The existence and comparison theorem of solutions is first established for the quasimonotone delayed reaction-diffusion equations on R by appealing to the theory of abstract functional differential equations. The global asymptotic stability, Liapunov stability and uniqueness of traveling wave solutions are then proved by the elementary superand sub-solution comparison and squeezing methods. Sup...

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...

MOTIVATION We compare stochastic computational methods accounting for space and discrete nature of reactants in biochemical systems. Implementations based on Brownian dynamics (BD) and the reaction-diffusion master equation are applied to a simplified gene expression model and to a signal transduction pathway in Escherichia coli. RESULTS In the regime where the number of molecules is small an...

Gas-diffusion electrodes have been successfully employed in electrochemical chlorine production, and they also hold great potential the field of CO2 reduction. Herein, we demonstrate how sprayed Ag-based gas-diffusion electrodes, which show outstanding performance for reduction oxygen, need to be modified produce CO from CO2. A computer-controlled automated airbrush-type spraying setup is used ...

The dynamics and stability of spike-type patterns to a sub-diffusive Gierer-Meinhardt reaction – diffusion system is studied in a one dimensional spatial domain. A differential algebraic system (DAE) is derived to characterise the dynamics of an n-spike quasi-equilibrium pattern in the presence of subdiffusion. With sub-diffusive effects it is shown that quasi-equilibrium spike patterns exist f...

Diffusive transport of particles or, more generally, small objects, is a ubiquitous feature of physical and chemical reaction systems. In configurations containing confining walls or constrictions, transport is controlled both by the fluctuation statistics of the jittering objects and the phase space available to their dynamics. Consequently, the study of transport at the macro- and nanoscales ...