We prove the uniqueness of the self-similar profile solution for a modified Boltzmann equation describing probabilistic ballistic annihilation. Such a model describes a system of hard spheres such that, whenever two particles meet, they either annihilate with probability α ∈ (0, 1) or they undergo an elastic collision with probability 1 − α. The existence of a self-similar profile for α smaller...

This paper analyzes various schemes for the Euler-Poisson-Boltzmann (EPB) model of plasma physics. This model consists of the pressureless gas dynamics equations coupled with the Poisson equation and where the Boltzmann relation relates the potential to the electron density. If the quasi-neutral assumption is made, the Poisson equation is replaced by the constraint of zero local charge and the ...

Higher-order intergrid transfer operators used within cell-centered multigrid can improve the convergence properties of the multigrid method compared to low-order operators. In this thesis those operators are analyzed and incorporated into the LSE (linear systems of equation) module of the waLBerla software framework. The aim is to provide a solver for Poisson and Poisson-Boltzmann partial di e...

We give an overview of the Stein{Chen method for establishing Poisson approximations of various random variables. Couplings of certain variables are used to gives explicit bounds for the total variation distance between the distribution of a random variable and a Poisson variable. Some applications are given. In some cases, explicit couplings may be used to obtain good estimates; in other appli...

1 The Boltzmann equation 6 1.1 The model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2 Physical properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3 Fluid limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.4 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.5 Other collis...

We assume a flat brane located at y = 0, surrounded by an AdS space, and consider the 5D Einstein equations when the energy flux component of the energy-momentum tensor is related to the Hubble parameter through a constant Q. We calculate the metric tensor, as well as the Hubble parameter on the brane, when Q is small. As a special case, if the brane is tensionless, the influence from Q on the ...

We consider a simple solution of a Yang-Baxter equation on loop algebra and deduce from it a Sklyanin Poisson structure which operates continuously on a Sobolev test algebra on the Wiener space of the Lie algebra. It is very classical that the solution of the classical Yang-Baxter equation on a finite dimensional algebra gives a Poisson structure on the algebra of smooth function on the finite ...

2014 Electrostatic interactions in an aqueous medium are analysed with amphiphile-water systems as models. It is concluded that the mean field Poisson-Boltzmann approximation is often adequate to describe electrostatic effects in ionic systems particularly with monovalent counterions. Two approximations inherent in the Poisson-Boltzmann equation are discussed in detail: (i) the neglect of ion-i...

A derivation is given of the Boltzmann–Vlasov equation beginning from multiple scattering considerations. The motivation for the discussion, which is purely pedagogical in nature, is the current interest in understanding the origins of transport equations in terms of rigorous field-theory descriptions, or, as in this case, exact nonrelativistic formulations.

In this paper we study the number of pure strategy Nash equilibria in large finite n-player games. A distinguishing feature of our study is that we allow general potentially multivalued best reply corresponsences. Given the number K of pure strategies to each player, we assign to each player a distribution over the number of his pure best replies against each strategy profile of his opponents. ...