252 research outputs found
Granular gravitational collapse and chute flow
Inelastic grains in a flow under gravitation tend to collapse into states in
which the relative normal velocities of two neighboring grains is zero. If the
time scale for this gravitational collapse is shorter than inverse strain rates
in the flow, we propose that this collapse will lead to the formation of
``granular eddies", large scale condensed structures of particles moving
coherently with one another. The scale of these eddies is determined by the
gradient of the strain rate. Applying these concepts to chute flow of granular
media, (gravitationally driven flow down inclined planes) we predict the
existence of a bulk flow region whose rheology is determined only by flow
density. This theory yields the experimental ``Pouliquen flow rule",
correlating different chute flows; it also correctly accounts for the different
flow regimes observed.Comment: LaTeX2e with epl class, 7 pages, 2 figures, submitted to Europhysics
Letter
High-Dimensional Diffusive Growth
We consider a model of aggregation, both diffusion-limited and ballistic,
based on the Cayley tree. Growth is from the leaves of the tree towards the
root, leading to non-trivial screening and branch competition effects. The
model exhibits a phase transition between ballistic and diffusion-controlled
growth, with non-trivial corrections to cluster size at the critical point.
Even in the ballistic regime, cluster scaling is controlled by extremal
statistics due to the branching structure of the Cayley tree; it is the
extremal nature of the fluctuations that enables us to solve the model.Comment: 5 pages, 3 figures; reference adde
Diffusion-limited aggregation as branched growth
I present a first-principles theory of diffusion-limited aggregation in two
dimensions. A renormalized mean-field approximation gives the form of the
unstable manifold for branch competition, following the method of Halsey and
Leibig [Phys. Rev. A {\bf 46}, 7793 (1992)]. This leads to a result for the
cluster dimensionality, D \approx 1.66, which is close to numerically obtained
values. In addition, the multifractal exponent \tau(3) = D in this theory, in
agreement with a proposed `electrostatic' scaling law.Comment: 13 pages, one figure not included (available by request, by ordinary
mail), Plain Te
Branched Growth with Walkers
Diffusion-limited aggregation has a natural generalization to the
"-models", in which random walkers must arrive at a point on the
cluster surface in order for growth to occur. It has recently been proposed
that in spatial dimensionality , there is an upper critical
above which the fractal dimensionality of the clusters is D=1. I compute the
first order correction to for , obtaining . The
methods used can also determine multifractal dimensions to first order in
.Comment: 6 pages, 1 figur
Multifractal Dimensions for Branched Growth
A recently proposed theory for diffusion-limited aggregation (DLA), which
models this system as a random branched growth process, is reviewed. Like DLA,
this process is stochastic, and ensemble averaging is needed in order to define
multifractal dimensions. In an earlier work [T. C. Halsey and M. Leibig, Phys.
Rev. A46, 7793 (1992)], annealed average dimensions were computed for this
model. In this paper, we compute the quenched average dimensions, which are
expected to apply to typical members of the ensemble. We develop a perturbative
expansion for the average of the logarithm of the multifractal partition
function; the leading and sub-leading divergent terms in this expansion are
then resummed to all orders. The result is that in the limit where the number
of particles n -> \infty, the quenched and annealed dimensions are {\it
identical}; however, the attainment of this limit requires enormous values of
n. At smaller, more realistic values of n, the apparent quenched dimensions
differ from the annealed dimensions. We interpret these results to mean that
while multifractality as an ensemble property of random branched growth (and
hence of DLA) is quite robust, it subtly fails for typical members of the
ensemble.Comment: 82 pages, 24 included figures in 16 files, 1 included tabl
Stability of Monomer-Dimer Piles
We measure how strong, localized contact adhesion between grains affects the
maximum static critical angle, theta_c, of a dry sand pile. By mixing dimer
grains, each consisting of two spheres that have been rigidly bonded together,
with simple spherical monomer grains, we create sandpiles that contain strong
localized adhesion between a given particle and at most one of its neighbors.
We find that tan(theta_c) increases from 0.45 to 1.1 and the grain packing
fraction, Phi, decreases from 0.58 to 0.52 as we increase the relative number
fraction of dimer particles in the pile, nu_d, from 0 to 1. We attribute the
increase in tan(theta_c(nu_d)) to the enhanced stability of dimers on the
surface, which reduces the density of monomers that need to be accomodated in
the most stable surface traps. A full characterization and geometrical
stability analysis of surface traps provides a good quantitative agreement
between experiment and theory over a wide range of nu_d, without any fitting
parameters.Comment: 11 pages, 12 figures consisting of 21 eps files, submitted to PR
Velocity Correlations in Dense Gravity Driven Granular Chute Flow
We report numerical results for velocity correlations in dense,
gravity-driven granular flow down an inclined plane. For the grains on the
surface layer, our results are consistent with experimental measurements
reported by Pouliquen. We show that the correlation structure within planes
parallel to the surface persists in the bulk. The two-point velocity
correlation function exhibits exponential decay for small to intermediate
values of the separation between spheres. The correlation lengths identified by
exponential fits to the data show nontrivial dependence on the averaging time
\dt used to determine grain velocities. We discuss the correlation length
dependence on averaging time, incline angle, pile height, depth of the layer,
system size and grain stiffness, and relate the results to other length scales
associated with the rheology of the system. We find that correlation lengths
are typically quite small, of the order of a particle diameter, and increase
approximately logarithmically with a minimum pile height for which flow is
possible, \hstop, contrary to the theoretical expectation of a proportional
relationship between the two length scales.Comment: 21 pages, 16 figure
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