Voronezh State University

About: Voronezh State University is a education organization based out in Voronezh, Russia. It is known for research contribution in the topics: Silicon & Boundary value problem. The organization has 5166 authors who have published 6097 publications receiving 31680 citations. The organization is also known as: VSU & Voronezh University.

Territory covered by N Lévy flights on d-dimensional lattices

Abstract: We study the territory covered by N L\'evy flights by calculating the mean number of distinct sites, 〈${\mathrm{S}}_{\mathrm{N}}$(n)〉, visited after n time steps on a d-dimensional, d\ensuremath{\geqslant}2, lattice. The L\'evy flights are initially at the origin and each has a probability A${\mathrm{\ensuremath{\ell}}}^{\mathrm{\ensuremath{-}}(\mathrm{d}+\mathrm{\ensuremath{\alpha}})}$ to perform an \ensuremath{\ell}-length jump in a randomly chosen direction at each time step. We obtain asymptotic results for different values of \ensuremath{\alpha}. For d=2 and N\ensuremath{\rightarrow}\ensuremath{\infty} we find 〈${\mathrm{S}}_{\mathrm{N}}$(n)〉\ensuremath{\propto}${\mathrm{C}}_{\mathrm{\ensuremath{\alpha}}}$${\mathrm{N}}^{2\mathrm{/}(2+\mathrm{\ensuremath{\alpha}})}$${\mathrm{n}}^{4\mathrm{/}(2+\mathrm{\ensuremath{\alpha}})}$, when \ensuremath{\alpha}2 and 〈${\mathrm{S}}_{\mathrm{N}}$(n)〉\ensuremath{\propto}${\mathrm{N}}^{2\mathrm{/}(2+\mathrm{\ensuremath{\alpha}})}$${\mathrm{n}}^{2\mathrm{/}\mathrm{\ensuremath{\alpha}}}$, when \ensuremath{\alpha}g2. For d=2 and n\ensuremath{\rightarrow}\ensuremath{\infty} we find 〈${\mathrm{S}}_{\mathrm{N}}$(n)〉\ensuremath{\propto}Nn for \ensuremath{\alpha}2 and 〈${\mathrm{S}}_{\mathrm{N}}$(n)〉\ensuremath{\propto}Nn/ln n for \ensuremath{\alpha}g2. The last limit corresponds to the result obtained by Larralde et al. [Phys. Rev. A 45, 7128 (1992)] for bounded jumps. We also present asymptotic results for 〈${\mathrm{S}}_{\mathrm{N}}$(n)〉 on d\ensuremath{\geqslant}3 dimensional lattices.

Spinodal Decomposition of Ga x In 1−x As y P 1−y Quaternary Alloys

Abstract: Using X-ray structural analysis, scanning electron microscopy, atomic force microscopy, and photoluminescent spectroscopy, it is shown that it is possible to obtain a small-scale domain structure on the surface of liquid-phase epitaxial heterostructures. The domain structure emerges as a result of spinodal decomposition of the Ga x In1 − x As y P1 − y quaternary alloy due to immiscibility of its components and relaxation of its lattice parameter to surrounding layers.