Biomedical subjects

K Showalter

Publications and source records attributed to K Showalter.

13 recordsLinked to original sources

PubMed2001

Spatial symmetry breaking in the Belousov-Zhabotinsky reaction with light-induced remote communication.

Domains containing spiral waves form on a stationary background in a photosensitive Belousov-Zhabotinsky reaction with light-induced alternating nonlocal feedback. Complex behavior of colliding and splitting wave fragments is found with feedback radii comparable to the spiral wavelength. A linear stability analysis of the uniform stationary states in an Oregonator model reveals a spatial symmetry breaking instability. Numerical simulations show behavior in agreement with that found experimentally and also predict a variety of other new patterns.

Journal Article↗

PubMed2001

Wave propagation in subexcitable media with periodically modulated excitability.

Wave propagation in a photosensitive, subexcitable Belousov-Zhabotinsky medium is made possible by periodic modulation of a homogeneous illumination field. The propagation can be understood in terms of an interplay between the radial expansion of the wave and the motion of its free ends as the excitability varies periodically. This description leads to a simple kinematic analysis that provides insights into the initial conditions and forcing parameters giving rise to sustained wave propagation.

Journal Article↗

PubMed2001

Experimental and theoretical studies of feedback stabilization of propagating wave segments.

Experimental and theoretical studies of the excitability boundary for spiral wave behavior are presented. The boundary is defined by unstable wave segments, which are stabilized by using a negative-feedback control algorithm. A kinematic description of the constant-size, constant-shape wave segments is presented.

Journal Article↗

PubMed2000

Self-segregation of competitive chaotic populations

The dynamical behavior of species competing for a common resource is studied with a reaction-diffusion system based on cubic autocatalysis. Randomly seeded populations self-segregate to form a complex network of domains separated by distinct interfaces. For chaotic populations in one-dimensional media, the interfaces exhibit irregular motions on long time scales. In two-dimensional media, the interface motions are governed by curvature-induced drift.

Journal Article↗

PubMed2000

Coherent structure analysis of spatiotemporal chaos

We introduce a measure to quantify spatiotemporal turbulence in extended systems. It is based on the statistical analysis of a coherent structure decomposition of the evolving system. Applied to a cellular excitable medium and a reaction-diffusion model describing the oxidation of CO on Pt(100), it reveals power-law scaling of the size distribution of coherent space-time structures for the state of spiral turbulence. The coherent structure decomposition is also used to define an entropy measure, which sharply increases in these systems at the transition to turbulence.

Journal Article↗

PubMed1999

Uncertain destination dynamics.

Certain dynamical systems exhibit a sensitivity to initial conditions in which the asymptotic state is selected from an infinite number of possible states. The phase space of such systems is foliated with "attractors," each of which is associated with a particular set of initial conditions. The associated uncertain destination dynamics can be analyzed by an appropriate reduction of the full system to a subsystem that explicitly yields the dynamics.

Journal Article↗

PubMed1996