2,649 research outputs found
Transient rectification of Brownian diffusion with asymmetric initial distribution
In an ensemble of non-interacting Brownian particles, a finite systematic
average velocity may temporarily develop, even if it is zero initially. The
effect originates from a small nonlinear correction to the dissipative force,
causing the equation for the first moment of velocity to couple to moments of
higher order. The effect may be relevant when a complex system dissociates in a
viscous medium with conservation of momentum
Generalized Fokker-Planck equation, Brownian motion, and ergodicity
Microscopic theory of Brownian motion of a particle of mass in a bath of
molecules of mass is considered beyond lowest order in the mass ratio
. The corresponding Langevin equation contains nonlinear corrections to
the dissipative force, and the generalized Fokker-Planck equation involves
derivatives of order higher than two. These equations are derived from first
principles with coefficients expressed in terms of correlation functions of
microscopic force on the particle. The coefficients are evaluated explicitly
for a generalized Rayleigh model with a finite time of molecule-particle
collisions. In the limit of a low-density bath, we recover the results obtained
previously for a model with instantaneous binary collisions. In general case,
the equations contain additional corrections, quadratic in bath density,
originating from a finite collision time. These corrections survive to order
and are found to make the stationary distribution non-Maxwellian.
Some relevant numerical simulations are also presented
Beyond the constraints underlying Kolmogorov-Johnson-Mehl-Avrami theory related to the growth laws
The theory of Kolmogorov-Johnson-Mehl-Avrami (KJMA) for phase transition
kinetics is subjected to severe limitations concerning the functional form of
the growth law. This paper is devoted to side step this drawback through the
use of correlation function approach. Moreover, we put forward an
easy-to-handle formula, written in terms of the experimentally accessible
actual extended volume fraction, which is found to match several types of
growths. Computer simulations have been done for corroborating the theoretical
approach.Comment: 18 pages ;11 figure
Vlasov Equation In Magnetic Field
The linearized Vlasov equation for a plasma system in a uniform magnetic
field and the corresponding linear Vlasov operator are studied. The spectrum
and the corresponding eigenfunctions of the Vlasov operator are found. The
spectrum of this operator consists of two parts: one is continuous and real;
the other is discrete and complex. Interestingly, the real eigenvalues are
infinitely degenerate, which causes difficulty solving this initial value
problem by using the conventional eigenfunction expansion method. Finally, the
Vlasov equation is solved by the resolvent method.Comment: 15 page
A model for alignment between microscopic rods and vorticity
Numerical simulations show that microscopic rod-like bodies suspended in a
turbulent flow tend to align with the vorticity vector, rather than with the
dominant eignevector of the strain-rate tensor. This paper investigates an
analytically solvable limit of a model for alignment in a random velocity field
with isotropic statistics. The vorticity varies very slowly and the isotropic
random flow is equivalent to a pure strain with statistics which are
axisymmetric about the direction of the vorticity. We analyse the alignment in
a weakly fluctuating uniaxial strain field, as a function of the product of the
strain relaxation time and the angular velocity about
the vorticity axis. We find that when , the rods are
predominantly either perpendicular or parallel to the vorticity
Field theoretic formulation of a mode-coupling equation for colloids
The only available quantitative description of the slowing down of the
dynamics upon approaching the glass transition has been, so far, the
mode-coupling theory, developed in the 80's by G\"otze and collaborators. The
standard derivation of this theory does not result from a systematic expansion.
We present a field theoretic formulation that arrives at very similar
mode-coupling equation but which is based on a variational principle and on a
controlled expansion in a small dimensioneless parameter. Our approach applies
to such physical systems as colloids interacting via a mildly repulsive
potential. It can in principle, with moderate efforts, be extended to higher
orders and to multipoint correlation functions
On Nonlinear Diffusion with Multiplicative Noise
Nonlinear diffusion is studied in the presence of multiplicative noise. The
nonlinearity can be viewed as a ``wall'' limiting the motion of the diffusing
field. A dynamic phase transition occurs when the system ``unbinds'' from the
wall. Two different universality classes, corresponding to the cases of an
``upper'' and a ``lower'' wall, are identified and their critical properties
are characterized. While the lower wall problem can be understood by applying
the knowledge of linear diffusion with multiplicative noise, the upper wall
problem exhibits an anomaly due to nontrivial dynamics in the vicinity of the
wall. Broad power-law distribution is obtained throughout the bound phase.Comment: 4 pages, LaTeX, text and figures also available at
http://matisse.ucsd.edu/~hw
Stochastic oscillations in models of epidemics on a network of cities
We carry out an analytic investigation of stochastic oscillations in a
susceptible-infected-recovered model of disease spread on a network of
cities. In the model a fraction of individuals from city commute
to city , where they may infect, or be infected by, others. Starting from a
continuous time Markov description of the model the deterministic equations,
which are valid in the limit when the population of each city is infinite, are
recovered. The stochastic fluctuations about the fixed point of these equations
are derived by use of the van Kampen system-size expansion. The fixed point
structure of the deterministic equations is remarkably simple: a unique
non-trivial fixed point always exists and has the feature that the fraction of
susceptible, infected and recovered individuals is the same for each city
irrespective of its size. We find that the stochastic fluctuations have an
analogously simple dynamics: all oscillations have a single frequency, equal to
that found in the one city case. We interpret this phenomenon in terms of the
properties of the spectrum of the matrix of the linear approximation of the
deterministic equations at the fixed point.Comment: 13 pages, 7 figure
On the Validity of the 0-1 Test for Chaos
In this paper, we present a theoretical justification of the 0-1 test for
chaos. In particular, we show that with probability one, the test yields 0 for
periodic and quasiperiodic dynamics, and 1 for sufficiently chaotic dynamics
The Barrier Method: A Technique for Calculating Very Long Transition Times
In many dynamical systems there is a large separation of time scales between
typical events and "rare" events which can be the cases of interest. Rare-event
rates are quite difficult to compute numerically, but they are of considerable
practical importance in many fields: for example transition times in chemical
physics and extinction times in epidemiology can be very long, but are quite
important. We present a very fast numerical technique that can be used to find
long transition times (very small rates) in low-dimensional systems, even if
they lack detailed balance. We illustrate the method for a bistable
non-equilibrium system introduced by Maier and Stein and a two-dimensional (in
parameter space) epidemiology model.Comment: 20 pages, 8 figure
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