1,347 research outputs found
An invariant in shock clustering and Burgers turbulence
1-D scalar conservation laws with convex flux and Markov initial data are now
known to yield a completely integrable Hamiltonian system. In this article, we
rederive the analogue of Loitsiansky's invariant in hydrodynamic turbulence
from the perspective of integrable systems. Other relevant physical notions
such as energy dissipation and spectrum are also discussed.Comment: 11 pages, no figures; v2: corrections mad
Orientation dynamics of weakly Brownian particles in periodic viscous flows
Evolution equations for the orientation distribution of axisymmetric
particles in periodic flows are derived in the regime of small but non-zero
Brownian rotations. The equations are based on a multiple time scale approach
that allows fast computation of the relaxation processes leading to statistical
equilibrium. The approach has been applied to the calculation of the effective
viscosity of a thin disk suspension in gravity waves.Comment: 16 pages, 7 eps figures include
Power Spectra of the Total Occupancy in the Totally Asymmetric Simple Exclusion Process
As a solvable and broadly applicable model system, the totally asymmetric
exclusion process enjoys iconic status in the theory of non-equilibrium phase
transitions. Here, we focus on the time dependence of the total number of
particles on a 1-dimensional open lattice, and its power spectrum. Using both
Monte Carlo simulations and analytic methods, we explore its behavior in
different characteristic regimes. In the maximal current phase and on the
coexistence line (between high/low density phases), the power spectrum displays
algebraic decay, with exponents -1.62 and -2.00, respectively. Deep within the
high/low density phases, we find pronounced \emph{oscillations}, which damp
into power laws. This behavior can be understood in terms of driven biased
diffusion with conserved noise in the bulk.Comment: 4 pages, 4 figure
Temperature-induced crossovers in the static roughness of a one-dimensional interface
At finite temperature and in presence of disorder, a one-dimensional elastic
interface displays different scaling regimes at small and large lengthscales.
Using a replica approach and a Gaussian Variational Method (GVM), we explore
the consequences of a finite interface width on the small-lengthscale
fluctuations. We compute analytically the static roughness of the
interface as a function of the distance between two points on the
interface. We focus on the case of short-range elasticity and random-bond
disorder. We show that for a finite width two temperature regimes exist.
At low temperature, the expected thermal and random-manifold regimes,
respectively for small and large scales, connect via an intermediate `modified'
Larkin regime, that we determine. This regime ends at a temperature-independent
characteristic `Larkin' length. Above a certain `critical' temperature that we
identify, this intermediate regime disappears. The thermal and random-manifold
regimes connect at a single crossover lengthscale, that we compute. This is
also the expected behavior for zero width. Using a directed polymer
description, we also study via a second GVM procedure and generic scaling
arguments, a modified toy model that provides further insights on this
crossover. We discuss the relevance of the two GVM procedures for the roughness
at large lengthscale in those regimes. In particular we analyze the scaling of
the temperature-dependent prefactor in the roughness B(r)\sim T^{2
\text{\thorn}} r^{2 \zeta} and its corresponding exponent \text{\thorn}. We
briefly discuss the consequences of those results for the quasistatic creep law
of a driven interface, in connection with previous experimental and numerical
studies
Density Matrix Renormalization for Model Reduction in Nonlinear Dynamics
We present a novel approach for model reduction of nonlinear dynamical
systems based on proper orthogonal decomposition (POD). Our method, derived
from Density Matrix Renormalization Group (DMRG), provides a significant
reduction in computational effort for the calculation of the reduced system,
compared to a POD. The efficiency of the algorithm is tested on the one
dimensional Burgers equations and a one dimensional equation of the Fisher type
as nonlinear model systems.Comment: 12 pages, 12 figure
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