F. Javier de la Rubia

Noise-induced spatial patterns

By modifying the spatial coupling a la Swift-Hohenberg in the model introduced in Phys. Rev. Lett. 73 (1994) 3395, we obtain a system that displays noise-induced spatial patterns. We present a mean field theory of this phenomenon and verify some of its predictions by numerical simulations.

Numerical analysis of transient behavior in the discrete random logistic equation with delay

Abstract The transient behavior of the discrete logistic equation with delay under parametric noise is numerically studied. Stability domains for different correlation times and intensities of the noise, and different memory strengths are established. An optimal correlation time for the appearance of the transient behavior is obtained.

Mixing and equilibrium probability densities in classical statistical mechanics

The effects of the mixing property of the microscopic dynamics on the limiting behaviour of macroscopic and microscopic probability densities in classical statistical mechanics are studied in detail.

On the “best Fokker-Planck equation” for systems driven by colored noise

Abstract The “best Fokker-Planck equation” for systems driven by colored noise has been criticized because it may lead to probability distributions that have a finite region of support. Herein we argue that sometimes this behavior might point to problems in the model used to represent the physical system. We illustrate this contention in the context of a stochastic model of a type frequently used to describe intensity fluctuations in a dye laser. A “parent” model that is bounded throughout the entire range of the variable leads to a probability density obtained with the BFPE technique that is well-behaved over the entire phase space. We compare the results of the BFPE with direct computer simulations of the stochastic differential equation, and suggest a combination of parameters whose value characterizes the applicability of the BFPE for this model.

Spiral wave annihilation by low-frequency planar fronts in a model of excitable media

We perform numerical lattice simulations of an excitable medium. We show that the interaction of a spiral wave with a periodic train of planar fronts leads to annihilation of the spiral wave even when i) the period of the fronts is longer than the period of the spiral and ii) the annihilating fronts are released at a significant distance from the spiral. The observed annihilation is not due to spiral drift, and occurs well inside the lattice.

Patterns of spiral wave attenuation by low-frequency periodic planar fronts

There is evidence that spiral waves and their breakup underlie mechanisms related to a wide spectrum of phenomena ranging from spatially extended chemical reactions to fatal cardiac arrhythmias [A. T. Winfree, The Geometry of Biological Time (Springer-Verlag, New York, 2001); J. Schutze, O. Steinbock, and S. C. Muller, Nature 356, 45 (1992); S. Sawai, P. A. Thomason, and E. C. Cox, Nature 433, 323 (2005); L. Glass and M. C. Mackey, From Clocks to Chaos: The Rhythms of Life (Princeton University Press, Princeton, 1988); R. A. Gray et al., Science 270, 1222 (1995); F. X. Witkowski et al., Nature 392, 78 (1998)]. Once initiated, spiral waves cannot be suppressed by periodic planar fronts, since the domains of the spiral waves grow at the expense of the fronts [A. N. Zaikin and A. M. Zhabotinsky, Nature 225, 535 (1970); A. T. Stamp, G. V. Osipov, and J. J. Collins, Chaos 12, 931 (2002); I. Aranson, H. Levine, and L. Tsimring, Phys. Rev. Lett. 76, 1170 (1996); K. J. Lee, Phys. Rev. Lett. 79, 2907 (1997); F. Xie, Z. Qu, J. N. Weiss, and A. Garfinkel, Phys. Rev. E 59, 2203 (1999)]. Here, we show that introducing periodic planar waves with long excitation duration and a period longer than the rotational period of the spiral can lead to spiral attenuation. The attenuation is not due to spiral drift and occurs periodically over cycles of several fronts, forming a variety of complex spatiotemporal patterns, which fall into two distinct general classes. Further, we find that these attenuation patterns only occur at specific phases of the descending fronts relative to the rotational phase of the spiral. We demonstrate these dynamics of phase-dependent spiral attenuation by performing numerical simulations of wave propagation in the excitable medium of myocardial cells. The effect of phase-dependent spiral attenuation we observe can lead to a general approach to spiral control in physical and biological systems with relevance for medical applications.

THE STOCHASTIC STABILIZED KURAMOTO-SIVASHINSKY EQUATION : A MODEL FOR COMPACT ELECTRODEPOSITION GROWTH

We report on numerical studies of the dynamical behavior of a stochastic version of the stabilized Kuramoto-Shivashinsky equation, in 1 + 1 dimensions, at short times and small length scales. The solution evolves as a rough growing interface, showing a well defined growth exponent /3 = 0.37f0.04 and a roughness exponent that saturates at a value (Y = 0.8010.04. A morphological instability may also develop for certain values of the control parameter and with a well-defined characteristic length. The resulting dynamical scenario and scaling properties compare fairly well with experimental results on slow compact electrodeposition growth. @ 1997 Elsevier Science B.V.

ANALYSIS OF THE BEHAVIOR OF A RANDOM NONLINEAR DELAY DISCRETE EQUATION

The stability problem for a class of nonlinear delay discrete equations under parametric noise perturbations is considered. The effect of the delay on the asymptotic behavior of the system is studied, and a power law dependency between an optimal noise correlation time for the escape from the physically meaningful region and the memory strength is numerically deduced. The influence of multiple delays is also analyzed.

A 3-states magnetic model of binary decisions in sociophysics

We study a diluted Blume–Capel model of 3-states sites as an attempt to understand how some social processes as cooperation or organization happen. For this aim, we study the effect of the complex network topology on the equilibrium properties of the model, by focusing on three different substrates: random graph, Watts–Strogatz and Newman substrates. Our computer simulations are in good agreement with the corresponding analytical results.

Initial non-equilibrium ensembles: Application to the ideal gas

Abstract We consider an ideal gas in non-equilibrium transient states in order to study the role of different initial ensembles that arise from the partial information about the initial state of the system. The ensembles are the generalized canonical ensemble and the generalized microcanonical ensemble. Special attention is paid to the correct definition of the latter when continous fields are taken into account. Averages of one-body functions are found to be equal in both ensembles up to terms of order 1 N whereas their fluctuations are essentially different in each ensemble. In particular we compute the density-density correlation function in different transient states for both ensembles.