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

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

Rotation sets of billiards with one obstacle

We investigate the rotation sets of billiards on the $m$-dimensional torus with one small convex obstacle and in the square with one small convex obstacle. In the first case the displacement function, whose averages we consider, measures the change of the position of a point in the universal covering of the torus (that is, in the Euclidean space), in the second case it measures the rotation around the obstacle. A substantial part of the rotation set has usual strong properties of rotation sets

The Lyapunov exponent in the Sinai billiard in the small scatterer limit

We show that Lyapunov exponent for the Sinai billiard is $\lambda = -2\log(R)+C+O(R\log^2 R)$ with $C=1-4\log 2+27/(2\pi^2)\cdot \zeta(3)$ where $R$ is the radius of the circular scatterer. We consider the disk-to-disk-map of the standard configuration where the disks is centered inside a unit square.Comment: 15 pages LaTeX, 3 (useful) figures available from the autho

Helium Porosity Formation in Vanadium Alloys of V-Ti-Cr, V-W-Zr and V-W-Ta Systems in Comparison with Binary Alloys

Vanadium alloys are considered candidates for use as structural materials of fusion reactors. A large amount of helium will be accumulated in such materials. The presence of helium in the materials may result in gas swelling. This paper presents the results on helium porosity formation researches in V–Ti–Cr, V–W–Zr and V–W–Ta alloys obtained by means of TEM. Samples were irradiated by 40 keV Не+ ions up to dose of 5 ⋅ 1020m−2 at 923 K. Alloy V–4%Ti–4%Cr has a smallest helium swelling among the ternary alloys and its swelling is significantly lower than swelling of dual V–Ti and V–Cr alloys. The swelling of the ternary V–2%W–1%Zr alloy is more than 3 times less than the swelling of vanadium, several times less than that of V–W alloys and slightly lower than the swelling of V– Zr alloys. Swelling increases by a factor of 1.5 with increasing of Zr content to 2% in the ternary V–2%W–1%Zr alloy. Similarly, gas swelling of ternary V–2%W–1%Ta alloy is significantly lower than that for binary V–W and V–Ta alloys. Assumptions are made about the possible mechanisms of the effect of alloying elements in vanadium on helium porosity formation. Keywords: vanadium alloys, swelling, helium, radiation resistance

Results and prospects on registration of reflected Cherenkov light of EAS from cosmic particles above 10^{15} eV

We give an overview of the SPHERE experiment based on detection of reflected Vavilov-Cherenkov radiation (Cherenkov light) from extensive air showers in the energy region E>10^{15} eV. A brief history of the reflected Cherenkov light technique is given; the observations carried out with the SPHERE-2 detector are summarized; the methods of the experimental datasample analysis are described. The first results on the primary cosmic ray all-nuclei energy spectrum and mass composition are presented. Finally, the prospects of the SPHERE experiment and the reflected Cherenkov light technique are given.Comment: 4 pages, 3 figures, Proc. PANIC-201

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