19 research outputs found
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
A kinetic theory of diffusion in general relativity with cosmological scalar field
A new model to describe the dynamics of particles undergoing diffusion in
general relativity is proposed. The evolution of the particle system is
described by a Fokker-Planck equation without friction on the tangent bundle of
spacetime. It is shown that the energy-momentum tensor for this matter model is
not divergence-free, which makes it inconsistent to couple the Fokker-Planck
equation to the Einstein equations. This problem can be solved by postulating
the existence of additional matter fields in spacetime or by modifying the
Einstein equations. The case of a cosmological scalar field term added to the
left hand side of the Einstein equations is studied in some details. For the
simplest cosmological model, namely the flat Robertson-Walker spacetime, it is
shown that, depending on the initial value of the cosmological scalar field,
which can be identified with the present observed value of the cosmological
constant, either unlimited expansion or the formation of a singularity in
finite time will occur in the future. Future collapse into a singularity also
takes place for a suitable small but positive present value of the cosmological
constant, in contrast to the standard diffusion-free scenario.Comment: 17 pages, no figures. The present version corrects an erroneous
statement on the physical interpretation of the results made in the original
publicatio
Future non-linear stability for reflection symmetric solutions of the Einstein-Vlasov system of Bianchi types II and VI
Using the methods developed for the Bianchi I case we have shown that a
boostrap argument is also suitable to treat the future non-linear stability for
reflection symmetric solutions of the Einstein-Vlasov system of Bianchi types
II and VI. These solutions are asymptotic to the Collins-Stewart solution
with dust and the Ellis-MacCallum solution respectively. We have thus
generalized the results obtained by Rendall and Uggla in the case of locally
rotationally symmetric Bianchi II spacetimes to the reflection symmetric case.
However we needed to assume small data. For Bianchi VI there is no
analogous previous result.Comment: 30 page
Asymptotic Stability of the Relativistic Boltzmann Equation for the Soft Potentials
In this paper it is shown that unique solutions to the relativistic Boltzmann
equation exist for all time and decay with any polynomial rate towards their
steady state relativistic Maxwellian provided that the initial data starts out
sufficiently close in . If the initial data are continuous then
so is the corresponding solution. We work in the case of a spatially periodic
box. Conditions on the collision kernel are generic in the sense of
(Dudy{\'n}ski and Ekiel-Je{\.z}ewska, Comm. Math. Phys., 1988); this resolves
the open question of global existence for the soft potentials.Comment: 64 page
On the supersymmetric nonlinear evolution equations
Supersymmetrization of a nonlinear evolution equation in which the bosonic
equation is independent of the fermionic variable and the system is linear in
fermionic field goes by the name B-supersymmetrization. This special type of
supersymmetrization plays a role in superstring theory. We provide
B-supersymmetric extension of a number of quasilinear and fully nonlinear
evolution equations and find that the supersymmetric system follows from the
usual action principle while the bosonic and fermionic equations are
individually non Lagrangian in the field variable. We point out that
B-supersymmetrization can also be realized using a generalized Noetherian
symmetry such that the resulting set of Lagrangian symmetries coincides with
symmetries of the bosonic field equations. This observation provides a basis to
associate the bosonic and fermionic fields with the terms of bright and dark
solitons. The interpretation sought by us has its origin in the classic work of
Bateman who introduced a reverse-time system with negative friction to bring
the linear dissipative systems within the framework of variational principle.Comment: 12 pages, no figure
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 Role of Stranger Harassment Experiences in College Women's Perceived Possibility of Gender Crimes Happening to Them
The present study examined the relation between stranger harassment experiences and college women's perceived possibility of gender and nongender crimes happening to them. Undergraduate women attending a British university completed selfâreport measures of stranger harassment and selfâobjectification (i.e., selfâsurveillance and body shame), and then evaluated four vignettes of various crimes on the severity of the crime and the likelihood of the crime happening to them. Results indicated that stranger harassment is a common experience for these British university women. Serial mediation analyses revealed a direct effect of stranger harassment on perceived likelihood of rape and perceived likelihood of intimate partner violence, and an indirect effect of stranger harassment on rape through selfâsurveillance, whereas stranger harassment and indices of selfâobjectification were unrelated to perceived likelihood of human trafficking and burglary. Discussion is centered on the role of objectifying experiences in perceptions of gender crimes where sexual and physical harm to women's bodies is emphasized, and the potential impact for those women on the receiving end of unwanted sexual objectification
Objectification processes and disordered eating in British women and men
The present study extended the applicability of Objectification Theory to predict disordered eating in British women and men. Participants completed measures of self-objectification, body surveillance, body shame and disordered eating. Path analyses indicated strong support for the theoretical model in women, with body shame fully mediating the relation between self-objectification and disordered eating. Patterns were similar for men with two exceptions; body shame increased with lower self-objectification and disordered eating was directly increased with higher self-objectification. Findings extend Objectification Theory as a useful framework for identifying sociocultural influences on disordered eating in British women and men