Condensed Matter Theory

Abstract:

We consider pattern formation in periodically forced binary systems. In particular, we focus on systems in which the two species are differentially forced, one being accelerated with respect to the other. Using a continuum model consisting of two isothermal ideal gases which interact via a frictional force we demonstrate analytically that stripes form spontaneously above a critical forcing amplitude. The wavelength of the stripes is found to be close to the wavelength of sound in the limit of small viscosity. The results are confirmed numerically. We suggest that the same mechanism may contribute to the formation of stripes in experiments on horizontally oscillated granular mixtures.

Abstract:

The dramatic appearance of luminescence rings with radius of several hundred microns in quantum well structures can be understood through a fairly simple nonlinear model of the diffusion and recombination of electrons and holes in a driven nonequilibrium system. The ring corresponds to the boundary between a positive hole gas and a negative electron gas in steady state. While this basic effect is now well understood, we discuss several other experimental results which cannot be explained by this simple model.

Abstract:

We describe a lattice Boltzmann algorithm to simulate liquid-crystal hydrodynamics in three dimensions. The equations of motion are written in terms of a tensor order parameter. This allows both the isotropic and the nematic phases to be considered. Backflow effects and the hydrodynamics of topological defects are naturally included in the simulations, as are viscoelastic effects such as shear-thinning and shear-banding. We describe the implementation of velocity boundary conditions and show that the algorithm can be used to describe optical bounce in twisted nematic devices and secondary flow in sheared nematics with an imposed twist.