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== Abstract ==
 
== Abstract ==
  
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El presente artículo estudia el efecto de incorporar el término de transporte en las ecuaciones de reacción-difusión de dominio fijo, a través de campos de velocidad toroidal. Se estudia especícamente la formación de patrones de Turing en problemas de difusión-advección-reacción, considerando los modelos de cinética de reacción de Schnackenberg y de glucólisis. Se analizan cuatro casos que se solucionan numéricamente empleando la técnica de elementos finitos. Se encuentra que, para los modelos de glucólisis, el efecto advectivo modfica totalmente la forma de los patrones de Turing obtenidos con difusión-reacción; mientras que para los problemas de Schnackenberg, los patrones originales se distorsionan levemente, haciéndolos rotar en el sentido del campo de velocidades. Además, se determinó, en cada caso, la velocidad límite para la cual el efecto advectivo supera el difusivo y se elimina la formación de patrones. Por otro lado para valores muy bajos en el campo de velocidad, el efecto advectivo no es considerable y no hay modficación en los patrones de Turing originales. Summary 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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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.
  
 
== Full document ==
 
== Full document ==
 
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Latest revision as of 11:02, 14 June 2017

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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