Biomedical subjects

John H Merkin

Publications and source records attributed to John H Merkin.

3 recordsLinked to original sources

PubMed2005

The emergence of wave emitting centres in an excitable medium.

The response of an excitable biological medium to a double local stimulus is considered within the context of a mathematical model for a layer of starving cells of Dictyostelium discoideum, with both spatially one- and two-dimensional (1D and 2D) system being investigated. In contrast to the response usually seen in excitable media, whereby each superthreshold stimulus delivered to the relaxed medium results in the initiation of just one travelling wave, a source emitting a sequence of waves can develop in the present excitable medium after the second stimulus. In a 1D system, only transient wave sources forming a limited number of waves are found. In 2D systems, a permanent wave sources consisting in a pair of spirals are observed as well as the transient wave sources forming circular wave patterns. The general features of the medium dynamics that underlie the observed responses to the double stimulus are discussed.

Animals↗

PubMed2003

Isothermal flame balls: effect of autocatalyst decay.

The steady, spherically symmetric solutions to the reaction-diffusion equations based on a simple autocatalytic reaction followed by the decay of the autocatalyst are considered. Three parameters-the orders with respect to the autocatalyst in the autocatalysis p and in the decay q and the rate of decay of the autocatalyst relative to its autocatalytic production K-determine the steady concentration profiles. Numerical integrations for a fixed value of the order of the autocatalyst show that the concentration profiles have different forms depending on whether q /=p. In the former case, there is a critical decay rate K(crit) for solutions to exist, with multiple solutions for K<K(crit). In the latter case, there is a single solution for each value of K. This difference in the nature of the solution is confirmed by an analysis for p large. The temporal stability of the isothermal flame balls is examined, with temporally stable solutions being possible, provided that the ratio of the diffusion coefficient of the autocatalyst to that of the reactant is sufficiently small. The change in stability appears only when there are multiple solutions and is through a subcritical Hopf bifurcation.

Journal Article↗

PubMed2002

Isothermal flame balls.

The existence of steady, spherically symmetric wave fronts ("isothermal flame balls") in chemical reaction systems exhibiting autocatalysis is demonstrated. Such solutions require relatively high kinetic orders p with respect to the autocatalytic species, with p>5, but occur even with equal diffusion coefficients. The flame balls are unstable, but have relevance as they indicate the minimum size for a perturbation to initiate a propagating front. A flame ball radius R(b) is identified and the dependence of this quantity on the autocatalytic order is determined. This shows R(b) tending to infinity as p-->5(+) and as p--> infinity, with a minimum for p approximately 6.71. Numerical computations are confirmed by asymptotic analysis appropriate for p-->5(+) and for systems with p large.

Journal Article↗