1,578 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
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
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