Biomedical subjects

Syed Shahed Riaz

Publications and source records attributed to Syed Shahed Riaz.

3 recordsLinked to original sources

PubMed2005

Spiral pattern in chlorite-iodide-malonic acid reaction: a theoretical and numerical study.

The development of spiral pattern in a model representing chlorite-iodide-malonic acid reaction is investigated theoretically and numerically. We have carried out a multiple scale analysis of the model to identify the experimentally admissible parameter range and the appropriate perturbation for shifting Hopf bifurcation boundary towards the oscillating region. Our theoretical analysis is corroborated by numerical simulation.

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PubMed2005

Noise-induced instability: an approach based on higher-order moments.

Noise-induced transitions in the organization of systems far from equilibrium have been of vital interest. Although the effects of additive and multiplicative noise have been widely studied, it is only the multiplicative noise that can be dealt with within the scope of a linear analysis of first moments of the spatiotemporal perturbations, by the application of Novikov's theorem. For the case of additive noise, the corresponding straightforward linear analysis of the first moment throws no light on the effect of the noise on stability conditions. We propose here a simple approach based on higher-order moments to show how additive noise can give rise to noise-induced instability in spatially extended systems, at times leading to pattern formation. Our theoretical analysis is corroborated by numerical simulations on two simple one-component reaction-diffusion systems in two dimensions.

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PubMed2004

Mobility-induced instability and pattern formation in a reaction-diffusion system.

Ions undergoing a reaction-diffusion process are susceptible to electric field. We show that a constant external field may induce a kind of instability on the state stabilized by diffusion in a reaction-diffusion system giving rise to formation of pattern even when the diffusion coefficients of the reactants are equal. The origin of the pattern is due to the difference in mobilities of the two species and is thus markedly different from that of deformed Turing pattern in presence of the field. While this differential flow instability had been shown earlier to result in traveling waves, we realize in the context of stationary pattern formation in a typical reaction-diffusion-advective system. Our analysis is based on a numerical simulation of a generic model on a two-dimensional domain.

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