791 research outputs found
Nonequilibrium dynamics of a growing interface
A growing interface subject to noise is described by the Kardar-Parisi-Zhang
equation or, equivalently, the noisy Burgers equation. In one dimension this
equation is analyzed by means of a weak noise canonical phase space approach
applied to the associated Fokker-Planck equation. The growth morphology is
characterized by a gas of nonlinear soliton modes with superimposed linear
diffusive modes. We also discuss the ensuing scaling properties.Comment: 14 pages, 11 figures, conference proceeding; a few corrections have
been adde
Vortex tubes in velocity fields of laboratory isotropic turbulence: dependence on the Reynolds number
The streamwise and transverse velocities are measured simultaneously in
isotropic grid turbulence at relatively high Reynolds numbers, Re(lambda) =
110-330. Using a conditional averaging technique, we extract typical
intermittency patterns, which are consistent with velocity profiles of a model
for a vortex tube, i.e., Burgers vortex. The radii of the vortex tubes are
several of the Kolmogorov length regardless of the Reynolds number. Using the
distribution of an interval between successive enhancements of a small-scale
velocity increment, we study the spatial distribution of vortex tubes. The
vortex tubes tend to cluster together. This tendency is increasingly
significant with the Reynolds number. Using statistics of velocity increments,
we also study the energetical importance of vortex tubes as a function of the
scale. The vortex tubes are important over the background flow at small scales
especially below the Taylor microscale. At a fixed scale, the importance is
increasingly significant with the Reynolds number.Comment: 8 pages, 3 PS files for 8 figures, to appear in Physical Review
Canonical phase space approach to the noisy Burgers equation: Probability distributions
We present a canonical phase space approach to stochastic systems described
by Langevin equations driven by white noise. Mapping the associated
Fokker-Planck equation to a Hamilton-Jacobi equation in the nonperturbative
weak noise limit we invoke a {\em principle of least action} for the
determination of the probability distributions. We apply the scheme to the
noisy Burgers and KPZ equations and discuss the time-dependent and stationary
probability distributions. In one dimension we derive the long-time skew
distribution approaching the symmetric stationary Gaussian distribution. In the
short-time region we discuss heuristically the nonlinear soliton contributions
and derive an expression for the distribution in accordance with the directed
polymer-replica and asymmetric exclusion model results. We also comment on the
distribution in higher dimensions.Comment: 18 pages Revtex file, including 8 eps-figures, submitted to Phys.
Rev.
Static avalanches and Giant stress fluctuations in Silos
We propose a simple model for arch formation in silos. We show that small
pertubations (such as the thermal expansion of the beads) may lead to giant
stress fluctuations on the bottom plate of the silo. The relative amplitude
of these fluctuations are found to be power-law distributed, as
, . These fluctuations are related to large
scale `static avalanches', which correspond to long-range redistributions of
stress paths within the silo.Comment: 10 pages, 4 figures.p
Merging and fragmentation in the Burgers dynamics
We explore the noiseless Burgers dynamics in the inviscid limit, the
so-called ``adhesion model'' in cosmology, in a regime where (almost) all the
fluid particles are embedded within point-like massive halos. Following
previous works, we focus our investigations on a ``geometrical'' model, where
the matter evolution within the shock manifold is defined from a geometrical
construction. This hypothesis is at variance with the assumption that the usual
continuity equation holds but, in the inviscid limit, both models agree in the
regular regions. Taking advantage of the formulation of the dynamics of this
``geometrical model'' in terms of Legendre transforms and convex hulls, we
study the evolution with time of the distribution of matter and the associated
partitions of the Lagrangian and Eulerian spaces. We describe how the halo mass
distribution derives from a triangulation in Lagrangian space, while the dual
Voronoi-like tessellation in Eulerian space gives the boundaries of empty
regions with shock nodes at their vertices. We then emphasize that this
dynamics actually leads to halo fragmentations for space dimensions greater or
equal to 2 (for the inviscid limit studied in this article). This is most
easily seen from the properties of the Lagrangian-space triangulation and we
illustrate this process in the two-dimensional (2D) case. In particular, we
explain how point-like halos only merge through three-body collisions while
two-body collisions always give rise to two new massive shock nodes (in 2D).
This generalizes to higher dimensions and we briefly illustrate the
three-dimensional (3D) case. This leads to a specific picture for the
continuous formation of massive halos through successive halo fragmentations
and mergings.Comment: 21 pages, final version published in Phys.Rev.
Exact solution of a one-parameter family of asymmetric exclusion processes
We define a family of asymmetric processes for particles on a one-dimensional
lattice, depending on a continuous parameter ,
interpolating between the completely asymmetric processes [1] (for ) and the n=1 drop-push models [2] (for ). For arbitrary \la,
the model describes an exclusion process, in which a particle pushes its right
neighbouring particles to the right, with rates depending on the number of
these particles. Using the Bethe ansatz, we obtain the exact solution of the
master equation .Comment: 14 pages, LaTe
Targeted combination therapies in oncology:Challenging regulatory frameworks designed for monotherapies in Europe
Analytical Investigation of Innovation Dynamics Considering Stochasticity in the Evaluation of Fitness
We investigate a selection-mutation model for the dynamics of technological
innovation,a special case of reaction-diffusion equations. Although mutations
are assumed to increase the variety of technologies, not their average success
("fitness"), they are an essential prerequisite for innovation. Together with a
selection of above-average technologies due to imitation behavior, they are the
"driving force" for the continuous increase in fitness. We will give analytical
solutions for the probability distribution of technologies for special cases
and in the limit of large times.
The selection dynamics is modelled by a "proportional imitation" of better
technologies. However, the assessment of a technology's fitness may be
imperfect and, therefore, vary stochastically. We will derive conditions, under
which wrong assessment of fitness can accelerate the innovation dynamics, as it
has been found in some surprising numerical investigations.Comment: For related work see http://www.helbing.or
Soliton approach to the noisy Burgers equation: Steepest descent method
The noisy Burgers equation in one spatial dimension is analyzed by means of
the Martin-Siggia-Rose technique in functional form. In a canonical formulation
the morphology and scaling behavior are accessed by mean of a principle of
least action in the asymptotic non-perturbative weak noise limit. The ensuing
coupled saddle point field equations for the local slope and noise fields,
replacing the noisy Burgers equation, are solved yielding nonlinear localized
soliton solutions and extended linear diffusive mode solutions, describing the
morphology of a growing interface. The canonical formalism and the principle of
least action also associate momentum, energy, and action with a
soliton-diffusive mode configuration and thus provides a selection criterion
for the noise-induced fluctuations. In a ``quantum mechanical'' representation
of the path integral the noise fluctuations, corresponding to different paths
in the path integral, are interpreted as ``quantum fluctuations'' and the
growth morphology represented by a Landau-type quasi-particle gas of ``quantum
solitons'' with gapless dispersion and ``quantum diffusive modes'' with a gap
in the spectrum. Finally, the scaling properties are dicussed from a heuristic
point of view in terms of a``quantum spectral representation'' for the slope
correlations. The dynamic eponent z=3/2 is given by the gapless soliton
dispersion law, whereas the roughness exponent zeta =1/2 follows from a
regularity property of the form factor in the spectral representation. A
heuristic expression for the scaling function is given by spectral
representation and has a form similar to the probability distribution for Levy
flights with index .Comment: 30 pages, Revtex file, 14 figures, to be submitted to Phys. Rev.
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