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

Advanced Chemical Engineering Professional Skills - Do We Teach Them Effectively?

Chemical engineering professional skills are essential in ensuring that the graduates are able to effectively face not only the current, but also future societal and technological challenges. Whilst the core chemical engineering knowledge in unit operations, such as reaction engineering and separations, remains a defining feature and a fundamental requirement of various accreditation criteria of the chemical engineering courses, it is clear that this in itself is not sufficient to provide the future generations of chemical engineers with the knowledge and skills to address the challenges they will face in their future professional careers. An important part of this skill set is the ability to deal with uncertainty, to innovate, to represent a conceptual model of a process or a unit operation in such a way that it allows the user to explore the response of the process / unit operation to dynamic disturbances and to optimise the performance of the given process / unit operation. At Newcastle University this forms the basis of the advanced design task presented in this contribution. Following a brief international review of the importance of core chemical engineering knowledge and skills (gathered by the authors during the recent EU sponsored iTeach project), the learning outcomes and the structure of the revised advanced design module will be presented. The emphasis will be placed on the assessment of critical professional skills as outlined above, indicating various approaches taken to ensure a broad professional skill set development

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

Coping with multiple adversities: Men who sought medico-legal care because of physical violence from a partner or ex-partner.

Objectives: To describe male victims of physical violence by an intimate partner who consulted a medico-legal unit, and information available on their perpetrators; to characterize the violent events and their contexts. Little research exists on male victims of physical intimate partner violence seeking medical care. Method: Based on Heise’s ecological framework, mixed methods were used to analyze quantitative and qualitative data collected during 122 medico-legal consultations attended by 115 men who sustained physical violence by an intimate partner from 2006–2012. Results: Quantitative and quantitative data collected from male victims concurred in showing that many of such victims, as well as their partners, faced at the time of the assault multiple adversities and challenges at individual and relationship levels. Among male victims, 26% had no paid job. Among perpetrators, 34% were third-country nationals subject to restricted residence permits. Health issues, worries about money or work combined with complex and conflictive family situations were often in the background of violent events. In a few cases, however, male victims reported no other problems than their partner’s assault. Conclusions: Our findings point out gender-specific aspects of female-to-male physical partner violence. The most common feature is that violence was experienced as one among several adversities. Even though wounds sustained by male victims were not necessarily severe, their emotional suffering was frequent. When underage children were involved, their situation was particularly noteworthy. Interventions with male victims of intimate partner violence should include protection of minors as a priority and as an incentive for fathers to seek help

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

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