Related papers: Coordinates in the relativistic Boltzmann theory

The spectrum structure of the linearized relativistic Boltzmann equation around a global Maxwellian is studied in this paper. Based on the spectrum analysis, we establish the optimal time-convergence rates of the global solution to the…

We study a fuzzy Boltzmann equation, where particles interact via delocalised collisions, in contrast to classical Boltzmann equations. We discuss the existence and uniqueness of solutions and provide a natural variational characterisation…

The proper handling of 3D orientations is a central element in many optimization problems in engineering. Unfortunately many researchers and engineers struggle with the formulation of such problems and often fall back to suboptimal…

The paper considers a linear system of Boltzmann transport equations modelling the evolution of three species of particles, photons, electrons and positrons. The system is coupled because of the collision term (an integral operator). The…

We study a regularity property for the gain part of the relativistic Boltzmann collision operator. Our assumptions on the collisional scattering kernel cover the full range of generic hard and soft potentials with angular cut-off.

We obtain a canonical representation for block matrices. The representation facilitates simple computation of the determinant, the matrix inverse, and other powers of a block matrix, as well as the matrix logarithm and the matrix…

This paper describes perturbative framework, on the basis of the closed-time-path formalism, in terms of quasiparticle picture for studying quasiuniform relativistic quantum field systems near equilibrium and nonequilibrium quasistationary…

The dynamical system of a point particle constrained on a torus is quantized \`a la Dirac with two kinds of coordinate systems respectively; the Cartesian and toric coordinate systems. In the Cartesian coordinate system, it is difficult to…

A set of equations is derived from the Boltzmann kinetic equation describing charge transport in semiconductors. The unknowns of these equations depend on the space-time coordinates and the electron energy. The non-parabolic and parabolic…

The paper considers existence results of solution for a linear coupled system of Boltzmann transport equations and related inverse problem. The system models the evolution of three species of particles, photons, electrons and positrons.…

We introduce another new type of combinations of Bernstein operators in this paper, which can be used to approximate the functions with inner singularities. The direct and inverse results of the weighted approximation of this new type…

Our previous work developed a framework for treating the motion of a small body in general relativity, based on a one-parameter-family of solutions to Einstein's equation. Here we give an analysis of the coordinate freedom allowed within…

We define Ptolemy coordinates for representations that are not necessarily boundary-unipotent. This gives rise to a new algorithm for computing the SL(2,C) A-polynomial, and more generally the SL(n,C) A-varieties. We also give a formula for…

We consider the effect of non-reciprocity in a binary mixture of self-propelled particles with anti-aligning interactions, where a particle of type A reacts differently to a particle of type B than vice versa. Starting from a well-known…

The use of complex networks as a modern approach to understanding the world and its dynamics is well-established in literature. The adjacency matrix, which provides a one-to-one representation of a complex network, can also yield several…

An equivalence relation in the symmetric group, where is a positive integer has been considered. An algorithm for calculation of the number of the equivalence classes by this relation for arbitrary integer has been described.

We propose new variational principles for traffic assignment problems. So to find equillibrium we have to solve large-scale convex optimization problem of special type. We propose some kind of "algebra" on different models and corresponding…

We present a new derivation of the conservative form of the general relativistic Boltzmann equation and specialize it to the 3+1 metric. The resulting transport equation is intended for use in simulations involving numerical relativity,…

We consider an inverse problem for the nonlinear Boltzmann equation near the equilibrium. Our goal is to determine the collision kernel in the Boltzmann equation from the knowledge of the Albedo operator. Our approach relies on a…

Hausdorff relation, topologically identifying points in a given space, belongs to elementary tools of modern mathematics. We show that if subtle enough mathematical methods are used to analyze this relation, the conclusions may be…