New Scenario to Chaos Transition in the Mappings with Discontinuities

We consider a many-parametric piecewise mapping with discontinuity. That is a one dimensional model of singular dynamic system. The stability boundary are calculated analytically and numerically. New typical features of stable cycle structures and scenario to chaos transition provoked by discontinuity are found.Comment: 10 pages LaTeX2e, 5 eps figures; submitted to Physics Letters

Geometry and dynamics of billiards in symmetric phase space

The billiard problem of statistical physics is considered in a new geometric approach with a symmetric phase space. The structure and topological features of typical billiard phase portrait are defined. The connection between geometric, dynamic and statistic properties of smooth billiard is established. Other directions of the theory on development are pointed out.Comment: 8 pages LaTeX2e, 1 eps figure; Paper presented at the International Conference dedicated to the 90th anniversary of A.I. Akhiezer (QEDSP 2001), October 30 - November 3, 2001, Kharkov, Ukrain

Reflection of nanoparticles

This work is devoted to molecular dynamics modeling of collision of nanoparticle having a small number of degrees of freedom with a structureless plain. The new regularities are established that determine properties of such particles. Generalized collision law is obtained where particle properties are determined by two coefficient, on of which corresponds to restitution coefficient. The discovered regularity predicts the existence of anomalous mode of particle reflection from a massive plain. In this mode, velocity of nanoparticle after reflection from a plain can exceed the initial one. The criterion of realization of such mode is obtained. Anomalous collision mode was observed during numerical modeling. Physical mechanism are discussed of phenomena that are observed during numerical experiments.Comment: 6 pages, 4 figure

Anomalies of Transport in Reflectionally Noninvariant Turbulence

We consider the transport of passive admixture in locally homogeneous isotropic reflectionally noninvariant turbulence of incompressible fluid. It is shown that anomalous convective flow appears which direction does not coincide with that of a mean flow.Comment: LaTeX, 12 page

Nonlinear vortex structures in obliquely rotating stratified fluids driven by small scale non helical forces

In this paper, we study a new type of large-scale instability in obliquely rotating stratified fluids with small scale non-helical turbulence. The small-scale turbulence is generated by the external force with zero helicity and low Reynolds number. The theory uses the method of multiscale asymptotic developments. The nonlinear equations for large scale motions are obtained in the third order of the perturbation theory. In this paper, we consider the linear instability and the stationary nonlinear modes. We obtain solutions in the form of nonlinear Beltrami waves and localized vortex structures as kinks of new type.Comment: 19 pages, 6 figure

The Large scale instability in rotating fluid with small scale force

In this paper, we find a new large scale instability displayed by a rotating flow in forced turbulence. The turbulence is generated by a small scale external force at low Reynolds number. The theory is built on the rigorous asymptotic method of multi-scale development. The nonlinear equations for the instability are obtained at the third order of the perturbation theory. In this article, we explain a detailed study of the nonlinear stage of the instability and generation vortex kinks.Comment: 14 pages, 3 figures. arXiv admin note: text overlap with arXiv:1311.273

Rayleigh-Benard convection in a nonuniformly rotating electrically conductive medium in an external spiral magnetic field

The research is devoted to the stability of convective flow in a nonuniformly rotating layer of an electrically conducting fluid in a spiral magnetic field. The stationary and oscillatory modes of magnetic convection are considered depending on the profile of the angular rotation velocity (Rossby number $\textrm{Ro}$) and on the profile of the external azimuthal magnetic field (magnetic Rossby number $\textrm{Rb}$). The nonlinear dynamic system of Lorentz type equations is obtained by using the Galerkin method. Numerical analysis of these equations has shown the presence of chaotic behavior of convective flows. The criteria of the occurrence of chaotic movements are found. It depends on the parameters of convection: dimensionless numbers of Rayleigh $\textrm{Ra}$, Chandrasekhar $\textrm{Q}$, Taylor $\textrm{Ta}$, and external azimuthal magnetic field with the Rossby magnetic number $\textrm{Rb}=-1$ for Rayleigh $(\textrm{Ro}=-1)$ and Kepler $(\textrm{Ro}=-3/4)$ profiles of the angular rotation velocity of the medium.Comment: 37 pages, 14 figure

Nonlinear dynamo in obliquely rotating electroconductive fluids

In the present paper, we study a new type of large-scale instability, which arises in obliquely rotating electroconductive fluids with a small-scale external force of zero helicity. This force excites small-scale velocity oscillations with a small Reynolds number. We used the method of multiscale asymptotic expansions. The nonlinear equations for vortex and magnetic perturbations motions are obtained up to third order in Reynolds number. The linear stage of the magneto-vortex dynamo, arising as a result of instabilities of the type of hydrodynamic and magnetohydrodynamic $\alpha$ - effects, is investigated. Stationary solutions of nonlinear equations of magneto-vortex dynamo in the form of localized chaotic structures are found numerically

Evolution of gas-filled pore in bounded particles

In the present work, evolution of gas-filled pore inside spherical nanoshells is considered. On the supposition that diffusion fluxes are quasistationary, the nonlinear equation system is obtained analytically, that describes completely the behaviour of gas-filled pore and matrix shell. Two limiting cases are considered: the case when the pore is small as compared to the matrix shell and the case of the pore close to the matrix shell boundary. The characteristic regularities of pore behaviour are established.Comment: 26 pages, 9 figures. arXiv admin note: substantial text overlap with arXiv:1809.0656

Multifractal Interpolation of Universal Multifractals

Basing on invariant properties of universal multifractals we propose a simple algorithm for interpolation of multifractal densities. The algorithm admits generalization to a multidimensional case. Analitically obtained are multifractal characteristics of the function interpolating initial data. We establish the relation between the parameter existing in the algorithm and the Levy index which is the main index for scaling function of universal multifractals.Comment: LaTeX, 9 pages, no figure