Does Reaction-diffusion Dynamics on a Fractal Space Imply Power Law Behaviour?

Riley, C.J. and Muldoon, M.R. and Huke, J.P. and Broomhead, D.S. (2007) Does Reaction-diffusion Dynamics on a Fractal Space Imply Power Law Behaviour? [MIMS Preprint]

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Abstract

In biological systems, chemical reactions often take place in complex spatial environments. For example, the translation of m-RNA to produce protein within eukaryotic cells takes place within the extremely crowded cytoplasmic environment and appears to require the spatial coordination of many translation factors. It is important, therefore, to understand the transport processes within such an environment. While there is growing interest in both experimental and computational studies of such environments, it is also important to develop suitable mathematical models. Here, as an example of such a model, we study a reaction-diffusion equation defined on the Sierpinski gasket. Both experimental and computational studies of analogous systems have shown power law behaviour and associated deviations from mass action kinetics. The analysis presented here allows us to distinguish the roles of the fractal domain and of the discreteness of molecular interactions in producing this effect. Indeed, we show that the fractal domain alone is insufficient.

Item Type: MIMS Preprint
Uncontrolled Keywords: Reaction-diffusion equations, fractal geometry, mass-action kinetics, mathematical biology
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 34 Ordinary differential equations
MSC 2010, the AMS's Mathematics Subject Classification > 35 Partial differential equations
MSC 2010, the AMS's Mathematics Subject Classification > 92 Biology and other natural sciences
PACS 2010, the AIP's Physics and Astronomy Classification Scheme > 00 GENERAL PHYSICS > 05 Statistical physics, thermodynamics, and nonlinear dynamical systems
PACS 2010, the AIP's Physics and Astronomy Classification Scheme > 80 INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY > 82 Physical chemistry and chemical physics molecular physics
PACS 2010, the AIP's Physics and Astronomy Classification Scheme > 80 INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY > 87 Biological and medical physics
Depositing User: Professor David Broomhead
Date Deposited: 04 Sep 2007
Last Modified: 08 Nov 2017 18:18
URI: http://eprints.maths.manchester.ac.uk/id/eprint/842

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