Biomedical subjects

Martin B Tarlie

Publications and source records attributed to Martin B Tarlie.

3 recordsLinked to original sources

PubMed2005

Quantifying stochastic outcomes.

A system consisting of two species in a fluctuating environment, when the interspecies competition for resources is strong, will have a stochastic outcome: only one of the species will survive, but there is no a priori way of knowing which one this will be. It is natural in such a situation to ask what will be the probability of one or another of the species surviving. This probability is calculated as a function of the average growth rates and the strengths of the interaction between the species and of the randomness. This is an example of a class of stochastic problems in which multiple final states are available for occupation. We refer to the choice of final states as state selection, and the probabilities of final states being occupied as state-selection probabilities. The calculation of these probabilities is carried out in the context of a model of the system which consists of two coupled stochastic differential equations. By reformulating these equations in terms of path integrals, the powerful methods based on the use of optimal paths may be utilized to calculate the probability of one outcome or the other. The analytical results obtained by using this technique agree well with numerical simulations when both species have the same growth rate. Although the method adopted rests on the assumption that the strength of the fluctuations, D , is small, remarkably the analytic results are still found to be in good agreement with the numerical results when D is of order 1.

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PubMed2004

Optimal paths and the calculation of state selection probabilities.

The addition of noise to a dynamical system means that initial states near points of instability may no longer decay to a unique stable state. A common example of this behavior occurs in a dynamical system with two degrees of freedom and with two or more stable states. If the initial state of the system is near the separatrices bounding the basins of attraction of these stable states, then the addition of noise to the system means that there is a nonzero probability that the stable state selected is in a different basin of attraction to that of the initial state. We discuss a method of calculating these state-selection probabilities based on a path-integral representation of the stochastic dynamics. The relationship of this approach to a method based on the solution of the backward Fokker-Planck equation is particularly stressed, since this was used in previous studies of problems of this type. However, while the method based on the backward Fokker-Planck equation is a powerful one for systems with one degree of freedom, in systems with more degrees of freedom it is much less useful. Since the standard method of solution in this case involves a series of mappings onto a deterministic dynamics which is simply the classical dynamics associated with the path-integral formulation, we argue that for systems with more than one degree of freedom, the path-integral method is a very natural way of calculating state-selection probabilities. We illustrate this on a simple example taken from population biology, and find that the state-selection probabilities are in excellent agreement with Monte Carlo simulations.

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PubMed2002

Instabilities and resistance fluctuations in thin accelerated superconducting rings.

The nonequilibrium properties of a driven quasi-one-dimensional superconducting ring subjected to a constant electromotive force (emf) is studied. The emf accelerates the superconducting electrons until the critical current is reached and a dissipative phase slip occurs that lowers the current. The phase-slip phenomena is examined as a function of the strength of the emf, thermal noise, and normal state resistivity. Numerical and analytic methods are used to make detailed predictions for the magnitude of phase slips and subsequent dissipation.

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