Given a classical r-matrix on a Poisson algebra, we show how to construct a natural family of compatible Poisson structures for the Hamiltonian formulation of Lax equations. Examples for which our formalism applies include the Benny hierachy, the dispersionless Toda lattice hierachy, the dispersionless KP and modified KP hierachies, the dispersionless Dym hierachy etc.

A model of the precipitation process in reverse micelles has been developed to calculate the size of fine particles obtained therein. While the method shares several features of particle nucleation and growth common to precipitation in large systems, complexities arise in describing the processes of nucleation, due to the extremely small size of a micelle and of particle growth caused by fusion...

We clarify the validity of a method that decouples a boundary value problem of biharmonic equation to two Poisson equations on polygonal domains. The method provides a way of computing deflections of simply supported polygonal plates by using Poisson solvers. We show that such decoupling is not valid if the polygonal domain is not convex. It may fail even when the right hand side function is in...

(ABSTRACT) Random variables defined on the natural numbers may often be approximated by Poisson variables. Just as normal approximations may be improved by saddlepoint methods, Pois-son approximations may be substantially improved by tilting, expansion, and other related methods. This work will develop and examine the use of these methods, as well as present examples where such methods may be n...

The paper is concerned with the accuracy in total variation of the approximation of the distribution of a sum of independent Bernoulli distributed random d–vectors by the product distribution with Poisson marginals which has the same mean. The best results, obtained using generating function methods, are those of Roos (1998, 1999). Stein’s method has so far yielded somewhat weaker bounds. We de...

The dynamics of the dilute electrons can be modeled by the fundamental Vlasov-PoissonBoltzmann system when the electrons interact with themselves through collisions in the selfconsistent electric field. In this paper, it is shown that any smooth initial perturbation of a given global Maxwellian leads to a unique global-in-time classical solution when either the mean free path is small or the ba...

We evaluate the relic density of the lightest neutralino, the lightest supersymmetric particle, in the Minimal Supersymmetric extension of the Standard Model (MSSM). For the first time, we include all coannihilation processes between neutralinos and charginos for any neutralino mass and composition. We use the most sophisticated routines for integrating the cross sections and the Boltzmann equa...

We consider Nambu-Poisson 3-algebras on three dimensional manifolds M3, such as the Euclidean 3-space R, the 3-sphere S as well as the 3-torus T . We demonstrate that in the Clebsch-Monge gauge, the Lie algebra of volume preserving diffeomorphisms SDiff(M3) is identical to the Nambu-Poisson algebra on M3. Moreover the fundamental identity for the Nambu 3-bracket is just the commutation relation...

We report here new electrical laws, derived from nonlinear electro-diffusion theory, about the effect of the local geometrical structure, such as curvature, on the electrical properties of a cell. We adopt the Poisson-Nernst-Planck (PNP) equations for charge concentration and electric potential as a model of electro-diffusion. In the case at hand, the entire boundary is impermeable to ions and ...

This short note complements the recent paper of the authors [2]. We revisit the results on propagation of regularity and stability using Lp estimates for the gain and loss collision operators which had the exponent range misstated for the loss operator. We show here the correct range of exponents. We require a Lebesgue’s exponent α > 1 in the angular part of the collision kernel in order to obt...