44,839 research outputs found
Relevance of Abelian Symmetry and Stochasticity in Directed Sandpiles
We provide a comprehensive view on the role of Abelian symmetry and
stochasticity in the universality class of directed sandpile models, in context
of the underlying spatial correlations of metastable patterns and scars. It is
argued that the relevance of Abelian symmetry may depend on whether the dynamic
rule is stochastic or deterministic, by means of the interaction of metastable
patterns and avalanche flow. Based on the new scaling relations, we conjecture
critical exponents for avalanche, which is confirmed reasonably well in
large-scale numerical simulations.Comment: 4 pages, 3 figures; published versio
Universality classes and crossover behaviors in non-Abelian directed sandpiles
We study universality classes and crossover behaviors in non-Abelian directed
sandpile models, in terms of the metastable pattern analysis. The non-Abelian
property induces spatially correlated metastable patterns, characterized by the
algebraic decay of the grain density along the propagation direction of an
avalanche. Crossover scaling behaviors are observed in the grain density due to
the interplay between the toppling randomness and the parity of the threshold
value. In the presence of such crossovers, we show that the broadness of the
grain distribution plays a crucial role in resolving the ambiguity of the
universality class. Finally, we claim that the metastable pattern analysis is
important as much as the conventional analysis of avalanche dynamics.Comment: 10 pages, 7 figures, 1 table; published in PRE as the full paper of
PRL v101, 218001 (2008
Determining White Noise Forcing From Eulerian Observations in the Navier Stokes Equation
The Bayesian approach to inverse problems is of paramount importance in
quantifying uncertainty about the input to and the state of a system of
interest given noisy observations. Herein we consider the forward problem of
the forced 2D Navier Stokes equation. The inverse problem is inference of the
forcing, and possibly the initial condition, given noisy observations of the
velocity field. We place a prior on the forcing which is in the form of a
spatially correlated temporally white Gaussian process, and formulate the
inverse problem for the posterior distribution. Given appropriate spatial
regularity conditions, we show that the solution is a continuous function of
the forcing. Hence, for appropriately chosen spatial regularity in the prior,
the posterior distribution on the forcing is absolutely continuous with respect
to the prior and is hence well-defined. Furthermore, the posterior distribution
is a continuous function of the data. We complement this theoretical result
with numerical simulation of the posterior distribution
Large magnetoresistance using hybrid spin filter devices
A magnetic "spin filter" tunnel barrier, sandwiched between a non-magnetic
metal and a magnetic metal, is used to create a new magnetoresistive tunnel
device, somewhat analogous to an optical polarizer-analyzer configuration. The
resistance of these trilayer structures depends on the relative magnetization
orientation of the spin filter and the ferromagnetic electrode. The spin
filtering in this configuration yields a previously unobserved
magnetoresistance effect, exceeding 100%.Comment: 3.5 pages, 3 figures, submitted to Appl. Phys. Let
Non-equilibrium melting of colloidal crystals in confinement
We report on a novel and flexible experiment to investigate the
non-equilibrium melting behaviour of model crystals made from charged colloidal
spheres. In a slit geometry polycrystalline material formed in a low salt
region is driven by hydrostatic pressure up an evolving gradient in salt
concentration and melts at large salt concentration. Depending on particle and
initial salt concentration, driving velocity and the local salt concentration
complex morphologic evolution is observed. Crystal-melt interface positions and
the melting velocity are obtained quantitatively from time resolved Bragg- and
polarization microscopic measurements. A simple theoretical model predicts the
interface to first advance, then for balanced drift and melting velocities to
become stationary at a salt concentration larger than the equilibrium melting
concentration. It also describes the relaxation of the interface to its
equilibrium position in a stationary gradient after stopping the drive in
different manners. We further discuss the influence of the gradient strength on
the resulting interface morphology and a shear induced morphologic transition
from polycrystalline to oriented single crystalline material before melting
Finite Size Polyelectrolyte Bundles at Thermodynamic Equilibrium
We present the results of extensive computer simulations performed on
solutions of monodisperse charged rod-like polyelectrolytes in the presence of
trivalent counterions. To overcome energy barriers we used a combination of
parallel tempering and hybrid Monte Carlo techniques. Our results show that for
small values of the electrostatic interaction the solution mostly consists of
dispersed single rods. The potential of mean force between the polyelectrolyte
monomers yields an attractive interaction at short distances. For a range of
larger values of the Bjerrum length, we find finite size polyelectrolyte
bundles at thermodynamic equilibrium. Further increase of the Bjerrum length
eventually leads to phase separation and precipitation. We discuss the origin
of the observed thermodynamic stability of the finite size aggregates
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