On the approach to equilibrium for a polymer with adsorption and repulsion.
On the approximate solution of the multi-group time-dependent transport equation by -method
This paper concerns -velocity model of the general linear time-dependent transport equation. The assumed probability of the collision (scattering, fission) depends only on the angle of the directions of the moving neutron before and after the collision. The weak formulation of the problem is given and a priori estimates are obtained. The construction of an approximate problem by -method is given. In the symmetric hyperbolic system obtained by -method dissipativity and -orthogonality of the relevant...
On the approximation of the dynamics of sandpile surfaces.
On the concept of the asymptotic Rényi distances for random fields
The asymptotic Rényi distances are explicitly defined and rigorously studied for a convenient class of Gibbs random fields, which are introduced as a natural infinite-dimensional generalization of exponential distributions.
On the convergence of numerical schemes for the Boltzmann equation
On the core property of the cylinder functions class in the construction of interacting particle systems
For general interacting particle systems in the sense of Liggett, it is proven that the class of cylinder functions forms a core for the associated Markov generator. It is argued that this result cannot be concluded by straightforwardly generalizing the standard proof technique that is applied when constructing interacting particle systems from their Markov pregenerators.
On the counting of fully packed loop configurations: some new conjectures.
On the decomposition of particle size distribution in the extraction replica method
This paper deals with the method for evaluating exposures of nickel alloy structures containing both extracted and sectioned particles. The presented stereological model makes it possible to estimate two unknown spatial parameters, the mean value of the particle size distribution and the depth of etching with the use of the information obtained from the combined structure of the exposures.
On the degenerate multiplicity of the loop algebra for the 6V transfer matrix at roots of unity.
On the derivation of a quantum Boltzmann equation from the periodic Von-Neumann equation
On the derivation of a quantum Boltzmann equation from the periodic Von-Neumann equation
We present the semi-conductor Boltzmann equation, which is time-reversible, and indicate that it can be formally derived by considering the large time and small perturbing potential limit in the Von-Neumann equation (time-reversible). We then rigorously compute the corresponding asymptotics in the case of the Von-Neumann equation on the Torus. We show that the limiting equation we obtain does not coincide with the physically realistic model. The former is indeed an equation of Boltzmann type, yet...
On the dimer problem and the Ising problem in finite 3-dimensional lattices.
On the distribution of free path lengths for the periodic Lorentz gas II
On the distribution of free path lengths for the periodic Lorentz gas II
Consider the domain and let the free path length be defined as In the Boltzmann-Grad scaling corresponding to , it is shown that the limiting distribution of is bounded from below by an expression of the form C/t, for some C> 0. A numerical study seems to indicate that asymptotically for large t, . This is an extension of a previous work [J. Bourgain et al., Comm. Math. Phys.190 (1998) 491-508]. As a consequence, it is proved that the linear Boltzmann type transport equation is inappropriate...
On the distribution of the free path length of the linear flow in a honeycomb
Consider the region obtained by removing from the discs of radius , centered at the points of integer coordinates with . We are interested in the distribution of the free path length (exit time) of a point particle, moving from along a linear trajectory of direction , as . For every integer number , we prove the weak convergence of the probability measures associated with the random variables , explicitly computing the limiting distribution. For , respectively , this result leads...
On the distributional solution of the inverse problem induced by the heat kernel method.
On the domination of a random walk on a discrete cylinder by random interlacements.
On the double critical-state model for type-II superconductivity in 3D
In this paper we mathematically analyse an evolution variational inequality which formulates the double critical-state model for type-II superconductivity in 3D space and propose a finite element method to discretize the formulation. The double critical-state model originally proposed by Clem and Perez-Gonzalez is formulated as a model in 3D space which characterizes the nonlinear relation between the electric field, the electric current, the perpendicular component of the electric current...
On the doubly refined enumeration of alternating sign matrices and totally symmetric self-complementary plane partitions.
On the dynamics of Bose-Einstein condensation