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...

An information-theoretic foundation for compound Poisson approximation limit theorems is presented, in analogy to the corresponding developments for the central limit theorem and for simple Poisson approximation. It is shown that the compound Poisson distributions satisfy a natural maximum entropy property within a natural class of distributions. Simple compound Poisson approximation bounds are...

We study the local-in-time hydrodynamic limit of the relativistic Boltzmann equation using a Hilbert expansion. More specifically, we prove the existence of local solutions to the relativistic Boltzmann equation that are nearby the local relativistic Maxwellian constructed from a class of solutions to the relativistic Euler equations that includes a large subclass of near-constant, non-vacuum f...

It is proved that the shape of the typical cell of a Poisson–Delaunay tessellation of R tends to the shape of a regular simplex, given that the surface area, or the inradius, or the minimal width, of the typical cell tends to infinity. Typical cells of large diameter tend to belong to a special class of simplices, distinct from the regular ones. In the plane, these are the rightangled triangles.

The effective surface charge obtained by fitting the Poisson-Boltzmann approximation to measured data is related to the actual surface charge. Evaluation of the formally exact expression, which depends upon the wall-ion direct correlation function, gives a precise measure of the amount of ion condensation in the planar double layer. Results are presented for 0.001, 0.01, and 0.1 M monovalent an...

We study thermal leptogenesis induced by decays of a scalar SU(2)L triplet. Despite the presence of gauge interactions, unexpected features of the Boltzmann equations make the efficiency close to maximal in most of the parameter space. We derive the maximal CP asymmetry in triplet decays, assuming that it is generated by heavier sources of neutrino masses: in this case successful leptogenesis n...

Recent results about spike-timing-dependent plasticity (STDP) in recurrently connected neurons are reviewed, with a focus on the relationship between the weight dynamics and the emergence of network structure. In particular, the evolution of synaptic weights in the two cases of incoming connections for a single neuron and recurrent connections are compared and contrasted. A theoretical framewor...

This paper discusses evaluation of data association hypotheses for a general class of multiple target tracking problems. We assume that the number of targets is random and unknown, and given the number of targets, that the joint target state distribution forms a system of independent, identically distributed (i.i.d.) probability distributions. We are particularly interested in the cases in whic...