arXiv subjects

Michael I. Tribelsky

Publications and source records attributed to Michael I. Tribelsky.

23 records · Page 2Linked to original sources

arXiv2007

Fano resonances at light scattering by an obstacle

It is shown that elastic resonance scattering of light by a finite-size obstacle with weak dissipation is analogous to quantum scattering by a potential with quasi-discrete levels and exhibits Fano resonances. Localized plasmons (polaritons), exited in the obstacle by the incident light, are equivalent to the quasi-discrete levels, while the radiative decay of these excitations plays exactly the same role as tunnelling from the quasi-discrete levels for the quantum problem. Mie scattering of light by a spherical particle and an exactly solvable discrete model with nonlocal coupling simulating wave scattering in systems with reduced spatial dimensionality are discussed as examples.

cond-mat.other↗

arXiv2001

Tails of probability density for sums of random independent variables

The exact expression for the probability density $p_{_N}(x)$ for sums of a finite number $N$ of random independent terms is obtained. It is shown that the very tail of $p_{_N}(x)$ has a Gaussian form if and only if all the random terms are distributed according to the Gauss Law. In all other cases the tail for $p_{_N}(x)$ differs from the Gaussian. If the variances of random terms diverge the non-Gaussian tail is related to a Levy distribution for $p_{_N}(x)$. However, the tail is not Gaussian even if the variances are finite. In the latter case $p_{_N}(x)$ has two different asymptotics. At small and moderate values of $x$ the distribution is Gaussian. At large $x$ the non-Gaussian tail arises. The crossover between the two asymptotics occurs at $x$ proportional to $N$. For this reason the non-Gaussian tail exists at finite $N$ only. In the limit $N$ tends to infinity the origin of the tail is shifted to infinity, i. e., the tail vanishes. Depending on the particular type of the distribution of the random terms the non-Gaussian tail may decay either slower than the Gaussian, or faster than it. A number of particular examples is discussed in detail.

math.PR↗

arXiv2001

Hydrodynamic Waves in Regions with Smooth Loss of Convexity of Isentropes. General Phenomenological Theory

General phenomenological theory of hydrodynamic waves in regions with smooth loss of convexity of isentropes is developed based on the fact that for most media these regions in p-V plane are anomalously small. Accordingly the waves are usually weak and can be described in the manner analogous to that for weak shock waves of compression. The corresponding generalized Burgers equation is derived and analyzed. The exact solution of the equation for steady shock waves of rarefaction is obtained and discusses.

physics.flu-dyn↗

arXiv2001

Nonlinear Pattern Selection in Binary Mixture Convection with Through-Flow

The pattern selection problem in binary-mixture convection in an extended channel with a lateral through-flow is presented. The through-flow breaks left--right parity and changes pattern dynamics dramatically. The problem is studied based on computer simulation of the complete set of hydrodynamic equations (Oberbeck-Boussinesq approximation) in the two-dimensional rectangular channel with aspect ratio $Γ= 12$ and convection-suppressing lateral boundary conditions. A wide variety of new dynamical patterns is obtained, discussed and classified.

nlin.PS↗

arXiv2000

Extensive Chaos in the Nikolaevskii Model

We carry out a systematic study of a novel type of chaos at onset ("soft-mode turbulence") based on numerical integration of the simplest one dimensional model. The chaos is characterized by a smooth interplay of different spatial scales, with defect generation being unimportant. The Lyapunov exponents are calculated for several system sizes for fixed values of the control parameter $ε$. The Lyapunov dimension and the Kolmogorov-Sinai entropy are calculated and both shown to exhibit extensive and microextensive scaling. The distribution functional is shown to satisfy Gaussian statistics at small wavenumbers and small frequency.

cond-mat↗