1,769 research outputs found
Two-Dimensional Diffusion in the Presence of Topological Disorder
How topological defects affect the dynamics of particles hopping between
lattice sites of a distorted, two-dimensional crystal is addressed.
Perturbation theory and numerical simulations show that weak, short-ranged
topological disorder leads to a finite reduction of the diffusion coefficient.
Renormalization group theory and numerical simulations suggest that
longer-ranged disorder, such as that from randomly placed dislocations or
random disclinations with no net disclinicity, leads to subdiffusion at long
times.Comment: 10 pages, 6 figure
Reaction-controlled diffusion: Monte Carlo simulations
We study the coupled two-species non-equilibrium reaction-controlled
diffusion model introduced by Trimper et al. [Phys. Rev. E 62, 6071 (2000)] by
means of detailed Monte Carlo simulations in one and two dimensions. Particles
of type A may independently hop to an adjacent lattice site provided it is
occupied by at least one B particle. The B particle species undergoes
diffusion-limited reactions. In an active state with nonzero, essentially
homogeneous B particle saturation density, the A species displays normal
diffusion. In an inactive, absorbing phase with exponentially decaying B
density, the A particles become localized. In situations with algebraic decay
rho_B(t) ~ t^{-alpha_B}, as occuring either at a non-equilibrium continuous
phase transition separating active and absorbing states, or in a power-law
inactive phase, the A particles propagate subdiffusively with mean-square
displacement ~ t^{1-alpha_A}. We find that within the accuracy of
our simulation data, \alpha_A = \alpha_B as predicted by a simple mean-field
approach. This remains true even in the presence of strong spatio-temporal
fluctuations of the B density. However, in contrast with the mean-field
results, our data yield a distinctly non-Gaussian A particle displacement
distribution n_A(x,t) that obeys dynamic scaling and looks remarkably similar
for the different processes investigated here. Fluctuations of effective
diffusion rates cause a marked enhancement of n_A(x,t) at low displacements
|x|, indicating a considerable fraction of practically localized A particles,
as well as at large traversed distances.Comment: Revtex, 19 pages, 27 eps figures include
The Reaction-Diffusion Front for in One Dimension
We study theoretically and numerically the steady state diffusion controlled
reaction , where currents of and particles
are applied at opposite boundaries. For a reaction rate , and equal
diffusion constants , we find that when the
reaction front is well described by mean field theory. However, for , the front acquires a Gaussian profile - a result of
noise induced wandering of the reaction front center. We make a theoretical
prediction for this profile which is in good agreement with simulation.
Finally, we investigate the intrinsic (non-wandering) front width and find
results consistent with scaling and field theoretic predictions.Comment: 11 pages, revtex, 4 separate PostScript figure
Functional Methods in Stochastic Systems
Field-theoretic construction of functional representations of solutions of
stochastic differential equations and master equations is reviewed. A generic
expression for the generating function of Green functions of stochastic systems
is put forward. Relation of ambiguities in stochastic differential equations
and in the functional representations is discussed. Ordinary differential
equations for expectation values and correlation functions are inferred with
the aid of a variational approach.Comment: Plenary talk presented at Mathematical Modeling and Computational
Science. International Conference, MMCP 2011, Star\'a Lesn\'a, Slovakia, July
4-8, 201
Diffusion-controlled annihilation with initially separated reactants: The death of an particle island in the particle sea
We consider the diffusion-controlled annihilation dynamics with
equal species diffusivities in the system where an island of particles is
surrounded by the uniform sea of particles . We show that once the initial
number of particles in the island is large enough, then at any system's
dimensionality the death of the majority of particles occurs in the {\it
universal scaling regime} within which of the particles die at
the island expansion stage and the remaining at the stage of its
subsequent contraction. In the quasistatic approximation the scaling of the
reaction zone has been obtained for the cases of mean-field ()
and fluctuation () dynamics of the front.Comment: 4 RevTex pages, 1 PNG figure and 1 EPS figur
Multiple Transitions to Chaos in a Damped Parametrically Forced Pendulum
We study bifurcations associated with stability of the lowest stationary
point (SP) of a damped parametrically forced pendulum by varying
(the natural frequency of the pendulum) and (the amplitude of the external
driving force). As is increased, the SP will restabilize after its
instability, destabilize again, and so {\it ad infinitum} for any given
. Its destabilizations (restabilizations) occur via alternating
supercritical (subcritical) period-doubling bifurcations (PDB's) and pitchfork
bifurcations, except the first destabilization at which a supercritical or
subcritical bifurcation takes place depending on the value of . For
each case of the supercritical destabilizations, an infinite sequence of PDB's
follows and leads to chaos. Consequently, an infinite series of period-doubling
transitions to chaos appears with increasing . The critical behaviors at the
transition points are also discussed.Comment: 20 pages + 7 figures (available upon request), RevTex 3.
