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Information Center for Mathematical Science

PAC

BIOMIXING BY CHEMOTAXIS AND EFFICIENCY OF BIOLOGICAL REACTIONS: THE CRITICAL REACTION CASE
Author LENYA RYZHIK (Stanford University)
Homepage Url http://math.stanford.edu/~ryzhik/
Coauthors ALEXANDER KISELEV
Abstract Many phenomena in biology involve both reactions and chemotaxis. These processes can clearly in uence each other, and chemotaxis can play an important role in sustaining and speeding up the reaction. In continuation of our work [14], we consider a model with a single density function involving di usion, advection, chemotaxis, and absorbing reaction. The model is motivated, in particular, by the studies of coral broadcast spawning, where experimental observations of the eciency of fertilization rates significantly exceed the data obtained from numerical models that do not take chemotaxis (attraction of sperm gametes by a chemical secreted by egg gametes) into account. We consider the case of the weakly coupled quadratic reaction term, which is the most natural from the biological point of view and was left open in [14]. The result is that similarly to [14], the chemotaxis plays a crucial role in ensuring eciency of reaction. However, mathematically, the picture is quite di erent in the quadratic reaction case and is more subtle. The reaction is now complete even in the absence of chemotaxis, but the timescales are very di erent. Without chemotaxis, the reaction is very slow, especially for the weak reaction coupling. With chemotaxis, the timescale and eciency of reaction are independent of the coupling parameter.
Abstract Url http://math.stanford.edu/~ryzhik/coralscritical-submit.pdf