A domain wall between single-mode and bimodal states and its transition to dynamical behavior in inhomogeneous systems

We consider domain walls (DW's) between single-mode and bimodal states that occur in coupled nonlinear diffusion (NLD), real Ginzburg-Landau (RGL), and complex Ginzburg-Landau (CGL) equations with a spatially dependent coupling coefficient. Group-velocity terms are added to the NLD and RGL equations, which breaks the variational structure of these models. In the simplest case of two coupled NLD equations, we reduce the description of stationary configurations to a single second-order ordinary differential equation. We demonstrate analytically that a necessary condition for existence of a stationary DW is that the group-velocity must be below a certain threshold value. Above this threshold, dynamical behavior sets in, which we consider in detail. In the CGL equations, the DW may generate spatio-temporal chaos, depending on the nonlinear dispersion.Comment: 16 pages (latex) including 11 figures; accepted for publication in Physica

Stresses in Smooth Flows of Dense Granular Media

The form of the stress tensor is investigated in smooth, dense granular flows which are generated in split-bottom shear geometries. We find that, within a fluctuation fluidized spatial region, the form of the stress tensor is directly dictated by the flow field: The stress and strain-rate tensors are co-linear. The effective friction, defined as the ratio between shear and normal stresses acting on a shearing plane, is found not to be constant but to vary throughout the flowing zone. This variation can not be explained by inertial effects, but appears to be set by the local geometry of the flow field. This is in agreement with a recent prediction, but in contrast with most models for slow grain flows, and points to there being a subtle mechanism that selects the flow profiles.Comment: 5 pages, 4 figure