularity estimates lead to a proof of global existence of classical solutions to the two-species relativistic Vlasov-Boltzmann-Maxwell system for charged particles near Maxwellian with hard ball interaction.Comment: 23 pages; made revisions which were suggested by the referee; to appear in Comm. Math. Phy

Uniqueness of the compactly supported weak solutions of the relativistic Vlasov-Darwin system

We use optimal transportation techniques to show uniqueness of the compactly supported weak solutions of the relativistic Vlasov-Darwin system. Our proof extends the method used by Loeper in J. Math. Pures Appl. 86, 68-79 (2006) to obtain uniqueness results for the Vlasov-Poisson system.Comment: AMS-LaTeX, 21 page

Self-Reported Violence Experienced by Swiss Prehospital Emergency Care Providers.

Workplace violence is a serious and increasing problem in health care. Nevertheless, only few studies were carried out concerning this topic and then mainly in English-speaking countries. The objectives were to describe the acts of violence experienced by prehospital emergency care providers (PECPs) in the western part of Switzerland between January and December 2016 and to assess the consequences for subsequent PECPs behaviors. An observational cross-sectional study, carried out using an online survey, has been sent to all 416 PECPs in the Canton of Vaud, in the western, French-speaking, part of Switzerland. The survey contained items of demographic data and items to assess the type and consequence of violence sustained. This was classified as five types: verbal assault, intimidation, physical assault, sexual harassment, and sexual assault. 273 (65.6%) PECPs participated in the survey. During 2016, workplace violence was reported by 229 survey participants (83.9%). Most declared to be the victim of such violence between one and three times during the year. In all cases of violence described, the patient and/or a relative initiated aggressive behavior in 96% of cases. Verbal assaults were the most common (99.2% of all acts), followed by intimidation (72.8%), physical assault (69.6%), and sexual harassment (16.3%). Concerning physical assault, PECPs were predominantly victims of spitting and/or jostling (50%). After a violent event, in 50% of cases, the PECPs modified their behavior owing to the experience of workplace violence; 82% now wear protective vests, and 16% carry weapons for self-defense, such as pepper sprays. Seventy-five percent changed their intervention strategies, acting more carefully and using verbal de-escalation techniques or physical restraints for violent patients. Workplace violence is frequent and has significant consequences for PECPs. In order to increase their own security, they increased their protection. These results illustrate their feelings of insecurity, which may have deleterious effects on work satisfaction and motivation. Trial Registration. Our article does not report the results of a health care intervention on human participants

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

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