383 research outputs found
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
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
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
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
) and on the profile of the external azimuthal magnetic field
(magnetic Rossby number ). 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 ,
Chandrasekhar , Taylor , and external azimuthal
magnetic field with the Rossby magnetic number for Rayleigh
and Kepler 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 - 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
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