Universal diffusion near the golden chaos border

We study local diffusion rate $D$ in Chirikov standard map near the critical golden curve. Numerical simulations confirm the predicted exponent $\alpha=5$ for the power law decay of $D$ as approaching the golden curve via principal resonances with period $q_n$ ($D \sim 1/q^{\alpha}_n$). The universal self-similar structure of diffusion between principal resonances is demonstrated and it is shown that resonances of other type play also an important role.Comment: 4 pages Latex, revtex, 3 uuencoded postscript figure

Asymptotic Statistics of Poincar\'e Recurrences in Hamiltonian Systems with Divided Phase Space

By different methods we show that for dynamical chaos in the standard map with critical golden curve the Poincar\'e recurrences P(\tau) and correlations C(\tau) asymptotically decay in time as P ~ C/\tau ~ 1/\tau^3. It is also explained why this asymptotic behavior starts only at very large times. We argue that the same exponent p=3 should be also valid for a general chaos border.Comment: revtex, 4 pages, 3 ps-figure

Magnetorheological properties of ferrofluids containing clustered particles

A theoretical model is proposed to describe experimental data on the magnetorheological properties of magnetic fluids containing clustered particles consisting of single-domain ferromagnetic nanoparticles distributed in a polymeric shell 80-100 nm in diameter. These fluids combine the sedimentation stability typical of nanodisperse ferrofluids with the high sensitivity of rheological parameters to magnetic fields. The developed model explains the experimentally found long-term rheological relaxation and residual stress that is retained after the medium ceases to flow. © 2013 Pleiades Publishing, Ltd

Theoretical study of the rheological properties of bidisperse magnetic fluids

Настоящая работа посвящена теоретическому исследованию реологических свойств суспензии, состоящей из микронных намагничивающихся частиц в нано-дисперсной феррожидкости. В последние годы, эти системы были синтезированы несколькими научными группами с целью повышения технологических свойств традиционных магнитных жидкостей. Предполагается, что микронные частицы под действием внешнего магнитного поля, образуют линейные цепочечные агрегаты. Анализ показывает, что присутствие магнитной жидкости может значительно увеличить магнитовязкий эффект в суспензии микронных частиц. В отличие от традиционной модели магнитореологических суспензий с цепочками, рассматривается эффект взаимного намагничивания частиц в цепочке. Оценки показывают, что этот эффект значительно увеличивает макроскопическое вязкое напряжение в суспензии, поэтому он должен быть принят во внимание при теоретическом описании и интерпретации экспериментов реологических свойств магнитных суспензий.This work deals with theoretical study of rheological properties of a suspension of mi-cron-sized magnetizable particles in a nanodisperse ferrofluid. For the recent years, these systems have been synthesized in several teams in order to enhance technological proper-ties of traditional magnetic fluids. It assumed that the micron-sized particles, under the action of an applied magnetic field, form the linear chain-like aggregates. Analysis shows that the presence of the ferrofluid can significantly increase the magnetoviscous effect in the suspension of the micron-sized particles. Unlike the traditional models of magnetorheological suspensions with the chains, studied effect of the mutual magnetiza-tion of the particles in the chains. Estimates show that this effect significantly increases the macroscopical viscous stress in the suspension, that is why it must be taken into ac-count while theoretical descriptions and interpretation of experiments on the rheological properties of magnetic suspensions.Программа развития УрФУ на 2013 год (п.2.1.1.1

Big Entropy Fluctuations in Nonequilibrium Steady State: A Simple Model with Gauss Heat Bath

