Splitting Schemes and Segregation in Reaction Cross-Diffusion Systems

Cross-diffusion and pattern formation in reaction-diffusion systems.

Cross-diffusion, the phenomenon in which a gradient in the concentration of one species induces a flux of another chemical species, has generally been neglected in the study of reaction-diffusion systems. We summarize experiments that demonstrate that cross-diffusion coefficients can be quite significant, even exceeding "normal," diagonal diffusion coefficients in magnitude in systems that invo...

Cross-diffusion Induced Instability and Stability in Reaction-diffusion Systems

In a reaction-diffusion system, diffusion can induce the instability of a uniform equilibrium which is stable with respect to a constant perturbation, as shown by Turing in 1950s. We show that cross-diffusion can destabilize a uniform equilibrium which is stable for the kinetic and self-diffusion reaction systems; on the other hand, cross-diffusion can also stabilize a uniform equilibrium which...

coordination of protective schemes in distribution and subtransmission systems including distributed generation

نصب منابع پراکنده در سیستم های توزیع و فوق توزیع علاوه بر مزیت های فراوان، مشکلاتی را هم به همراه دارد. یکی از این مشکلات تأثیر این منابع روی اندازه جریان های اتصال کوتاه است. به طور معمول از حفاظت های مبتنی بر اصل جریان زیاد در سیستم های توزیع و فوق توزیع استفاده می شود. از مهمترین طرح های حفاظتی استفاده شده در فیدرهای توزیع، حفاظت فیوز- ریکلوزر است. همچنین از طرح های حفاظتی جریان زیاد جهتی در...

Stochastic operator-splitting method for reaction-diffusion systems.

Many biochemical processes at the sub-cellular level involve a small number of molecules. The local numbers of these molecules vary in space and time, and exhibit random fluctuations that can only be captured with stochastic simulations. We present a novel stochastic operator-splitting algorithm to model such reaction-diffusion phenomena. The reaction and diffusion steps employ stochastic simul...

Pattern formation in reaction-diffusion and reaction-diffusion-convection systems