Abstract

This article studies the effect of the inclusion of the transport term in the reaction-diffusion equations, through toroidal velocity fields. The formation of Turing patterns in diffusion-advection-reaction problems is studied specifically, considering the Schnacken- berg reaction kinetics and glycolysis models. Four cases are analyzed and solved numerically using finite elements. Is found that, for the glycolysis models, the advective effect totally modifies the form of the obtained Turing patterns with diffusion-reaction; whereas for the problems of Schnackenberg, the original patterns distort themselves slightly, making them to rotate in the direction of the velocity field. Also this work was able to determine, that for high values of velocity, the advective effect surpasses the difusive one and the instability by diffusion is eliminated. On the other hand for very low values in the velocity field, the advective effect is not considerable and there is no modification in the original Turing pattern.

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Published on 01/04/10
Accepted on 01/04/10
Submitted on 01/04/10

Volume 26, Issue 2, 2010
Licence: CC BY-NC-SA license

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