3,784 research outputs found
Current-Induced Step Bending Instability on Vicinal Surfaces
We model an apparent instability seen in recent experiments on current
induced step bunching on Si(111) surfaces using a generalized 2D BCF model,
where adatoms have a diffusion bias parallel to the step edges and there is an
attachment barrier at the step edge. We find a new linear instability with
novel step patterns. Monte Carlo simulations on a solid-on-solid model are used
to study the instability beyond the linear regime.Comment: 4 pages, 4 figure
On U_q(SU(2))-symmetric Driven Diffusion
We study analytically a model where particles with a hard-core repulsion
diffuse on a finite one-dimensional lattice with space-dependent, asymmetric
hopping rates. The system dynamics are given by the
\mbox{U[SU(2)]}-symmetric Hamiltonian of a generalized anisotropic
Heisenberg antiferromagnet. Exploiting this symmetry we derive exact
expressions for various correlation functions. We discuss the density profile
and the two-point function and compute the correlation length as well
as the correlation time . The dynamics of the density and the
correlations are shown to be governed by the energy gaps of a one-particle
system. For large systems and depend only on the asymmetry. For
small asymmetry one finds indicating a dynamical exponent
as for symmetric diffusion.Comment: 10 pages, LATE
Dual Monte Carlo and Cluster Algorithms
We discuss the development of cluster algorithms from the viewpoint of
probability theory and not from the usual viewpoint of a particular model. By
using the perspective of probability theory, we detail the nature of a cluster
algorithm, make explicit the assumptions embodied in all clusters of which we
are aware, and define the construction of free cluster algorithms. We also
illustrate these procedures by rederiving the Swendsen-Wang algorithm,
presenting the details of the loop algorithm for a worldline simulation of a
quantum 1/2 model, and proposing a free cluster version of the
Swendsen-Wang replica method for the random Ising model. How the principle of
maximum entropy might be used to aid the construction of cluster algorithms is
also discussed.Comment: 25 pages, 4 figures, to appear in Phys.Rev.
On generalized cluster algorithms for frustrated spin models
Standard Monte Carlo cluster algorithms have proven to be very effective for
many different spin models, however they fail for frustrated spin systems.
Recently a generalized cluster algorithm was introduced that works extremely
well for the fully frustrated Ising model on a square lattice, by placing bonds
between sites based on information from plaquettes rather than links of the
lattice. Here we study some properties of this algorithm and some variants of
it. We introduce a practical methodology for constructing a generalized cluster
algorithm for a given spin model, and investigate apply this method to some
other frustrated Ising models. We find that such algorithms work well for
simple fully frustrated Ising models in two dimensions, but appear to work
poorly or not at all for more complex models such as spin glasses.Comment: 34 pages in RevTeX. No figures included. A compressed postscript file
for the paper with figures can be obtained via anonymous ftp to
minerva.npac.syr.edu in users/paulc/papers/SCCS-527.ps.Z. Syracuse University
NPAC technical report SCCS-52
Synchronization and Redundancy: Implications for Robustness of Neural Learning and Decision Making
Learning and decision making in the brain are key processes critical to
survival, and yet are processes implemented by non-ideal biological building
blocks which can impose significant error. We explore quantitatively how the
brain might cope with this inherent source of error by taking advantage of two
ubiquitous mechanisms, redundancy and synchronization. In particular we
consider a neural process whose goal is to learn a decision function by
implementing a nonlinear gradient dynamics. The dynamics, however, are assumed
to be corrupted by perturbations modeling the error which might be incurred due
to limitations of the biology, intrinsic neuronal noise, and imperfect
measurements. We show that error, and the associated uncertainty surrounding a
learned solution, can be controlled in large part by trading off
synchronization strength among multiple redundant neural systems against the
noise amplitude. The impact of the coupling between such redundant systems is
quantified by the spectrum of the network Laplacian, and we discuss the role of
network topology in synchronization and in reducing the effect of noise. A
range of situations in which the mechanisms we model arise in brain science are
discussed, and we draw attention to experimental evidence suggesting that
cortical circuits capable of implementing the computations of interest here can
be found on several scales. Finally, simulations comparing theoretical bounds
to the relevant empirical quantities show that the theoretical estimates we
derive can be tight.Comment: Preprint, accepted for publication in Neural Computatio
Cluster update and recognition
We present a fast and robust cluster update algorithm that is especially
efficient in implementing the task of image segmentation using the method of
superparamagnetic clustering. We apply it to a Potts model with spin
interactions that are are defined by gray-scale differences within the image.
Motivated by biological systems, we introduce the concept of neural inhibition
to the Potts model realization of the segmentation problem. Including the
inhibition term in the Hamiltonian results in enhanced contrast and thereby
significantly improves segmentation quality. As a second benefit we can - after
equilibration - directly identify the image segments as the clusters formed by
the clustering algorithm. To construct a new spin configuration the algorithm
performs the standard steps of (1) forming clusters and of (2) updating the
spins in a cluster simultaneously. As opposed to standard algorithms, however,
we share the interaction energy between the two steps. Thus the update
probabilities are not independent of the interaction energies. As a
consequence, we observe an acceleration of the relaxation by a factor of 10
compared to the Swendson and Wang procedure.Comment: 4 pages, 2 figure
Exact field-driven interface dynamics in the two-dimensional stochastic Ising model with helicoidal boundary conditions
We investigate the interface dynamics of the two-dimensional stochastic Ising
model in an external field under helicoidal boundary conditions. At
sufficiently low temperatures and fields, the dynamics of the interface is
described by an exactly solvable high-spin asymmetric quantum Hamiltonian that
is the infinitesimal generator of the zero range process. Generally, the
critical dynamics of the interface fluctuations is in the Kardar-Parisi-Zhang
universality class of critical behavior. We remark that a whole family of RSOS
interface models similar to the Ising interface model investigated here can be
described by exactly solvable restricted high-spin quantum XXZ-type
Hamiltonians.Comment: LaTeX2e, 15 pages, 1 figure, 40 references. This paper is dedicated
to Professor Silvio R. A. Salinas (IF/USP) on the occasion of his 70th
birthda
Time-dependent correlation functions in a one-dimensional asymmetric exclusion process
We study a one-dimensional anisotropic exclusion process describing particles
injected at the origin, moving to the right on a chain of sites and being
removed at the (right) boundary. We construct the steady state and compute the
density profile, exact expressions for all equal-time n-point density
correlation functions and the time-dependent two-point function in the steady
state as functions of the injection and absorption rates. We determine the
phase diagram of the model and compare our results with predictions from
dynamical scaling and discuss some conjectures for other exclusion models.Comment: LATEX-file, 32 pages, Weizmann preprint WIS/93/01/Jan-P
Cluster Algorithm for a Solid-On-Solid Model with Constraints
We adapt the VMR (valleys-to-mountains reflections) algorithm, originally
devised by us for simulations of SOS models, to the BCSOS model. It is the
first time that a cluster algorithm is used for a model with constraints. The
performance of this new algorithm is studied in detail in both phases of the
model, including a finite size scaling analysis of the autocorrelations.Comment: 10 pages, 3 figures appended as ps-file
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