977 research outputs found
Exact solutions for a mean-field Abelian sandpile
We introduce a model for a sandpile, with N sites, critical height N and each
site connected to every other site. It is thus a mean-field model in the
spin-glass sense. We find an exact solution for the steady state probability
distribution of avalanche sizes, and discuss its asymptotics for large N.Comment: 10 pages, LaTe
Novel Quenched Disorder Fixed Point in a Two-Temperature Lattice Gas
We investigate the effects of quenched randomness on the universal properties
of a two-temperature lattice gas. The disorder modifies the dynamical
transition rates of the system in an anisotropic fashion, giving rise to a new
fixed point. We determine the associated scaling form of the structure factor,
quoting critical exponents to two-loop order in an expansion around the upper
critical dimension d. The close relationship with another quenched
disorder fixed point, discovered recently in this model, is discussed.Comment: 11 pages, no figures, RevTe
Stability of a Nonequilibrium Interface in a Driven Phase Segregating System
We investigate the dynamics of a nonequilibrium interface between coexisting
phases in a system described by a Cahn-Hilliard equation with an additional
driving term. By means of a matched asymptotic expansion we derive equations
for the interface motion. A linear stability analysis of these equations
results in a condition for the stability of a flat interface. We find that the
stability properties of a flat interface depend on the structure of the driving
term in the original equation.Comment: 14 pages Latex, 1 postscript-figur
Review of the k-Body Embedded Ensembles of Gaussian Random Matrices
The embedded ensembles were introduced by Mon and French as physically more
plausible stochastic models of many--body systems governed by one--and
two--body interactions than provided by standard random--matrix theory. We
review several approaches aimed at determining the spectral density, the
spectral fluctuation properties, and the ergodic properties of these ensembles:
moments methods, numerical simulations, the replica trick, the eigenvector
decomposition of the matrix of second moments and supersymmetry, the binary
correlation approximation, and the study of correlations between matrix
elements.Comment: Final version. 29 pages, 4 ps figures, uses iopart.st
Hirota's virtual multi-soliton solutions of N=2 supersymmetric Korteweg-de Vries equations
We prove that Mathieu's N=2 supersymmetric Korteweg-de Vries equations with
a=1 or a=4 admit Hirota's n-supersoliton solutions, whose nonlinear interaction
does not produce any phase shifts. For initial profiles that can not be
distinguished from a one-soliton solution at times t<<0, we reveal the
possibility of a spontaneous decay and, within a finite time, transformation
into a solitonic solution with a different wave number. This paradoxal effect
is realized by the completely integrable N=2 super-KdV systems, whenever the
initial soliton is loaded with other solitons that are virtual and become
manifest through the tau-function as the time grows.
Key words and phrases: Hirota's solitons, N=2 supersymmetric KdV,
Krasil'shchik-Kersten system, phase shift, spontaneous decay.Comment: Proc. 5th International Workshop `Nonlinear Physics: Theory and
Experiment' (June 12-21, 2008; Gallipoli, Italy), 11 page
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