Uniform Estimate of the Relative Free Energy by the Dissipation Rate for Finite Volume Discretized Reaction-Diffusion Systems

2014 ◽  
pp. 275-283 ◽  
Author(s):  
André Fiebach ◽  
Annegret Glitzky
Keyword(s):  
Free Energy ◽  
Finite Volume ◽  
Dissipation Rate ◽  
Uniform Estimate ◽  
Reaction Diffusion ◽  
Reaction Diffusion Systems ◽  
Relative Free Energy ◽  
Diffusion Systems

PATTERN FORMATION IN CHEMOTAXIC REACTION-DIFFUSION SYSTEMS

2012 ◽  
Vol 05 (03) ◽  
pp. 1260013
Author(s):  
HIROTO SHOJI ◽  
KEITARO SAITOH
Keyword(s):  
Free Energy ◽  
Pattern Formation ◽  
Three Dimensional ◽  
Reaction Diffusion ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Volume Filling ◽  
Reaction Diffusion Systems ◽  
Receptor Aggregation ◽  
Diffusion Systems

In this study, we investigate two-dimensional patterns generated by chemotaxis reaction-diffusion systems. We numerically examine the Keller–Segel models with the volume-filling aggregation term and the receptor aggregation term in two dimensions. Spotted, striped and reversed spotted patterns are obtained as stable motionless equilibrium patterns. The relative stability of these patterns is studied numerically on the basis of the derived free energy. The intuitive understanding of these generated patterns and the relation with three-dimensional patterns are also discussed.

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