Measuring Lateral Magnetic Structure in Thin Films Using Polarized Neutron Reflectometry
Polarized neutron reflectometry (PNR) has long been applied to measure the
magnetic depth profile of thin films. In recent years, interest has increased
in observing lateral magnetic structures in a film. While magnetic arrays
patterned by lithography and submicron-sized magnetic domains in thin films
often give rise to off-specular reflections, micron-sized ferromagnetic domains
on a thin film produce few off-specular reflections and the domain distribution
information is contained within the specular reflection. In this paper, we will
first present some preliminary results of off-specular reflectivity from arrays
of micron-sized permalloy rectangular bars. We will then use specular
reflections to study the domain dispersion of an exchange-biased Co/CoO bilayer
at different locations of the hysteresis loop.Comment: 10 pages, 3 figurres, PNCMI 2002, Juelich, German
Persistence in q-state Potts model: A Mean-Field approach
We study the Persistence properties of the T=0 coarsening dynamics of one
dimensional -state Potts model using a modified mean-field approximation
(MMFA). In this approximation, the spatial correlations between the interfaces
separating spins with different Potts states is ignored, but the correct time
dependence of the mean density of persistent spins is imposed. For this
model, it is known that follows a power-law decay with time, where is the -dependent persistence exponent. We
study the spatial structure of the persistent region within the MMFA. We show
that the persistent site pair correlation function has the scaling
form for all values of the persistence
exponent . The scaling function has the limiting behaviour () and (). We then show within the
Independent Interval Approximation (IIA) that the distribution of
separation between two consecutive persistent spins at time has the
asymptotic scaling form where the
dynamical exponent has the form =max(). The behaviour of
the scaling function for large and small values of the arguments is found
analytically. We find that for small separations where =max(), while for large
separations , decays exponentially with . The
unusual dynamical scaling form and the behaviour of the scaling function is
supported by numerical simulations.Comment: 11 pages in RevTeX, 10 figures, submitted to Phys. Rev.
Long Range Hops and the Pair Annihilation Reaction A+A->0: Renormalization Group and Simulation
A simple example of a non-equilibrium system for which fluctuations are
important is a system of particles which diffuse and may annihilate in pairs on
contact. The renormalization group can be used to calculate the time dependence
of the density of particles, and provides both an exact value for the exponent
governing the decay of particles and an epsilon-expansion for the amplitude of
this power law. When the diffusion is anomalous, as when the particles perform
Levy flights, the critical dimension depends continuously on the control
parameter for the Levy distribution. The epsilon-expansion can then become an
expansion in a small parameter. We present a renormalization group calculation
and compare these results with those of a simulation.Comment: As-published version; two significant errors fixed, two references
adde
Reaction, Levy Flights, and Quenched Disorder
We consider the A + A --> emptyset reaction, where the transport of the
particles is given by Levy flights in a quenched random potential. With a
common literature model of the disorder, the random potential can only increase
the rate of reaction. With a model of the disorder that obeys detailed balance,
however, the rate of reaction initially increases and then decreases as a
function of the disorder strength. The physical behavior obtained with this
second model is in accord with that for reactive turbulent flow, indicating
that Levy flight statistics can model aspects of turbulent fluid transport.Comment: 6 pages, 5 pages. Phys. Rev. E. 65 (2002) 011109--1-
- …