We present three different fractional versions of the Poisson process and some related results concerning the distribution of order statistics and the compound Poisson process. The main version is constructed by considering the difference-differential equation governing the distribution of the standard Poisson process, N(t), t > 0, and by replacing the time-derivative with the fractional Dzerba...

In the present paper we investigate a method to describe lowenergy scattering events of pions and nuclei within a Boltzmann-UehlingUhlenbeck (BUU) transport model. Implementing different scenarios of medium modifications, we studied the mean free path of pions in nuclear matter at low momenta and compared pion absorption simulations to data. Pursuing these studies we have shown, that also in a ...

The lattice evolution method for solving the nonlinear Poisson-Boltzmann equation in confined domain is developed by introducing the second-order accurate Dirichlet and Neumann boundary implements, which are consistent with the non-slip model in lattice Boltzmann method for fluid flows. The lattice evolution method is validated by comparing with various analytical solutions and shows superior t...

We begin with a short presentation of the basic concepts related to Lie groupoids and Lie algebroids, but the main part of this paper deals with Lie algebroids. A Lie algebroid over a manifold is a vector bundle over that manifold whose properties are very similar to those of a tangent bundle. Its dual bundle has properties very similar to those of a cotangent bundle: in the graded algebra of s...

is a LerayLions operator defined on W 1,x 0 LM (Ω), M is an appropriate N -function and which grows like M̄M(β K |∇u|) with respect to ∇u, but which is not restricted by any growth condition with respect to u (see assumptions (3.3)-(3.6)). The function Φ is just assumed to be continuous on R. Under these assumptions, the above problem does not admit, in general, a weak solution since the fields ...

In this paper we show that if A is a Poisson algebra equipped with a set of maps ∆ (i) λ : A → A ⊗ N satisfying suitable conditions, then the images of the Casimir functions of A under the maps ∆ (i) λ (that we call " loop coproducts ") are in involution. Rational, trigonometric and elliptic Gaudin models can be recovered as particular cases of this result, and we show that the same happens for...

Based on the global existence theory of the Vlasov-Poisson-Boltzmann system around vacuum in the N -dimensional phase space, in this paper, we prove the uniform L1 stability of classical solutions for small initial data when N ≥ 4. In particular, we show that the stability can be established directly for the soft potentials, while for the hard potentials and hard sphere model it is obtained thr...

We present a derivation of Boltzmann principle SB = kB lnW based on classical mechanical models of thermodynamics. The argument is based on the heat theorem and can be traced back to the second half of the nineteenth century with the works of Helmholtz and Boltzmann. Despite its simplicity, this argument has remained almost unknown. We present it in a modern, self-contained and accessible form....

In 1956 Mark Kac [5] invented a microscopic, linear model, from which the nonlinear Boltzmann equation describing the evolution of the velocity distribution for a system of colliding particles could be rigorously derived. Consider N particles in one dimension that interact through random collisions. We consider the spatially homogeneous case only, i.e., the case where the particles are uniforml...