Related papers: Coordinates in the relativistic Boltzmann theory
The construction of discrete velocity models or numerical methods for the Boltzmann equation, may lead to the necessity of computing the collision operator as a sum over lattice points. The collision operator involves an integral over a…
We show that the widely used relaxation time approximation to the relativistic Boltzmann equation contains basic flaws, being incompatible with microscopic and macroscopic conservation laws. We propose a new approximation that fixes such…
We extend the $L^p$-theory of the Boltzmann collision operator by using classical techniques based in the Carleman representation and Fourier analysis, allied to new ideas that exploit the radial symmetry of this operator. We are then able…
In order to solve the Boltzmann equation numerically, in the present work, we propose a new model equation to approximate the Boltzmann equation without angular cutoff. Here the approximate equation incorporates Boltzmann collision operator…
Several local elliptic coordinates are used to build a new polyelliptic coordinate system which is orthogonal and admits the separation of variables. Such coordinate systems can give the exact solutions of some unsolved problems in quantum…
Problems associated with the Boltzmann collisional operator are unveiled and discussed. By careful investigation it is shown that collective effects of molecular collisions in the six-dimensional position and velocity space are more…
We introduce the concept of monodromy coordinates for representing solutions to large polynomial systems. Representing solutions this way provides a time-memory trade-off in a monodromy solving algorithm. We describe an algorithm, which…
A systematic derivation of Boltzmann equation is presented in the framework of closed-time-path formalism. Introducing a new type of probe, the expectation value of number operator is calculated as a functional of source. Then solving for…
Lorentzian frames may belong to one of the 199 causal classes. Of these numerous causal classes, people are essentially aware only of two of them. Nevertheless, other causal classes are present in some well-known solutions, or present a…
In this paper, we prove the propagation of uniform upper bounds for the spatially homogeneous relativistic Boltzmann equation. These $L^\infty$ bounds have been known to be a challenging open problem in relativistic kinetic theory. To…
The Operator axioms have produced new real numbers with new operators. New operators naturally produce new equations and thus extend the traditional mathematical models which are selected to describe various scientific rules. So new…
We introduce a class of Boltzmann equations on the real line, which constitute extensions of the classical Kac caricature. The collisional gain operators are defined by smoothing transformations with quite general properties. By…
The paper considers a class of linear Boltzmann transport equations which models a charged particle transport. The equation is an approximation of the original exact transport equation which involves hyper-singular integrals in their…
Generic models of propelled particle systems posit that the emergence of polar order is driven by the competition between local alignment and noise. Although this notion has been confirmed employing the Boltzmann equation, the range of…
Representations and relative Rota-Baxter operators with respect to representations of Hom-Leibniz Poisson algebras are introduced and studied. Some characterizations of these operators are obtained. The notion of matched pair and Nijenhuis…
It is widely known that Boltzmann machines are capable of representing arbitrary probability distributions over the values of their visible neurons, given enough hidden ones. However, sampling -- and thus training -- these models can be…
The Boltzmann equation has been a driving force behind significant mathematical research over the years. Its challenging theoretical complexity, combined with a wide variety of current scientific and technological problems that require…
A field theoretical perturbation theory in inverse powers of coupling constant is developed which is manifestly covariant in every order of the expansion. A dilatation operator serves as an evolution dynamical one in a scale non-invariant…
The status of our understanding of relativistic sum rules is reviewed. The recent development of new theoretical methods for the evaluation of these sum rules offers hope for further advances in this challenging field. These new techniques…
The Lorentz transformations are represented by Einstein velocity addition on the ball of relativistically admissible velocities. This representation is by projective maps. The Lie algebra of this representation defines the relativistic…