Showing papers by "David A. Kessler published in 1993"
TL;DR: In this article, a set of reaction-diffusion equations coupled to dynamical biological entities (bions), each of which is endowed with signal receptors and response rules, is proposed.
Abstract: The cellular slime mold Dictyostelium discoideum exhibits a variety of spatial patterns as it aggregates to form a multicellular slug. These patterns arise via the interaction of the aggregating amoebae, either via contact or as mediated by chemical signals involving cyclic adenosine monophosphate (AMP). We model this system as a set of reaction-diffusion equations coupled to dynamical biological entities (bions), each of which is endowed with signal receptors and response rules. Simulations of our model reveal a close correspondence with the observed structures. Also, the general framework we propose should be suitable for modeling other biological pattern-forming processes.
130 citations
TL;DR: This work model the myocardium as a simple excitable medium and study via simulation the interaction between a drifting spiral and one or more such defects, interpreting the results in terms of a criterion for the transition between trapped and untrapped drifting spirals.
Abstract: Spiral waves, a type of ``reentrant excitation,'' are believed to be associated with the most dangerous cardiac arrhythmias, including ventricular tachycardia and fibrillation. Recent experimental findings have implicated defective regions as a means of trapping spirals which would otherwise drift and (eventually) disappear. Here, we model the myocardium as a simple excitable medium and study via simulation the interaction between a drifting spiral and one or more such defects. We interpret our results in terms of a criterion for the transition between trapped and untrapped drifting spirals.
33 citations
01 Jan 1993
TL;DR: In this paper, the statistical properties of MBE growth are given by the fourth order continuum equation (COCE) for nonequilibrium surfaces, where ρ is the height of the surface and η is a noise source with correlations.
Abstract: There has been much recent interest in the statistical properties of nonequilibrium surfaces. In particular, much attention has been focussed on theoretical models to describe thin film growth by Molecular Beam Epitaxy. A number of groups 1,2,3 have proposed that the statistical properties of MBE growth are given by the fourth order continuum equation1
$$\mathop h\limits^ \cdot = - {D_4}{
abla ^4}h + {\lambda _4}{
abla ^2}{(
abla h)^2} + \eta$$
(1)
where \(h({\vec x_\parallel },t)\) is the height of the surface and η is a noise source with correlations
$$ \begin{array}{*{20}{c}} {\left\langle {\eta ({{\vec x}_\parallel },t)} \right\rangle = 0} \\ {\left\langle {\eta ({{\vec x}_\parallel },t)\eta ({{\vec x'}_\parallel },t')} \right\rangle = S{\delta ^d}({{\vec x}_\parallel } - {{\vec x'}_\parallel })\delta (t - t')} \end{array} $$
(2)