262 research outputs found
Shock statistics in higher-dimensional Burgers turbulence
We conjecture the exact shock statistics in the inviscid decaying Burgers
equation in D>1 dimensions, with a special class of correlated initial
velocities, which reduce to Brownian for D=1. The prediction is based on a
field-theory argument, and receives support from our numerical calculations. We
find that, along any given direction, shocks sizes and locations are
uncorrelated.Comment: 4 pages, 8 figure
Large time off-equilibrium dynamics of a manifold in a random potential
We study the out of equilibrium dynamics of an elastic manifold in a random
potential using mean-field theory. We find two asymptotic time regimes: (i)
stationary dynamics, (ii) slow aging dynamics with violation of equilibrium
theorems. We obtain an analytical solution valid for all large times with
universal scalings of two-time quantities with space. A non-analytic scaling
function crosses over to ultrametricity when the correlations become
long-range. We propose procedures to test numerically or experimentally the
extent to which this scenario holds for a given system.Comment: 12 page
Universal interface width distributions at the depinning threshold
We compute the probability distribution of the interface width at the
depinning threshold, using recent powerful algorithms. It confirms the
universality classes found previously. In all cases, the distribution is
surprisingly well approximated by a generalized Gaussian theory of independant
modes which decay with a characteristic propagator G(q)=1/q^(d+2 zeta); zeta,
the roughness exponent, is computed independently. A functional renormalization
analysis explains this result and allows to compute the small deviations, i.e.
a universal kurtosis ratio, in agreement with numerics. We stress the
importance of the Gaussian theory to interpret numerical data and experiments.Comment: 4 pages revtex4. See also the following article cond-mat/030146
Higher correlations, universal distributions and finite size scaling in the field theory of depinning
Recently we constructed a renormalizable field theory up to two loops for the
quasi-static depinning of elastic manifolds in a disordered environment. Here
we explore further properties of the theory. We show how higher correlation
functions of the displacement field can be computed. Drastic simplifications
occur, unveiling much simpler diagrammatic rules than anticipated. This is
applied to the universal scaled width-distribution. The expansion in
d=4-epsilon predicts that the scaled distribution coincides to the lowest
orders with the one for a Gaussian theory with propagator G(q)=1/q^(d+2 \zeta),
zeta being the roughness exponent. The deviations from this Gaussian result are
small and involve higher correlation functions, which are computed here for
different boundary conditions. Other universal quantities are defined and
evaluated: We perform a general analysis of the stability of the fixed point.
We find that the correction-to-scaling exponent is omega=-epsilon and not
-epsilon/3 as used in the analysis of some simulations. A more detailed study
of the upper critical dimension is given, where the roughness of interfaces
grows as a power of a logarithm instead of a pure power.Comment: 15 pages revtex4. See also preceding article cond-mat/030146
Statics and dynamics of elastic manifolds in media with long-range correlated disorder
We study the statics and dynamics of an elastic manifold in a disordered
medium with quenched defects correlated as r^{-a} for large separation r. We
derive the functional renormalization-group equations to one-loop order, which
allow us to describe the universal properties of the system in equilibrium and
at the depinning transition. Using a double epsilon=4-d and delta=4-a
expansion, we compute the fixed points characterizing different universality
classes and analyze their regions of stability. The long-range
disorder-correlator remains analytic but generates short-range disorder whose
correlator exhibits the usual cusp. The critical exponents and universal
amplitudes are computed to first order in epsilon and delta at the fixed
points. At depinning, a velocity-versus-force exponent beta larger than unity
can occur. We discuss possible realizations using extended defects.Comment: 16 pages, 11 figures, revtex
Creep via dynamical functional renormalization group
We study a D-dimensional interface driven in a disordered medium. We derive
finite temperature and velocity functional renormalization group (FRG)
equations, valid in a 4-D expansion. These equations allow in principle for a
complete study of the the velocity versus applied force characteristics. We
focus here on the creep regime at finite temperature and small velocity. We
show how our FRG approach gives the form of the v-f characteristics in this
regime, and in particular the creep exponent, obtained previously only through
phenomenological scaling arguments.Comment: 4 pages, 3 figures, RevTe
Diffusion and Creep of a Particle in a Random Potential
We investigate the diffusive motion of an overdamped classical particle in a
1D random potential using the mean first-passage time formalism and demonstrate
the efficiency of this method in the investigation of the large-time dynamics
of the particle. We determine the -time diffusion {<{<
x^{2}(t)>}_{th}>}_{dis}=A\ln^{\beta} \left ({t}/{t_{r}}) and relate the
prefactor the relaxation time and the exponent to the
details of the (generally non-gaussian) long-range correlated potential.
Calculating the moments {}_{th}>}_{dis} of the first-passage time
distribution we reconstruct the large time distribution function itself
and draw attention to the phenomenon of intermittency. The results can be
easily interpreted in terms of the decay of metastable trapped states. In
addition, we present a simple derivation of the mean velocity of a particle
moving in a random potential in the presence of a constant external force.Comment: 6 page
Freezing of dynamical exponents in low dimensional random media
A particle in a random potential with logarithmic correlations in dimensions
is shown to undergo a dynamical transition at . In
exact results demonstrate that , the static glass transition
temperature, and that the dynamical exponent changes from at high temperature to in the glass phase. The same
formulae are argued to hold in . Dynamical freezing is also predicted in
the 2D random gauge XY model and related systems. In a mapping between
dynamics and statics is unveiled and freezing involves barriers as well as
valleys. Anomalous scaling occurs in the creep dynamics.Comment: 5 pages, 2 figures, RevTe
Aging in the glass phase of a 2D random periodic elastic system
Using RG we investigate the non-equilibrium relaxation of the (Cardy-Ostlund)
2D random Sine-Gordon model, which describes pinned arrays of lines. Its
statics exhibits a marginal () glass phase for described by a
line of fixed points. We obtain the universal scaling functions for two-time
dynamical response and correlations near for various initial conditions,
as well as the autocorrelation exponent. The fluctuation dissipation ratio is
found to be non-trivial and continuously dependent on .Comment: 5 pages, RevTex, Modified Versio
Localization of thermal packets and metastable states in Sinai model
We consider the Sinai model describing a particle diffusing in a 1D random
force field. As shown by Golosov, this model exhibits a strong localization
phenomenon for the thermal packet: the disorder average of the thermal
distribution of the relative distance y=x-m(t), with respect to the
(disorder-dependent) most probable position m(t), converges in the limit of
infinite time towards a distribution P(y). In this paper, we revisit this
question of the localization of the thermal packet. We first generalize the
result of Golosov by computing explicitly the joint asymptotic distribution of
relative position y=x(t)-m(t) and relative energy u=U(x(t))-U(m(t)) for the
thermal packet. Next, we compute in the infinite-time limit the localization
parameters Y_k, representing the disorder-averaged probabilities that k
particles of the thermal packet are at the same place, and the correlation
function C(l) representing the disorder-averaged probability that two particles
of the thermal packet are at a distance l from each other. We moreover prove
that our results for Y_k and C(l) exactly coincide with the thermodynamic limit
of the analog quantities computed for independent particles at equilibrium in a
finite sample of length L. Finally, we discuss the properties of the
finite-time metastable states that are responsible for the localization
phenomenon and compare with the general theory of metastable states in glassy
systems, in particular as a test of the Edwards conjecture.Comment: 17 page
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