Biomedical subjects

Irving R Epstein

Publications and source records attributed to Irving R Epstein.

7 recordsLinked to original sources

PubMed2003

Superlattice Turing structures in a photosensitive reaction-diffusion system.

Families of complex superlattice structures, consisting of combinations of basic hexagonal or square patterns, are found in a photosensitive reaction-diffusion system. The structures are induced by simple illumination patterns whose wavelengths are appropriately related to that of the system's intrinsic Turing pattern. Computer simulations agree with the structures and their stability. The technique offers a general approach to generating superlattices for use in information storage and other applications.

Journal Article↗

PubMed2003

Oscillatory Turing patterns in reaction-diffusion systems with two coupled layers.

A model reaction-diffusion system with two coupled layers yields oscillatory Turing patterns when oscillation occurs in one layer and the other supports stationary Turing structures. Patterns include "twinkling eyes," where oscillating Turing spots are arranged as a hexagonal lattice, and localized spiral or concentric waves within spot-like or stripe-like Turing structures. A new approach to generating the short-wave instability is proposed.

Journal Article↗

PubMed2003

Dash waves in a reaction-diffusion system.

Patterns in reaction-diffusion systems generally consist of smooth traveling waves or of stationary, discontinuous Turing structures. Hybrid patterns that blend the properties of waves and Turing structures have not previously been observed. We report observation of dash waves, which consist of wave segments regularly separated by gaps, moving coherently in the Belousov-Zhabotinsky system dispersed in water-in-oil microemulsion. Dash waves emerge from the interaction between excitable and pseudo-Turing-unstable steady states. We are able to generate dash waves in simulations with simple models.

Journal Article↗

PubMed2003

Optimization of robustness and connectivity in complex networks.

Scale-free networks rely on a relatively small number of highly connected nodes to achieve a high degree of interconnectivity and robustness to random failure, but suffer from a high sensitivity to directed attack. In this paper we describe a parameterized family of networks and analyze their connectivity and sensitivity, identifying a network that has an interconnectedness closer to that of a scale-free network, a robustness to attack closer to that of an exponential network, and a resistance to failure better than that of either of those networks.

Models, Biological↗

PubMed2002

Oscillatory photochemical decomposition of tetrathionate ion.

When subject to illumination, tetrathionate ion decomposes in an oscillatory fashion with a period of about 1 h to yield products identified as colloidal sulfur and trithionate ion. This system represents the first experimental example of a stirred, batch photochemical oscillator. A simple model consisting of four reaction steps and four adjustable rate parameters gives good agreement with the observed oscillatory behavior.

Journal Article↗

PubMed2002

Spatial resonances and superposition patterns in a reaction-diffusion model with interacting Turing modes.

Spatial resonances leading to superlattice hexagonal patterns, known as "black-eyes," and superposition patterns combining stripes and/or spots are studied in a reaction-diffusion model of two interacting Turing modes with different wavelengths. A three-phase oscillatory interlacing hexagonal lattice pattern is also found, and its appearance is attributed to resonance between a Turing mode and its subharmonic.

Diffusion↗

PubMed2002

Packet waves in a reaction-diffusion system.

The finite-wavelength instability gives rise to a new type of wave in reaction-diffusion systems: packet waves, which propagate only within a wave packet, are found in experiments on the Belousov-Zhabotinsky reaction dispersed in water-in-oil AOT microemulsion (BZ-AOT) as well as in model simulations. Inwardly moving packet waves with negative curvature occur in experiments and in a model of the BZ-AOT system when the dispersion d omega(k)/dk is negative at the characteristic wave number k(0). This result sheds light on the origin of anti-spirals.

Journal Article↗