In this paper, we consider a mathematical model motivated by patterned growth of bacteria. The model is a system of differential equations that consists of two sub-systems. One is a system of ordinary differential equations and the other one is a reaction-diffusion system. Pattern formation in this model is caused by an initial instability of the ordinary differential equations. However, nonlin...

We report an example of subcritical wave instability in a model of a reaction-diffusion system and discuss the potential implications for localized patterns found in experiments on the Belousov-Zhabotinsky reaction in a microemulsion.

The stationary state of stochastic processes such as reaction-diffusion systems can be related to the ground state of a suitably defined quantum Hamiltonian. Using this analogy, we investigate the applicability of a real space renormalisation group approach, originally developped for quantum spin systems, to interacting particle systems. We apply the technique to an exactly solvable reaction-di...

In biological systems, biochemical networks play a crucial role, implementing a broad range of vital functions from regulation and communication to resource transport and shape alteration. While biochemical networks naturally occur at low copy numbers and in a spatial setting, this fact often is ignored and well-stirred conditions are assumed for simplicity. Yet, it is now increasingly becoming...

We introduce a class of reaction diffusion systems of which weak solution exists global-in-time with relatively compact orbit in L. Reaction term in this class is quasi-positive, dissipative, and up to with quadratic growth rate. If the space dimension is less than or equal to two, the solution is classical and uniformly bounded. Provided with the entropy structure, on the other hand, this weak...

The aim of this work is to find efficient and reliable numerical solutions of two complex problems under consideration. In the first application problem, an improved continuum model has been derived to describe the temperature and concentration distributions in gas-solid-fluidized beds with spray injection. The model equations for the nozzle spray are also reformulated to achieve reliable numer...

The computer vision research aims at a better understanding of the human visual system and building artificial visual systems. Vision researchers in psychology and physiology have explored biological visual systems including the human vision, and obtained much knowledge on nature and architecture of their visual information processing. For example, some of previous results in experimental psych...

In this paper, bifurcations of stationary and time-periodic solutions to reactiondiffusion systems are studied. We develop a center-manifold and normal form theory for radial dynamics which allows for a complete description of radially symmetric patterns. In particular, we show the existence of localized pulses near saddle-nodes, critical Gibbs kernels in the cusp, focus patterns in Turing inst...

This paper describes a technique for determining a classiication map or a hypothesis selection map using a system of reaction-diiusion equations. The reaction term of the equations is a replicator equation and provides a mutually exclusive solution. The diffusion term exploits the local consistency of the solution. The technique is eecient for problems with a small labeling space compared to an...

A power-law distribution is found in the density profile of reacting systems A+B-->C+D and 2A-->2C under a flow in two and three dimensions. Different densities of reactants A and B are fixed at both ends. For the reaction A+B , the concentration of reactants asymptotically decay in space as x-1/2 and x-3/4 in two dimensions and three dimensions, respectively. For 2A , it decays as log(x)/x in ...