Biomedical subjects

Ehud Meron

Publications and source records attributed to Ehud Meron.

6 recordsLinked to original sources

PubMed2006

Resonant and nonresonant patterns in forced oscillators.

Uniform oscillations in spatially extended systems resonate with temporal periodic forcing within the Arnold tongues of single forced oscillators. The Arnold tongues are wedge-like domains in the parameter space spanned by the forcing amplitude and frequency, within which the oscillator's frequency is locked to a fraction of the forcing frequency. Spatial patterning can modify these domains. We describe here two pattern formation mechanisms affecting frequency locking at half the forcing frequency. The mechanisms are associated with phase-front instabilities and a Turing-like instability of the rest state. Our studies combine experiments on the ruthenium catalyzed light-sensitive Belousov-Zhabotinsky reaction forced by periodic illumination, and numerical and analytical studies of two model systems, the FitzHugh-Nagumo model and the complex Ginzburg-Landau equation, with additional terms describing periodic forcing.

Biomechanical Phenomena↗

PubMed2004

BLOCH-front turbulence in a periodically forced Belousov-Zhabotinsky reaction.

Experiments on a periodically forced Belousov-Zhabotinsky chemical reaction show front breakup into a state of spatiotemporal disorder involving continual events of spiral-vortex nucleation and destruction. Using the amplitude equation for forced oscillatory systems and the normal form equations for a curved front line, we identify the mechanism of front breakup and explain the experimental observations.

Biological Clocks↗

PubMed2004

Resonance tongues and patterns in periodically forced reaction-diffusion systems.

Various resonant and near-resonant patterns form in a light-sensitive Belousov-Zhabotinsky (BZ) reaction in response to a spatially homogeneous time-periodic perturbation with light. The regions (tongues) in the forcing frequency and forcing amplitude parameter plane where resonant patterns form are identified through analysis of the temporal response of the patterns. Resonant and near-resonant responses are distinguished. The unforced BZ reaction shows both spatially uniform oscillations and rotating spiral waves, while the forced system shows patterns such as standing-wave labyrinths and rotating spiral waves. The patterns depend on the amplitude and frequency of the perturbation, and also on whether the system responds to the forcing near the uniform oscillation frequency or the spiral wave frequency. Numerical simulations of a forced FitzHugh-Nagumo reaction-diffusion model show both resonant and near-resonant patterns similar to the BZ chemical system.

Journal Article↗

PubMed2003

Vortex-pair dynamics in anisotropic bistable media: a kinematic approach.

In isotropic bistable media, a vortex pair typically evolves into rotating spiral waves. In an anisotropic system, instead of spiral waves, the vortices can form wave fragments that propagate with a constant speed in a given direction determined by the system's anisotropy. The fragments may propagate invariably, shrink, or expand. We develop a kinematic approach for the study of vortex-pair dynamics in anisotropic bistable media and use it to capture the wave fragment dynamics.

Journal Article↗

PubMed2002

Pattern formation on anisotropic and heterogeneous catalytic surfaces.

We review experimental and theoretical work addressing pattern formation on anisotropic and heterogeneous catalytic surfaces. These systems are typically modeled by reaction-diffusion equations reflecting the kinetics and transport of the involved chemical species. Here, we demonstrate the influence of anisotropy and heterogeneity in a simplified model, the FitzHugh-Nagumo equations. Anisotropy causes stratification of labyrinthine patterns and spiral defect chaos in bistable media. For heterogeneous media, we study the situation where the heterogeneity appears on a length scale shorter than the typical pattern length scale. Homogenization, i.e., computation of effective medium properties, is applied to an example and illustrated with simulations in one (fronts) and two dimensions (spirals). We conclude with a discussion of open questions and promising directions that comprise the coupling of the microscopic structure of the surface to the macroscopic concentration patterns and the fabrication of nanostructures with heterogeneous surfaces as templates. (c) 2002 American Institute of Physics.

Journal Article↗

PubMed1994

Complex patterns in reaction-diffusion systems: A tale of two front instabilities.

Two front instabilities in a reaction-diffusion system are shown to lead to the formation of complex patterns. The first is an instability to transverse modulations that drives the formation of labyrinthine patterns. The second is a nonequilibrium Ising-Bloch (NIB) bifurcation that renders a stationary planar front unstable and gives rise to a pair of counterpropagating fronts. Near the NIB bifurcation the relation of the front velocity to curvature is highly nonlinear and transitions between counterpropagating fronts become feasible. Nonuniformly curved fronts may undergo local front transitions that nucleate spiral-vortex pairs. These nucleation events provide the ingredient needed to initiate spot splitting and spiral turbulence. Similar spatiotemporal processes have been observed recently in the ferrocyanide-iodate-sulfite reaction.

Journal Article↗