Spatiotemporal patterns in CO oxidation on Pt(110): the role of nonlinear diffusion.

Standing-wave patterns observed in the CO + O2 reaction on Pt(110) are described by a model that explicitly takes into account the coupling between the transport of adsorbed CO and the adsorbate-induced structural transformation of the substrate. We show that synchronization of the surface is achieved through nucleation and growth processes even in the absence of gas-phase coupling.

Pattern formation and spatial self-entrainment in bistable chemical systems.

We describe the formation of spatial structures generated by diffusive instabilities in bistable systems. The coupling between the different spatial modes emanating from the two homogeneous steady states can then give rise to self-parametric instabilities favoring the occurrence of resonant rhombic or quasiperiodic structures such as superlattices or quasicrystalline patterns.

Comment on "Flow-distributed oscillations: stationary chemical waves in a reacting flow"

In a recent paper by Kaern and Menzinger [Phys. Rev. E 60, R3471 (1999)] a successful verification of the stationary space-periodic structures predicted by Andresen et al. [Phys. Rev. E 60, 297 (1999)] was reported. Kaern and Menzinger suggest a mechanism for the formation of such structures that yields a linear relationship between the selected wavelength and the flow rate. We find this mechanism too simple and produce numerical simulations that support the original interpretation of these structures.

Spatial multistability and nonvariational effects.

We investigate the phenomenon of spatial multistability of fronts in thin bistable systems and stress the important role played by the absence of a variational principle. Nonvariational effects allow, for instance, two different immobilized fronts to coexist. The morphological instability of the corresponding nucleating solution can then lead, even in the absence of any diffusive instability, to nontrivial patterns in the depth of one-side-fed reactors.

Stationary space-periodic structures with equal diffusion coefficients.

The paper investigates a chemical reaction-diffusion model in an open flow system. It is shown that such a system may, with particular boundary conditions, exhibit stationary space-periodic structures even in the case of equal diffusion coefficients. This is confirmed through numerical simulations.

Twist grain boundaries in three-dimensional lamellar Turing structures.

Steady spatial self-organization of three-dimensional chemical reaction-diffusion systems is discussed with the emphasis put on the possible defects that may alter the Turing patterns. It is shown that one of the stable defects of a three-dimensional lamellar Turing structure is a twist grain boundary embedding a Scherk minimal surface.

Spatial patterns and double diffusion in chemical reactions.

Spatial ordering has been observed recently during various photochemical reactions. Convoluted concentration bands first appear near the surface of shallow irradiated solutions. They thereafter extend into the bulk, and finger-like structures spontaneously develop. We discuss here the possible role of double-diffusion effects in the onset of this phenomenon. Indeed, chemical reactions occurring near the surface or evaporation of the solvent, or both, induce in the bulk adverse gradients of a pair of properties (concentrations of solute or concentration and temperature) having different diffusivities. This difference can then destabilize the homogeneous solution and trigger the observed patterns.