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J Luczka

Publications and source records attributed to J Luczka.

6 recordsLinked to original sources
PubMed2002

Nonequilibrium coupled Brownian phase oscillators.

A model of globally coupled phase oscillators under equilibrium (driven by Gaussian white noise) and nonequilibrium (driven by symmetric dichotomic fluctuations) is studied. For the equilibrium system, the mean-field state equation takes a simple form and the stability of its solution is examined in the full space of order parameters. For the nonequilbrium system, various asymptotic regimes are obtained in a closed analytical form. In a general case, the corresponding master equations are solved numerically. Moreover, the Monte Carlo simulations of the coupled set of Langevin equations of motion is performed. The phase diagram of the nonequilibrium system is presented. For the long time limit, we have found five regimes. Three of them can be obtained from the mean-field theory. One of them, the oscillating regime, cannot be predicted by the mean-field method and has been detected in the Monte Carlo numerical experiments.

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PubMed2002

Kinetics of growth process controlled by convective fluctuations.

A model of the spherical (compact) growth process controlled by a fluctuating local convective velocity field of the fluid particles is introduced. It is assumed that the particle velocity fluctuations are purely noisy, Gaussian, of zero mean, and of various correlations: Dirac delta, exponential, and algebraic (power law). It is shown that for a large class of the velocity fluctuations, the long-time asymptotics of the growth kinetics is universal (i.e., it does not depend on the details of the statistics of fluctuations) and displays the power-law time dependence with the classical exponent 1/2 resembling the diffusion limited growth. For very slow decay of algebraic correlations of fluctuations asymptotically like t(-gamma), gamma in (0,1]), kinetics is anomalous and depends strongly on the exponent gamma. For the averaged radius of the crystal approximately t(1-gamma/2) for 0 approximately (t ln t)1/2 for gamma=1.

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PubMed2001

Multiple current reversal in Brownian ratchets.

We address the problem of stationary transport of overdamped Brownian particles in a one-dimensional spatially periodic potential composed of N hills within one period. We show that in a system driven by both thermal equilibrium fluctuations and symmetric dichotomic fluctuations, a proper manipulation of the barrier heights and slopes of the potential leads to multiple drift velocity reversal. Under optimal conditions, the drift velocity as a function of temperature and intensity of dichotomic fluctuations possesses as many as N extrema of alternating signs. There exist N-1 values of a critical temperature which separate regimes of opposite directions of particle transport.

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