630 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
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
Chaotic versus stochastic behavior in active-dissipative nonlinear systems
We study the dynamical state of the one-dimensional noisy generalized Kuramoto-Sivashinsky (gKS) equation by making use of time-series techniques based on symbolic dynamics and complex networks. We focus on analyzing temporal signals of global measure in the spatiotemporal patterns as the dispersion parameter of the gKS equation and the strength of the noise are varied, observing that a rich variety of different regimes, from high-dimensional chaos to pure stochastic behavior, emerge. Permutation entropy, permutation spectrum, and network entropy allow us to fully classify the dynamical state exposed to additive noise
Phase Separation Driven by External Fluctuations
The influence of external fluctuations in phase separation processes is
analysed. These fluctuations arise from random variations of an external
control parameter. A linear stability analysis of the homogeneous state shows
that phase separation dynamics can be induced by external noise. The spatial
structure of the noise is found to have a relevant role in this phenomenon.
Numerical simulations confirm these results. A comparison with order-disorder
noise induced phase transitions is also made.Comment: 4 pages, 4 Postscript figures included in text. LaTeX (with Revtex
macros
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
Switching Dynamics in Reaction Networks Induced by Molecular Discreteness
To study the fluctuations and dynamics in chemical reaction processes,
stochastic differential equations based on the rate equation involving chemical
concentrations are often adopted. When the number of molecules is very small,
however, the discreteness in the number of molecules cannot be neglected since
the number of molecules must be an integer. This discreteness can be important
in biochemical reactions, where the total number of molecules is not
significantly larger than the number of chemical species. To elucidate the
effects of such discreteness, we study autocatalytic reaction systems
comprising several chemical species through stochastic particle simulations.
The generation of novel states is observed; it is caused by the extinction of
some molecular species due to the discreteness in their number. We demonstrate
that the reaction dynamics are switched by a single molecule, which leads to
the reconstruction of the acting network structure. We also show the strong
dependence of the chemical concentrations on the system size, which is caused
by transitions to discreteness-induced novel states.Comment: 11 pages, 5 figure
Arrival time distribution for a driven system containing quenched dichotomous disorder
We study the arrival time distribution of overdamped particles driven by a
constant force in a piecewise linear random potential which generates the
dichotomous random force. Our approach is based on the path integral
representation of the probability density of the arrival time. We explicitly
calculate the path integral for a special case of dichotomous disorder and use
the corresponding characteristic function to derive prominent properties of the
arrival time probability density. Specifically, we establish the scaling
properties of the central moments, analyze the behavior of the probability
density for short, long, and intermediate distances. In order to quantify the
deviation of the arrival time distribution from a Gaussian shape, we evaluate
the skewness and the kurtosis.Comment: 18 pages, 5 figure
Steady-State L\'evy Flights in a Confined Domain
We derive the generalized Fokker-Planck equation associated with a Langevin
equation driven by arbitrary additive white noise. We apply our result to study
the distribution of symmetric and asymmetric L\'{e}vy flights in an infinitely
deep potential well. The fractional Fokker-Planck equation for L\'{e}vy flights
is derived and solved analytically in the steady state. It is shown that
L\'{e}vy flights are distributed according to the beta distribution, whose
probability density becomes singular at the boundaries of the well. The origin
of the preferred concentration of flying objects near the boundaries in
nonequilibrium systems is clarified.Comment: 10 pages, 1 figur
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