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. ...

We extend the calculus of multiplicative vector fields and differential forms and their intrinsic derivatives from Lie groups to Lie groupoids; this generalization turns out to include also the classical process of complete lifting from arbitrary manifolds to tangent and cotangent bundles. Using this calculus we give a new description of the Lie bialgebroid structure associated with a Poisson g...

In this paper, we address the problem of denoising images degraded by Poisson noise. We propose a new patchbased approach based on best linear prediction to estimate the underlying clean image. A simplified prediction formula is derived for Poisson observations, which requires the covariance matrix of the underlying clean patch. We use the assumption that similar patches in a neighborhood share...

f0(v) log f0(v)dv for all t ≥ 0. Assume that in a dilute gas or plasma, particles collide by pairs, due to a repulsive force proportional to 1/r, where r stands for the distance between the two particles. Then if s ∈ (2,∞), the velocity distribution solves the corresponding Boltzmann equation [14, 15]. But if s = 2, the Boltzmann equation is meaningless [14] and is often replaced by the Landau ...

This paper includes results centered around three topics, all of them related with the nonlinear stability of equilibria in Poisson dynamical systems. Firstly, we prove an energy-Casimir type sufficient condition for stability that uses functions that are not necessarily conserved by the flow and that takes into account certain asymptotically stable behavior that may occur in the Poisson catego...