We study the high-energy asymptotics of the steady velocity distributions for model systems of granular media in various regimes. The main results obtained are integral estimates of solutions of the hard-sphere Boltzmann equations, which imply that the velocity distribution functions f(v) behave in a certain sense as C exp(−r|v|s) for |v| large. The values of s, which we call the orders of tail...

The stationary Boltzmann equation for hard and soft forces in the context of a two component gas is considered in the slab when the molecular masses of the 2 component are different. An L existence theorem is proved when one component satisfies a given indata profile and the other component satisfies diffuse reflection at the boundaries. Weak L compactness is extracted from the control of the e...

The Poisson-Boltzmann theory has become widely accepted in modeling electrostatic solvation interactions in biomolecular calculations. However the standard practice of atomic point charges in molecular mechanics force fields introduces singularity into the Poisson-Boltzmann equation. The finite-difference/finite-volume discretization approach to the Poisson-Boltzmann equation alleviates the num...

The measure problem of cosmology is how to obtain normalized probabilities of observations from the quantum state of the universe. This is particularly a problem when eternal inflation leads to a universe of unbounded size so that there are apparently infinitely many realizations or occurrences of observations of each of many different kinds or types, making the ratios ambiguous. There is also ...

A graph technique analogous to the usual Feynman technique in field theory is developed for calculating Green's functions for particles in a statistical system which under the action of an external field deviates to any arbitrary extent from the state of thermodynamic equilibrium. It is found that in order to describe such a system it is necessary to introduce two Green's functions for each typ...

The problem of computing the electrostatic energy of a large molecule is considered. It is reduced to solving the Poisson equation inside and the linear Poisson-Boltzmann equation in the exterior, coupled by boundary conditions. A Monte Carlo estimate for the potential point values, their derivatives, and the energy is constructed. The estimate is based on the walk on spheres and Green’s functi...

The formalism of graded Poisson-sigma models allows the construction of N = (2, 2) dilaton supergravity in terms of a minimal number of fields. For the gauged chiral U(1) symmetry the full action, involving all fermionic contributions , is derived. The twisted chiral case follows by simple redefinition of fields. The equivalence of our approach to the standard second order one in terms of super...

We study the acoustic limit from the Boltzmann equation in the framework of classical solutions. For a solution Fε = μ+ε √ μfε to the rescaled Boltzmann equation in the acoustic time scaling ∂tFε + v·∇xFε = 1 ε Q(Fε, Fε) , inside a periodic box T, we establish the global-in-time uniform energy estimates of fε in ε and prove that fε converges strongly to f whose dynamics is governed by the acous...

1 Riemann Poisson manifolds were introduced by the author in [1] and studied in more details in [2]. Kähler-Riemann foliations form an interesting subset of the Riemannian foliations with remarkable properties ( see [3]). In this paper we will show that to give a regular Riemann Poisson structure on a manifold M is equivalent to to give a Kähler-Riemann foliation on M such that the leafwise sym...

The adsorption of large ions from solution to a charged surface is investigated theoretically. A generalized Poisson-Boltzmann equation which takes into account the finite size of the ions is presented. We obtain analytical expressions for the electrostatic potential and ion concentrations at the surface, leading to a modified Grahame equation. At high surface charge densities the ionic concent...