2,823 research outputs found
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
Particle Diffusion in Slow Granular Bulk Flows
We probe the diffusive motion of particles in slowly sheared three
dimensional granular suspensions. For sufficiently large strains, the particle
dynamics exhibits diffusive Gaussian statistics, with the diffusivity
proportional to the local strain rate - consistent with a local, quasi static
picture. Surprisingly, the diffusivity is also inversely proportional to the
depth of the particles within the flow - at the free surface, diffusivity is
thus ill defined. We find that the crossover to Gaussian displacement
statistics is governed by the same depth dependence, evidencing a non-trivial
strain scale in three dimensional granular flows.Comment: 6 page
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
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