Wavelength Selection by Interrupted Coarsening in Reaction-Diffusion Systems

Coarsening of precipitation patterns in a moving reaction-diffusion front.

Precipitation patterns emerging in a two-dimensional moving front are investigated on the example of NaOH diffusing into a gel containing AlCl3 . The time evolution of the precipitate Al(OH)_{3} can be observed since the precipitate redissolves in the excess outer electrolyte NaOH and thus it exists only in a narrow optically accessible region of the reaction front. The patterns display self-si...

Interrupted coarsening of anisotropic step meander.

We report on the effect of anisotropy on the step meandering instability on vicinal surfaces during molecular beam epitaxy growth. A scenario of interrupted coarsening is found: the lateral length scale of the structure first significantly increases with time and then freezes at a larger length scale. The wavelength selection mechanism results from a nontrivial nonlinear effect of anisotropy. A...

Selection and coexistence by reaction-diffusion dynamics in fitness landscapes

The phenomena of selection and coexistence are modelled as chemical pattern formation by competition for a given Ž . resource in heterogeneous spatial fields fitness landscapes . The reactions form a closed reproductive cycle so that total concentration of species and their building-blocks is kept constant in time. Eigen’s ‘constant overall organization’ conditions can be view as a particular c...

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

Diffusion-Driven Instability in Reaction Diffusion Systems

For a stable matrix A with real entries, sufficient and necessary conditions for A D to be stable for all non-negative diagonal matrices D are obtained. Implications of these conditions for the stability and instability of constant steadystate solutions to reaction diffusion systems are discussed and an example is given to show applications. 2001 Academic Press