63 research outputs found
Galilean invariance and homogeneous anisotropic randomly stirred flows
The Ward-Takahashi (WT) identities for incompressible flow implied by
Galilean invariance are derived for the randomly forced Navier-Stokes equation
(NSE), in which both the mean and fluctuating velocity components are
explicitly present. The consequences of Galilean invariance for the vertex
renormalization are drawn from this identity.Comment: REVTeX 4, 4 pages, no figures. To appear as a Brief Report in the
Physical Review
Local Spin Glass Order in 1D
We study the behavior of one dimensional Kac spin glasses as function of the
interaction range. We verify by Montecarlo numerical simulations the crossover
from local mean field behavior to global paramagnetism. We investigate the
behavior of correlations and find that in the low temperature phase
correlations grow at a faster rate then the interaction range. We completely
characterize the growth of correlations in the vicinity of the mean-field
critical region
On Critical Exponents and the Renormalization of the Coupling Constant in Growth Models with Surface Diffusion
It is shown by the method of renormalized field theory that in contrast to a
statement based on a mathematically ill-defined invariance transformation and
found in most of the recent publications on growth models with surface
diffusion, the coupling constant of these models renormalizes nontrivially.
This implies that the widely accepted supposedly exact scaling exponents are to
be corrected. A two-loop calculation shows that the corrections are small and
these exponents seem to be very good approximations.Comment: 4 pages, revtex, 2 postscript figures, to appear in Phys.Rev.Let
Logarithmic Corrections in Dynamic Isotropic Percolation
Based on the field theoretic formulation of the general epidemic process we
study logarithmic corrections to scaling in dynamic isotropic percolation at
the upper critical dimension d=6. Employing renormalization group methods we
determine these corrections for some of the most interesting time dependent
observables in dynamic percolation at the critical point up to and including
the next to leading correction. For clusters emanating from a local seed at the
origin we calculate the number of active sites, the survival probability as
well as the radius of gyration.Comment: 9 pages, 3 figures, version to appear in Phys. Rev.
Response Functions in Phase Ordering Kinetics
We discuss the behavior of response functions in phase ordering kinetics
within the perturbation theory approach developed earlier. At zeroth order the
results agree with previous gaussian theory calculations. At second order the
nonequilibrium exponents \lambda and \lambda_{R} are changed but remain equal.Comment: 29 page
Crystallization and melting of bacteria colonies and Brownian Bugs
Motivated by the existence of remarkably ordered cluster arrays of bacteria
colonies growing in Petri dishes and related problems, we study the spontaneous
emergence of clustering and patterns in a simple nonequilibrium system: the
individual-based interacting Brownian bug model. We map this discrete model
into a continuous Langevin equation which is the starting point for our
extensive numerical analyses. For the two-dimensional case we report on the
spontaneous generation of localized clusters of activity as well as a
melting/freezing transition from a disordered or isotropic phase to an ordered
one characterized by hexagonal patterns. We study in detail the analogies and
differences with the well-established Kosterlitz-Thouless-Halperin-Nelson-Young
theory of equilibrium melting, as well as with another competing theory. For
that, we study translational and orientational correlations and perform a
careful defect analysis. We find a non standard one-stage, defect-mediated,
transition whose nature is only partially elucidated.Comment: 13 Figures. 14 pages. Submitted to Phys. Rev.
Renormalized field theory of collapsing directed randomly branched polymers
We present a dynamical field theory for directed randomly branched polymers
and in particular their collapse transition. We develop a phenomenological
model in the form of a stochastic response functional that allows us to address
several interesting problems such as the scaling behavior of the swollen phase
and the collapse transition. For the swollen phase, we find that by choosing
model parameters appropriately, our stochastic functional reduces to the one
describing the relaxation dynamics near the Yang-Lee singularity edge. This
corroborates that the scaling behavior of swollen branched polymers is governed
by the Yang-Lee universality class as has been known for a long time. The main
focus of our paper lies on the collapse transition of directed branched
polymers. We show to arbitrary order in renormalized perturbation theory with
-expansion that this transition belongs to the same universality
class as directed percolation.Comment: 18 pages, 7 figure
Spontaneous Symmetry Breaking in Directed Percolation with Many Colors: Differentiation of Species in the Gribov Process
A general field theoretic model of directed percolation with many colors that
is equivalent to a population model (Gribov process) with many species near
their extinction thresholds is presented. It is shown that the multicritical
behavior is always described by the well known exponents of Reggeon field
theory. In addition this universal model shows an instability that leads in
general to a total asymmetry between each pair of species of a cooperative
society.Comment: 4 pages, 2 Postscript figures, uses multicol.sty, submitte
Probability currents as principal characteristics in the statistical mechanics of non-equilibrium steady states
One of the key features of non-equilibrium steady states (NESS) is the
presence of nontrivial probability currents. We propose a general
classification of NESS in which these currents play a central distinguishing
role. As a corollary, we specify the transformations of the dynamic transition
rates which leave a given NESS invariant. The formalism is most transparent
within a continuous time master equation framework since it allows for a
general graph-theoretical representation of the NESS. We discuss the
consequences of these transformations for entropy production, present several
simple examples, and explore some generalizations, to discrete time and
continuous variables.Comment: 39 pages, 5 figures. Invited article for JSTAT Special Issue on
'Principles of Dynamics of Nonequilibrium Systems', held at the Newton
Institute, Cambridge, UK, in 200
Strongly anisotropic roughness in surfaces driven by an oblique particle flux
Using field theoretic renormalization, an MBE-type growth process with an
obliquely incident influx of atoms is examined. The projection of the beam on
the substrate plane selects a "parallel" direction, with rotational invariance
restricted to the transverse directions. Depending on the behavior of an
effective anisotropic surface tension, a line of second order transitions is
identified, as well as a line of potentially first order transitions, joined by
a multicritical point. Near the second order transitions and the multicritical
point, the surface roughness is strongly anisotropic. Four different roughness
exponents are introduced and computed, describing the surface in different
directions, in real or momentum space. The results presented challenge an
earlier study of the multicritical point.Comment: 11 pages, 2 figures, REVTeX
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