5,413 research outputs found
Dynamics and Scaling of Noise-Induced Domain Growth
The domain growth processes originating from noise-induced nonequilibrium
phase transitions are analyzed, both for non-conserved and conserved dynamics.
The existence of a dynamical scaling regime is established in the two cases,
and the corresponding growth laws are determined. The resulting universal
dynamical scaling scenarios are those of Allen-Cahn and Lifshitz-Slyozov,
respectively. Additionally, the effect of noise sources on the behaviour of the
pair correlation function at short distances is studied.Comment: 11 pages (including 13 figures) LaTeX file. Accepted in EPJ
Spatial Coherence Resonance near Pattern-Forming Instabilities
The analogue of temporal coherence resonance for spatial degrees of freedom
is reported. Specifically, we show that spatiotemporal noise is able to
optimally extract an intrinsic spatial scale in nonlinear media close to (but
before) a pattern-forming instability. This effect is observed in a model of
pattern-forming chemical reaction and in the Swift-Hohenberg model of fluid
convection. In the latter case, the phenomenon is described analytically via an
approximate approach.Comment: 4 pages, 4 figure
Coherence and synchronization in diode-laser arrays with delayed global coupling
The dynamics of a semiconductor-laser array whose individual elements are
coupled in a global way through an external mirror is numerically analysed. A
coherent in-phase solution is seen to be preferred by the system at
intermediate values of the feedback coupling strength. At low values of this
parameter, a strong amplification of the spontaneous emission noise is
observed. A tendency towards chaos synchronization is also observed at large
values of the feedback strength.Comment: 8 pages, LaTeX, 6 PS figures, to appear in International Journal of
Bifurcation and Chao
Self-sustained spatiotemporal oscillations induced by membrane-bulk coupling
We propose a novel mechanism leading to spatiotemporal oscillations in
extended systems that does not rely on local bulk instabilities. Instead,
oscillations arise from the interaction of two subsystems of different spatial
dimensionality. Specifically, we show that coupling a passive diffusive bulk of
dimension d with an excitable membrane of dimension d-1 produces a
self-sustained oscillatory behavior. An analytical explanation of the
phenomenon is provided for d=1. Moreover, in-phase and anti-phase
synchronization of oscillations are found numerically in one and two
dimensions. This novel dynamic instability could be used by biological systems
such as cells, where the dynamics on the cellular membrane is necessarily
different from that of the cytoplasmic bulk.Comment: Accepted for publication in Physical Review Letter
Non-Markovian Random Walks and Non-Linear Reactions: Subdiffusion and Propagating Fronts
We propose a reaction-transport model for CTRW with non-linear reactions and
non-exponential waiting time distributions. We derive non-linear evolution
equation for mesoscopic density of particles. We apply this equation to the
problem of fronts propagation into unstable state of reaction-transport systems
with anomalous diffusion. We have found an explicit expression for the speed of
propagating front in the case of subdiffusion transport.Comment: 7 page
Soliton-dynamical approach to a noisy Ginzburg-Landau model
We present a dynamical description and analysis of non-equilibrium
transitions in the noisy Ginzburg-Landau equation based on a canonical phase
space formulation. The transition pathways are characterized by nucleation and
subsequent propagation of domain walls or solitons. We also evaluate the
Arrhenius factor in terms of an associated action and find good agreement with
recent numerical optimization studies.Comment: 4 pages (revtex4), 3 figures (eps
Dynamics of active membranes with internal noise
We study the time-dependent height fluctuations of an active membrane
containing energy-dissipating pumps that drive the membrane out of equilibrium.
Unlike previous investigations based on models that neglect either curvature
couplings or random fluctuations in pump activities, our formulation explores
two new models that take both of these effects into account. In the first
model, the magnitude of the nonequilibrium forces generated by the pumps is
allowed to fluctuate temporally. In the second model, the pumps are allowed to
switch between "on" and "off" states. We compute the mean squared displacement
of a membrane point for both models, and show that they exhibit distinct
dynamical behaviors from previous models, and in particular, a superdiffusive
regime specifically arising from the shot noise.Comment: 7 pages, 4 figure
Temporally correlated fluctuations drive epileptiform dynamics
Published onlineJournal ArticleMacroscopic models of brain networks typically incorporate assumptions regarding the characteristics of afferent noise, which is used to represent input from distal brain regions or ongoing fluctuations in non-modelled parts of the brain. Such inputs are often modelled by Gaussian white noise which has a flat power spectrum. In contrast, macroscopic fluctuations in the brain typically follow a 1/f(b) spectrum. It is therefore important to understand the effect on brain dynamics of deviations from the assumption of white noise. In particular, we wish to understand the role that noise might play in eliciting aberrant rhythms in the epileptic brain. To address this question we study the response of a neural mass model to driving by stochastic, temporally correlated input. We characterise the model in terms of whether it generates "healthy" or "epileptiform" dynamics and observe which of these dynamics predominate under different choices of temporal correlation and amplitude of an Ornstein-Uhlenbeck process. We find that certain temporal correlations are prone to eliciting epileptiform dynamics, and that these correlations produce noise with maximal power in the δ and θ bands. Crucially, these are rhythms that are found to be enhanced prior to seizures in humans and animal models of epilepsy. In order to understand why these rhythms can generate epileptiform dynamics, we analyse the response of the model to sinusoidal driving and explain how the bifurcation structure of the model gives rise to these findings. Our results provide insight into how ongoing fluctuations in brain dynamics can facilitate the onset and propagation of epileptiform rhythms in brain networks. Furthermore, we highlight the need to combine large-scale models with noise of a variety of different types in order to understand brain (dys-)function.This work was supported by the European Commission through the FP7 Marie Curie Initial Training Network 289146 (NETT: Neural Engineering Transformative Technologies), by the Spanish Ministry of Economy and Competitiveness and FEDER (project FIS2012-37655-C02-01). J.G.O. also acknowledges support from the ICREA Academia programme, the Generalitat de Catalunya (project 2014SGR0947), and the “MarĂa de Maeztu” Programme for Units of Excellence in R&D (Spanish Ministry of Economy and Competitiveness, MDM-2014-0370) M.G. gratefully acknowledges the financial support of the EPSRC via grant EP/N014391/1. The contribution of M.G. was generously supported by a Wellcome Trust Institutional Strategic Support Award (WT105618MA)
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