575 research outputs found
Spatio-temporal patterns driven by autocatalytic internal reaction noise
The influence that intrinsic local density fluctuations can have on solutions
of mean-field reaction-diffusion models is investigated numerically by means of
the spatial patterns arising from two species that react and diffuse in the
presence of strong internal reaction noise. The dynamics of the Gray-Scott (GS)
model with constant external source is first cast in terms of a continuum field
theory representing the corresponding master equation. We then derive a
Langevin description of the field theory and use these stochastic differential
equations in our simulations. The nature of the multiplicative noise is
specified exactly without recourse to assumptions and turns out to be of the
same order as the reaction itself, and thus cannot be treated as a small
perturbation. Many of the complex patterns obtained in the absence of noise for
the GS model are completely obliterated by these strong internal fluctuations,
but we find novel spatial patterns induced by this reaction noise in regions of
parameter space that otherwise correspond to homogeneous solutions when
fluctuations are not included.Comment: 12 pages, 18 figure
Diffusion-induced bistability of driven nanomechanical resonators
We study nanomechanical resonators with frequency fluctuations due to
diffusion of absorbed particles. The diffusion depends on the vibration
amplitude through inertial effect. We find that, if the diffusion coefficient
is sufficiently large, the resonator response to periodic driving displays
bistability. The lifetime of the coexisting vibrational states scales
exponentially with the diffusion coefficient. It also displays a characteristic
scaling dependence on the distance to bifurcation points.Comment: 4 pages, 3 figure
Quantum State Diffusion and Time Correlation Functions
In computing the spectra of quantum mechanical systems one encounters the
Fourier transforms of time correlation functions, as given by the quantum
regression theorem for systems described by master equations. Quantum state
diffusion (QSD) gives a useful method of solving these problems by unraveling
the master equation into stochastic trajectories; but there is no generally
accepted definition of a time correlation function for a single QSD trajectory.
In this paper we show how QSD can be used to calculate these spectra directly;
by formally solving the equations which arise, we arrive at a natural
definition for a two-time correlation function in QSD, which depends explicitly
on both the stochastic noise of the particular trajectory and the time of
measurement, and which agrees in the mean with the ensemble average definition
of correlation functions.Comment: 16 pages standard LaTeX + 1 figure (uuencoded postscript) Numerous
minor revisions and clarifications. To appear in J. Mod. Optic
Anomalous diffusion for overdamped particles driven by cross-correlated white noise sources
We study the statistical properties of overdamped particles driven by two
cross-correlated multiplicative Gaussian white noises in a time-dependent
environment. Using the Langevin and Fokker-Planck approaches, we derive the
exact probability distribution function for the particle positions, calculate
its moments and find their corresponding long-time, asymptotic behaviors. The
generally anomalous diffusive regimes of the particles are classified, and
their dependence on the friction coefficient and the characteristics of the
noises is analyzed in detail. The asymptotic predictions are confirmed by exact
solutions for two examples.Comment: 15 page
Emergence of stability in a stochastically driven pendulum: beyond the Kapitsa effect
We consider a prototypical nonlinear system which can be stabilized by
multiplicative noise: an underdamped non-linear pendulum with a stochastically
vibrating pivot. A numerical solution of the pertinent Fokker-Planck equation
shows that the upper equilibrium point of the pendulum can become stable even
when the noise is white, and the "Kapitsa pendulum" effect is not at work. The
stabilization occurs in a strong-noise regime where WKB approximation does not
hold.Comment: 4 pages, 7 figure
Multiplicative Noise: Applications in Cosmology and Field Theory
Physical situations involving multiplicative noise arise generically in
cosmology and field theory. In this paper, the focus is first on exact
nonlinear Langevin equations, appropriate in a cosmologica setting, for a
system with one degree of freedom. The Langevin equations are derived using an
appropriate time-dependent generalization of a model due to Zwanzig. These
models are then extended to field theories and the generation of multiplicative
noise in such a context is discussed. Important issues in both the cosmological
and field theoretic cases are the fluctuation-dissipation relations and the
relaxation time scale. Of some importance in cosmology is the fact that
multiplicative noise can substantially reduce the relaxation time. In the field
theoretic context such a noise can lead to a significant enhancement in the
nucleation rate of topological defects.Comment: 21 pages, LaTex, LA-UR-93-210
Noise-Induced Synchronization of a Large Population of Globally Coupled Nonidentical Oscillators
We study a large population of globally coupled phase oscillators subject to
common white Gaussian noise and find analytically that the critical coupling
strength between oscillators for synchronization transition decreases with an
increase in the intensity of common noise. Thus, common noise promotes the
onset of synchronization. Our prediction is confirmed by numerical simulations
of the phase oscillators as well as of limit-cycle oscillators
Macroscopic description of particle systems with non-local density-dependent diffusivity
In this paper we study macroscopic density equations in which the diffusion
coefficient depends on a weighted spatial average of the density itself. We
show that large differences (not present in the local density-dependence case)
appear between the density equations that are derived from different
representations of the Langevin equation describing a system of interacting
Brownian particles. Linear stability analysis demonstrates that under some
circumstances the density equation interpreted like Ito has pattern solutions,
which never appear for the Hanggi-Klimontovich interpretation, which is the
other one typically appearing in the context of nonlinear diffusion processes.
We also introduce a discrete-time microscopic model of particles that confirms
the results obtained at the macroscopic density level.Comment: 4 pages, 3 figure
Analysis of noise-induced transitions from regular to chaotic oscillations in the Chen system
The stochastically perturbed Chen system is studied within the parameter region which permits both regular and chaotic oscillations. As noise intensity increases and passes some threshold value, noise-induced hopping between close portions of the stochastic cycle can be observed. Through these transitions, the stochastic cycle is deformed to be a stochastic attractor that looks like chaotic. In this paper for investigation of these transitions, a constructive method based on the stochastic sensitivity function technique with confidence ellipses is suggested and discussed in detail. Analyzing a mutual arrangement of these ellipses, we estimate the threshold noise intensity corresponding to chaotization of the stochastic attractor. Capabilities of this geometric method for detailed analysis of the noise-induced hopping which generates chaos are demonstrated on the stochastic Chen system. © 2012 American Institute of Physics
State selection in the noisy stabilized Kuramoto-Sivashinsky equation
In this work, we study the 1D stabilized Kuramoto Sivashinsky equation with
additive uncorrelated stochastic noise. The Eckhaus stable band of the
deterministic equation collapses to a narrow region near the center of the
band. This is consistent with the behavior of the phase diffusion constants of
these states. Some connections to the phenomenon of state selection in driven
out of equilibrium systems are made.Comment: 8 pages, In version 3 we corrected minor/typo error
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