Beam propagation in a Randomly Inhomogeneous Medium

An integro-differential equation describing the angular distribution of beams is analyzed for a medium with random inhomogeneities. Beams are trapped because inhomogeneities give rise to wave localization at random locations and random times. The expressions obtained for the mean square deviation from the initial direction of beam propagation generalize the "3/2 law".Comment: 4 page

From Discrete Hopping to Continuum Modeling on Vicinal Surfaces with Applications to Si(001) Electromigration

Coarse-grained modeling of dynamics on vicinal surfaces concentrates on the diffusion of adatoms on terraces with boundary conditions at sharp steps, as first studied by Burton, Cabrera and Frank (BCF). Recent electromigration experiments on vicinal Si surfaces suggest the need for more general boundary conditions in a BCF approach. We study a discrete 1D hopping model that takes into account asymmetry in the hopping rates in the region around a step and the finite probability of incorporation into the solid at the step site. By expanding the continuous concentration field in a Taylor series evaluated at discrete sites near the step, we relate the kinetic coefficients and permeability rate in general sharp step models to the physically suggestive parameters of the hopping models. In particular we find that both the kinetic coefficients and permeability rate can be negative when diffusion is faster near the step than on terraces. These ideas are used to provide an understanding of recent electromigration experiment on Si(001) surfaces where step bunching is induced by an electric field directed at various angles to the steps.Comment: 10 pages, 4 figure

Dielectric response function PdHx system

The calculations of electron structure of pure Pd and PdHx (x=1,2,3) system have been made ab initio in the range of local density approximation. Total energy of PdHx system has been calculated for the cases of different coordination of hydrogen atom (oct-and tetrahedral), the conclusion on their most probable location in metal lattice has been made. In the approximation of constant matrix element the imaginary part of permittivity constant function ?2(?) has been calculated. It was stated that dissolution of hydrogen in palladium increases values of the function ?2(?) in the investigated range of energies from 2 to 24 eV. Therefore in the case of radiation impact on PdHx system one can expect intensive excitement of the crystal electron subsystem, and, hence, decrease of potential barriers for hydrogen atom movement

Oseledets' Splitting of Standard-like Maps

For the class of differentiable maps of the plane and, in particular, for standard-like maps (McMillan form), a simple relation is shown between the directions of the local invariant manifolds of a generic point and its contribution to the finite-time Lyapunov exponents (FTLE) of the associated orbit. By computing also the point-wise curvature of the manifolds, we produce a comparative study between local Lyapunov exponent, manifold's curvature and splitting angle between stable/unstable manifolds. Interestingly, the analysis of the Chirikov-Taylor standard map suggests that the positive contributions to the FTLE average mostly come from points of the orbit where the structure of the manifolds is locally hyperbolic: where the manifolds are flat and transversal, the one-step exponent is predominantly positive and large; this behaviour is intended in a purely statistical sense, since it exhibits large deviations. Such phenomenon can be understood by analytic arguments which, as a by-product, also suggest an explicit way to point-wise approximate the splitting.Comment: 17 pages, 11 figure

Vacuum shell in the Schwarzschild-de Sitter world

We construct the classification scheme for all possible evolution scenarios and find the corresponding global geometries for dynamics of a thin spherical vacuum shell in the Schwarzschild-de Sitter metric. This configuration is suitable for the modelling of vacuum bubbles arising during cosmological phase transitions in the early Universe. The distinctive final types of evolution from the local point of view of a rather distant observer are either the unlimited expansion of the shell or its contraction with a formation of black hole (with a central singularity) or wormhole (with a baby universe in interior).Comment: 15 pages, 8 figure