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

Mobile object location discovery in unpredictable environments

Emerging mobile and ubiquitous computing environments present hard challenges to software engineering. The use of mobile code has been suggested as a natural fit for simplifing software development for these environments. However, the task of discovering mobile code location becomes a problem in unpredictable environments when using existing strategies, designed with fixed and relatively stable networks in mind. This paper introduces AMOS, a mobile code platform augmented with a structured overlay network. We demonstrate how the location discovery strategy of AMOS has better reliability and scalability properties than existing approaches, with minimal communication overhead. Finally, we demonstrate how AMOS can provide autonomous distribution of effort fairly throughout a network using probabilistic methods that requires no global knowledge of host capabilities

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

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 existence of solutions for the relativistic Boltzmann equation with arbitrarily large initial data on a Bianchi type I space-time

We prove, for the relativistic Boltzmann equation on a Bianchi type I space-time, a global existence and uniqueness theorem, for arbitrarily large initial data.Comment: 17 page

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

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

Exploring the perceived effectiveness of a life skills development program for high-performance athletes

The purpose of this study was to explore attitudes towards, experiences of, and perceived effectiveness of a life-skills programme for high-performance young athletes from multiple perspectives, including the athletes, coaches, parents, programme facilitators, and sport administrators. Six focus groups were conducted with 54 high-performance athletes from six sports: squash, softball, baseball, netball, triathlon, and surfing. Three focus groups were conducted with parents (n = 8) of athletes and a further eight semi-structured interviews were conducted with coaches (n = 4) and lead facilitators (n = 4) of the life-skills programme. Four semi-structured interviews were also held with representatives from State Sporting Associations (SSAs) from the sports involved. Thematic content analysis revealed seven main themes: achieving balance and managing stress, time management, goal setting, confidence and control, information overload and repetition, credible role-models, coach reinforcement and follow-up. The programme was perceived to be moderately successful in developing adaptive behaviours and motives including better engagement in training and in adopting time management and planning skills in contexts outside of sport such as homework and academic study. The programme also fostered the development of skills, attitudes, and motives important for sport success such as goal setting and having confidence to succeed. To improve the effectiveness of such programmes, more emphasis should be placed on the practice of, and engagement with, applied techniques to develop skills with less emphasis on information giving and theory. Facilitators of programmes should also be more pro-active in involving parents and coaches as a way to improve continuity and provide post-program reinforcement and support

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

A sharp stability criterion for the Vlasov-Maxwell system

We consider the linear stability problem for a 3D cylindrically symmetric equilibrium of the relativistic Vlasov-Maxwell system that describes a collisionless plasma. For an equilibrium whose distribution function decreases monotonically with the particle energy, we obtained a linear stability criterion in our previous paper. Here we prove that this criterion is sharp; that is, there would otherwise be an exponentially growing solution to the linearized system. Therefore for the class of symmetric Vlasov-Maxwell equilibria, we establish an energy principle for linear stability. We also treat the considerably simpler periodic 1.5D case. The new formulation introduced here is applicable as well to the nonrelativistic case, to other symmetries, and to general equilibria