Related papers: Ballistic Annihilation
We consider a system of annihilating particles where particles start from the points of a Poisson process on either the full-line or positive half-line and move at constant i.i.d. speeds until collision. When two particles collide, they…
We study existence and uniqueness of the solution to the gravitational Vlasov-Poisson system evolving in $\mathbb{R}^3$. It is assumed that initially the particles are distributed according to a spatial density with a power-law decay in…
We derive a Lorentz invariant distribution of velocities for a relativistic gas. Our derivation is based on three pillars: the special theory of relativity, the central limit theorem and the Lobachevskyian structure of the velocity space of…
The departure of a granular gas in the instable region of parameters from the initial homogeneous cooling state is studied. Results from Molecular Dynamics and from Direct Monte Carlo simulation of the Boltzmann equation are compared. It is…
The distribution of dark matter at the galactic center, crucial for indirect searches, remains uncertain. In particular, in the vicinity of the massive black hole in the center of a galaxy where indirect signals may be stronger, the density…
Coalescing ballistic annihilation is an interacting particle system intended to model features of certain chemical reactions. Particles are placed with independent and identically distributed spacings on the real line and begin moving with…
We investigate the regularity issue for the diffuse reflection boundary problem to the stationary linearized Boltzmann equation for hard sphere potential, cutoff hard potential, or cutoff Maxwellian molecular gases in a strictly convex…
Pair annihilation of heavy stable particles that occurs in the early universe is reconsidered including the off-shell effect not properly taken into account by the conventional Boltzmann equation approach. Our new calculation of the time…
This paper gives the first full proof of the justification of the linear Boltzmann equation from an underlying long range particle evolution. We suppose that a tagged particle is interacting with a background via a two body potential that…
The present paper discusses the diffusion approximation of the linear Boltzmann equation in cases where the collision frequency is not uniformly large in the spatial domain. Our results apply for instance to the case of radiative transfer…
To obtain further insight on possible power law generalizations of Boltzmann equilibrium concepts, a stochastic collision model is investigated. We consider the dynamics of a tracer particle of mass $M$, undergoing elastic collisions with…
A convenient form of kinetic equation is derived for pair annihilation of heavy stable particles relevant to the dark matter problem in cosmology. The kinetic equation thus derived extends the on-shell Boltzmann equation in a most…
In this paper, convergence results on the solutions of a time and space discrete model approximation of the Boltzmann equation for a gas of Maxwellian particles in a bounded domain, obtained by Babovsky and Illner [1989], are extended to…
We study the evolution of the one particle distribution function that solves exactly the relativistic Boltzmann equation within the relaxation time approximation for a conformal system undergoing simultaneously azimuthally symmetric…
The reaction process $A+B->C$ is modelled for ballistic reactants on an infinite line with particle velocities $v_A=c$ and $v_B=-c$ and initially segregated conditions, i.e. all A particles to the left and all B particles to the right of…
We establish pointwise polynomial decay estimates in velocity space for the spatially inhomogeneous Boltzmann equation without cutoff, in the case of hard potentials ($\gamma +2s > 2$), under the assumption that the mass, energy, and…
Boltzmann equation describes the time development of the velocity distribution in the continuum fluid matter. We formulate the equation using the field theory where the {\it velocity-field} plays the central role. The properties of the…
We study the dynamics defined by the Boltzmann equation set in the Euclidean space $\mathbb{R}^D$ in the vicinity of global Maxwellians with finite mass. A global Maxwellian is a special solution of the Boltzmann equation for which the…
Boltzmann equation describes the time development of the velocity distribution in the continuum fluid matter. We formulate the equation using the field theory where the {\it velocity-field} plays the central role. The matter (constituent…
We consider a one-dimensional system consisting of a granular tracer particle of mass $M$ in a bath of thermalized particles each of mass $m$. When the mass ratio, $M/m$, is equal to the coefficient of restitution, $\alpha$, the system maps…