124 research outputs found
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
Anisotropic Scaling in Threshold Critical Dynamics of Driven Directed Lines
The dynamical critical behavior of a single directed line driven in a random
medium near the depinning threshold is studied both analytically (by
renormalization group) and numerically, in the context of a Flux Line in a
Type-II superconductor with a bulk current . In the absence of
transverse fluctuations, the system reduces to recently studied models of
interface depinning. In most cases, the presence of transverse fluctuations are
found not to influence the critical exponents that describe longitudinal
correlations. For a manifold with internal dimensions,
longitudinal fluctuations in an isotropic medium are described by a roughness
exponent to all orders in , and a
dynamical exponent . Transverse
fluctuations have a distinct and smaller roughness exponent
for an isotropic medium. Furthermore, their
relaxation is much slower, characterized by a dynamical exponent
, where is the
correlation length exponent. The predicted exponents agree well with numerical
results for a flux line in three dimensions. As in the case of interface
depinning models, anisotropy leads to additional universality classes. A
nonzero Hall angle, which has no analogue in the interface models, also affects
the critical behavior.Comment: 26 pages, 8 Postscript figures packed together with RevTeX 3.0
manuscript using uufiles, uses multicol.sty and epsf.sty, e-mail
[email protected] in case of problem
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
Novel universality classes of coupled driven diffusive systems
Motivated by the phenomenologies of dynamic roughening of strings in random
media and magnetohydrodynamics, we examine the universal properties of driven
diffusive system with coupled fields. We demonstrate that cross-correlations
between the fields lead to amplitude-ratios and scaling exponents varying
continuosly with the strength of these cross-correlations. The implications of
these results for experimentally relevant systems are discussed.Comment: To appear in Phys. Rev. E (Rapid Comm.) (2003
The Origin of a Repose Angle: Kinetics of Rearrangements for Granular Materials
A microstructural theory of dense granular materials is presented, based on
two main ideas. Firstly, that macroscopic shear results form activated local
rearrangements at a mesoscopic scale. Secondly, that the update frequency of
microscopic processes is determined by granular temperature. In a shear cell,
the resulting constitutive equations account for Bagnold's scaling and for the
existence of a Coulomb criterion of yield. In the case of a granular flow down
an inclined plane, they account for the rheology observed in recent experiments
and for the temperature and velocity profiles measured numerically.Comment: submitted to PR
A Model Ground State of Polyampholytes
The ground state of randomly charged polyampholytes is conjectured to have a
structure similar to a necklace, made of weakly charged parts of the chain,
compacting into globules, connected by highly charged stretched `strings'. We
suggest a specific structure, within the necklace model, where all the neutral
parts of the chain compact into globules: The longest neutral segment compacts
into a globule; in the remaining part of the chain, the longest neutral segment
(the 2nd longest neutral segment) compacts into a globule, then the 3rd, and so
on. We investigate the size distributions of the longest neutral segments in
random charge sequences, using analytical and Monte Carlo methods. We show that
the length of the n-th longest neutral segment in a sequence of N monomers is
proportional to N/(n^2), while the mean number of neutral segments increases as
sqrt(N). The polyampholyte in the ground state within our model is found to
have an average linear size proportional to sqrt(N), and an average surface
area proportional to N^(2/3).Comment: 8 two-column pages. 5 eps figures. RevTex. Submitted to Phys. Rev.
Finite Temperature Depinning of a Flux Line from a Nonuniform Columnar Defect
A flux line in a Type-II superconductor with a single nonuniform columnar
defect is studied by a perturbative diagrammatic expansion around an annealed
approximation. The system undergoes a finite temperature depinning transition
for the (rather unphysical) on-the-average repulsive columnar defect, provided
that the fluctuations along the axis are sufficiently large to cause some
portions of the column to become attractive. The perturbative expansion is
convergent throughout the weak pinning regime and becomes exact as the
depinning transition is approached, providing an exact determination of the
depinning temperature and the divergence of the localization length.Comment: RevTeX, 4 pages, 3 EPS figures embedded with epsf.st
Gutenberg Richter and Characteristic Earthquake Behavior in Simple Mean-Field Models of Heterogeneous Faults
The statistics of earthquakes in a heterogeneous fault zone is studied
analytically and numerically in the mean field version of a model for a
segmented fault system in a three-dimensional elastic solid. The studies focus
on the interplay between the roles of disorder, dynamical effects, and driving
mechanisms. A two-parameter phase diagram is found, spanned by the amplitude of
dynamical weakening (or ``overshoot'') effects (epsilon) and the normal
distance (L) of the driving forces from the fault. In general, small epsilon
and small L are found to produce Gutenberg-Richter type power law statistics
with an exponential cutoff, while large epsilon and large L lead to a
distribution of small events combined with characteristic system-size events.
In a certain parameter regime the behavior is bistable, with transitions back
and forth from one phase to the other on time scales determined by the fault
size and other model parameters. The implications for realistic earthquake
statistics are discussed.Comment: 21 pages, RevTex, 6 figures (ps, eps
A Ball in a Groove
We study the static equilibrium of an elastic sphere held in a rigid groove
by gravity and frictional contacts, as determined by contact mechanics. As a
function of the opening angle of the groove and the tilt of the groove with
respect to the vertical, we identify two regimes of static equilibrium for the
ball. In the first of these, at large opening angle or low tilt, the ball rolls
at both contacts as it is loaded. This is an analog of the "elastic" regime in
the mechanics of granular media. At smaller opening angles or larger tilts, the
ball rolls at one contact and slides at the other as it is loaded, analogously
with the "plastic" regime in the mechanics of granular media. In the elastic
regime, the stress indeterminacy is resolved by the underlying kinetics of the
ball response to loading.Comment: RevTeX 3.0, 4 pages, 2 eps figures included with eps
Strong Phase Separation in a Model of Sedimenting Lattices
We study the steady state resulting from instabilities in crystals driven
through a dissipative medium, for instance, a colloidal crystal which is
steadily sedimenting through a viscous fluid. The problem involves two coupled
fields, the density and the tilt; the latter describes the orientation of the
mass tensor with respect to the driving field. We map the problem to a 1-d
lattice model with two coupled species of spins evolving through conserved
dynamics. In the steady state of this model each of the two species shows
macroscopic phase separation. This phase separation is robust and survives at
all temperatures or noise levels--- hence the term Strong Phase Separation.
This sort of phase separation can be understood in terms of barriers to
remixing which grow with system size and result in a logarithmically slow
approach to the steady state. In a particular symmetric limit, it is shown that
the condition of detailed balance holds with a Hamiltonian which has
infinite-ranged interactions, even though the initial model has only local
dynamics. The long-ranged character of the interactions is responsible for
phase separation, and for the fact that it persists at all temperatures.
Possible experimental tests of the phenomenon are discussed.Comment: To appear in Phys Rev E (1 January 2000), 16 pages, RevTex, uses
epsf, three ps figure
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