Systems of reaction-diffusion equations with spatially distributed hysteresis

Hysteresis in one-dimensional reaction-diffusion systems.

We introduce a simple nonequilibrium model for a driven diffusive system with nonconservative reaction kinetics in one dimension. The steady state exhibits a phase with broken ergodicity and hysteresis which has no analog in systems investigated previously. We identify the main dynamical mode, viz., the random motion of a shock in an effective potential, which provides a unified framework for u...

Reaction-Diffusion equations with applications

Traveling avalanche waves in spatially discrete bistable reaction–diffusion systems

Infinitely extended two-dimensional reaction–diffusion lattices composed of bistable cells are considered. A class of particular stable stationary solutions, called pattern solutions, is introduced and examples are given. Pattern solutions persist at high diffusion coefficients whereas all other stable stationary solutions, with the exception of the constant solutions, disappear one after the o...

Generalized reaction–diffusion equations

This Letter proposes generalized reaction–diffusion equations for treating noisy magnetic resonance images. An edge-enhancing functional is introduced for image enhancement. A number of super-diffusion operators are introduced for fast and effective smoothing. Statistical information is utilized for robust edge-stopping and diffusion-rate estimation. A quasi-interpolating wavelet algorithm is u...

Reaction-diffusion Equations

I have recently worked in the area of partial differential equations (PDE), specifically reaction-diffusion equations, drift-diffusion equations, and fluid dynamics. These equations model physical processes such as combustion, mixing, or turbulence, and my main interest has been in long term dynamics of their solutions as well as in the formation of singularities. I consider myself an applied a...