Aggregation of chemotactic organisms in a differential flow

We study the effect of advection on the aggregation and pattern formation in chemotactic systems described by Keller-Segel type models. The evolution of small perturbations is studied analytically in the linear regime complemented by numerical simulations. We show that a uniform differential flow can significantly alter the spatial structure and dynamics of the chemotactic system. The flow leads to the formation of anisotropic aggregates that move following the direction of the flow, even when the chemotactic organisms are not directly advected by the flow. Sufficiently strong advection can stop the aggregation and coarsening process that is then restricted to the direction perpendicular to the flow

Coupling of morphology to surface transport in ion-beam irradiated surfaces. I. Oblique incidence

We propose and study a continuum model for the dynamics of amorphizable surfaces undergoing ion-beam sputtering (IBS) at intermediate energies and oblique incidence. After considering the current limitations of more standard descriptions in which a single evolution equation is posed for the surface height, we overcome (some of) them by explicitly formulating the dynamics of the species that transport along the surface, and by coupling it to that of the surface height proper. In this we follow recent proposals inspired by ``hydrodynamic'' descriptions of pattern formation in aeolian sand dunes and ion-sputtered systems. From this enlarged model, and by exploiting the time-scale separation among various dynamical processes in the system, we derive a single height equation in which coefficients can be related to experimental parameters. This equation generalizes those obtained by previous continuum models and is able to account for many experimental features of pattern formation by IBS at oblique incidence, such as the evolution of the irradiation-induced amorphous layer, transverse ripple motion with non-uniform velocity, ripple coarsening, onset of kinetic roughening and other. Additionally, the dynamics of the full two-field model is compared with that of the effective interface equation.Comment: 23 pages, 14 figures. Movies of figures 6, 7, and 8 available at http://gisc.uc3m.es/~javier/Movies

Stable Continuous Orthonormalization Techniques for Linear Boundary Value Problems

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