arXiv subjects

Victor M. Eguiluz

Publications and source records attributed to Victor M. Eguiluz.

43 records · Page 3Linked to original sources

arXiv2000

The Complex Ginzburg-Landau Equation in the Presence of Walls and Corners

We investigate the influence of walls and corners (with Dirichlet and Neumann boundary conditions) in the evolution of twodimensional autooscillating fields described by the complex Ginzburg-Landau equation. Analytical solutions are found, and arguments provided, to show that Dirichlet walls introduce strong selection mechanisms for the wave pattern. Corners between walls provide additional synchronization mechanisms and associated selection criteria. The numerical results fit well with the theoretical predictions in the parameter range studied.

nlin.CD↗

arXiv2000

Transmission of Information and Herd Behavior: an Application to Financial Markets

We propose a model for stochastic formation of opinion clusters, modelled by an evolving network, and herd behaviour to account for the observed fat-tail distribution in returns of financial-price data. The only parameter of the model is h, the rate of information dispersion per trade, which is a measure of herding behavior. For h below a critical h* the system displays a power-law distribution of the returns with exponential cut-off. However for h>h* an increase in the probability of large returns is found, and may be associated to the occurrence of large crashes.

cond-mat↗

arXiv1999

Average Patterns of Spatiotemporal Chaos: A Boundary Effect

Chaotic pattern dynamics in many experimental systems show structured time averages. We suggest that simple universal boundary effects underly this phenomenon and exemplify them with the Kuramoto-Sivashinsky equation in a finite domain. As in the experiments, averaged patterns in the equation recover global symmetries locally broken in the chaotic field. Plateus in the average pattern wavenumber as a function of the system size are observed and studied and the different behaviors at the central and boundary regions are discussed. Finally, the structure strenght of average patterns is investigated as a function of system size.

chao-dyn↗

arXiv1999

Frozen spatial chaos induced by boundaries

We show that rather simple but non-trivial boundary conditions could induce the appearance of spatial chaos (that is stationary, stable, but spatially disordered configurations) in extended dynamical systems with very simple dynamics. We exemplify the phenomenon with a nonlinear reaction-diffusion equation in a two-dimensional undulated domain. Concepts from the theory of dynamical systems, and a transverse-single-mode approximation are used to describe the spatially chaotic structures.

chao-dyn↗

arXiv1999

Dynamics of Elastic Excitable Media

The Burridge-Knopoff model of earthquake faults with viscous friction is equivalent to a van der Pol-FitzHugh-Nagumo model for excitable media with elastic coupling. The lubricated creep-slip friction law we use in the Burridge-Knopoff model describes the frictional sliding dynamics of a range of real materials. Low-dimensional structures including synchronized oscillations and propagating fronts are dominant, in agreement with the results of laboratory friction experiments. Here we explore the dynamics of fronts in elastic excitable media.

chao-dyn↗

arXiv1998

Boundary Effects in The Complex Ginzburg-Landau Equation

The effect of a finite geometry on the two-dimensional complex Ginzburg-Landau equation is addressed. Boundary effects induce the formation of novel states. For example target like-solutions appear as robust solutions under Dirichlet boundary conditions. Synchronization of plane waves emitted by boundaries, entrainment by corner emission, and anchoring of defects by shock lines are also reported.

chao-dyn↗

arXiv1998

Instability and `Sausage-String' Appearance in Blood Vessels during High Blood Pressure

A new Rayleigh-type instability is proposed to explain the `sausage-string' pattern of alternating constrictions and dilatations formed in blood vessels under influence of a vasoconstricting agent. Our theory involves the nonlinear elasticity characteristics of the vessel wall, and provides predictions for the conditions under which the cylindrical form of a blood vessel becomes unstable.

physics.bio-ph↗