Large entropy fluctuations in a nonequilibrium steady state of classical mechanics were studied in extensive numerical experiments on a simple 2-freedom model with the so-called Gauss time-reversible thermostat. The local fluctuations (on a set of fixed trajectory segments) from the average heat entropy absorbed in thermostat were found to be non-Gaussian. Approximately, the fluctuations can be discribed by a two-Gaussian distribution with a crossover independent of the segment length and the number of trajectories ('particles'). The distribution itself does depend on both, approaching the single standard Gaussian distribution as any of those parameters increases. The global time-dependent fluctuations turned out to be qualitatively different in that they have a strict upper bound much less than the average entropy production. Thus, unlike the equilibrium steady state, the recovery of the initial low entropy becomes impossible, after a sufficiently long time, even in the largest fluctuations. However, preliminary numerical experiments and the theoretical estimates in the special case of the critical dynamics with superdiffusion suggest the existence of infinitely many Poincar\'e recurrences to the initial state and beyond. This is a new interesting phenomenon to be farther studied together with some other open questions. Relation of this particular example of nonequilibrium steady state to a long-standing persistent controversy over statistical 'irreversibility', or the notorious 'time arrow', is also discussed. In conclusion, an unsolved problem of the origin of the causality 'principle' is touched upon.Comment: 21 pages, 7 figure

Big Entropy Fluctuations in Statistical Equilibrium: The Macroscopic Kinetics

Large entropy fluctuations in an equilibrium steady state of classical mechanics were studied in extensive numerical experiments on a simple 2--freedom strongly chaotic Hamiltonian model described by the modified Arnold cat map. The rise and fall of a large separated fluctuation was shown to be described by the (regular and stable) "macroscopic" kinetics both fast (ballistic) and slow (diffusive). We abandoned a vague problem of "appropriate" initial conditions by observing (in a long run)spontaneous birth and death of arbitrarily big fluctuations for any initial state of our dynamical model. Statistics of the infinite chain of fluctuations, reminiscent to the Poincar\'e recurrences, was shown to be Poissonian. A simple empirical relation for the mean period between the fluctuations (Poincar\'e "cycle") has been found and confirmed in numerical experiments. A new representation of the entropy via the variance of only a few trajectories ("particles") is proposed which greatly facilitates the computation, being at the same time fairly accurate for big fluctuations. The relation of our results to a long standing debates over statistical "irreversibility" and the "time arrow" is briefly discussed too.Comment: Latex 2.09, 26 pages, 6 figure

Fractal Weyl law for quantum fractal eigenstates

The properties of the resonant Gamow states are studied numerically in the semiclassical limit for the quantum Chirikov standard map with absorption. It is shown that the number of such states is described by the fractal Weyl law and their Husimi distributions closely follow the strange repeller set formed by classical orbits nonescaping in future times. For large matrices the distribution of escape rates converges to a fixed shape profile characterized by a spectral gap related to the classical escape rate.Comment: 4 pages, 5 figs, minor modifications, research at http://www.quantware.ups-tlse.fr

Microchannel avalanche photodiode with wide linearity range

Design and physical operation principles of new microchannel avalanche photodiode (MC APD) with gain up to 10^5 and linearity range improved an order of magnitude compared to known similar devices. A distinctive feature of the new device is a directly biased p-n junction under each pixel which plays role of an individual quenching resistor. This allows increasing pixel density up to 40000 per mm^2 and making entire device area sensitive.Comment: Submitted to Journal of Technical Physic

Chaos in the Einstein-Yang-Mills Equations

Yang-Mills color fields evolve chaotically in an anisotropically expanding universe. The chaotic behaviour differs from that found in anisotropic Mixmaster universes. The universe isotropizes at late times, approaching the mean expansion rate of a radiation-dominated universe. However, small chaotic oscillations of the shear and color stresses continue indefinitely. An invariant, coordinate-independent characterisation of the chaos is provided by means of fractal basin boundaries.Comment: 3 pages LaTeX + 3 pages of figure

Evolution of wave packets in quasi-1D and 1D random media: diffusion versus localization

We study numerically the evolution of wavepackets in quasi one-dimensional random systems described by a tight-binding Hamiltonian with long-range random interactions. Results are presented for the scaling properties of the width of packets in three time regimes: ballistic, diffusive and localized. Particular attention is given to the fluctuations of packet widths in both the diffusive and localized regime. Scaling properties of the steady-state distribution are also analyzed and compared with theoretical expression borrowed from one-dimensional Anderson theory. Analogies and differences with the kicked rotator model and the one-dimensional localization are discussed.Comment: 32 pages, LaTex, 11 PostScript figure