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Intermittency, metastability and coarse graining for coupled deterministic-stochastic lattice systems

Katsoulakis, M.A.; Majda, A.J. and Sopasakis, Alexandros LU (2006) In Nonlinearity 19(5). p.1021-1047
Abstract
We study the role of strong particle/particle interactions and stochastic fluctuations

emanating from the micro-/sub-grid scale, in the context of a simple prototype hybrid system con-

sisting of a scalar linear ordinary differential equation (ODE), coupled to a microscopic spin flip

Ising lattice system. Due to the presence of strong interactions in the lattice model, the mean-field

approximation of this system is a Fitzhugh-Nagumo-type system of ODEs. However, microscopic

noise and local interactions will significantly alter the deterministic and spatially homogeneous

mean-field Fitzhugh-Nagumo behaviours (excitable, bistable and oscillatory) and will yield cor-

responding... (More)
We study the role of strong particle/particle interactions and stochastic fluctuations

emanating from the micro-/sub-grid scale, in the context of a simple prototype hybrid system con-

sisting of a scalar linear ordinary differential equation (ODE), coupled to a microscopic spin flip

Ising lattice system. Due to the presence of strong interactions in the lattice model, the mean-field

approximation of this system is a Fitzhugh-Nagumo-type system of ODEs. However, microscopic

noise and local interactions will significantly alter the deterministic and spatially homogeneous

mean-field Fitzhugh-Nagumo behaviours (excitable, bistable and oscillatory) and will yield cor-

responding regimes with phenomena driven by the interaction of nonlinearity and noise across

scales, such as strong intermittency, metastability and random oscillations. Motivated by these

observations we consider a class of stochastic numerical approximations based on systematic

coarse-grainings of stochastic lattice dynamics. The resulting stochastic closures give rise to com-

putationally inexpensive reduced hybrid models that capture correctly the transient and long-time

behaviour of the full system; this is demonstrated by detailed time series analysis that includes

comparisons of power spectra and auto- and cross-correlations in time and space, especially in

examples dominated by strong interactions between scales and fluctuations, such as nucleation,

intermittent and random oscillation regimes. (Less)
Please use this url to cite or link to this publication:
author
publishing date
type
Contribution to journal
publication status
published
subject
in
Nonlinearity
volume
19
issue
5
pages
1021 - 1047
publisher
London Mathematical Society / IOP Science
external identifiers
  • scopus:33645975836
ISSN
0951-7715
DOI
10.1088/0951-7715/19/5/002
language
English
LU publication?
no
id
b4da9297-4415-4833-ba29-65e250e1f7bf (old id 2201814)
date added to LUP
2011-12-30 19:44:22
date last changed
2019-02-20 03:58:20
@article{b4da9297-4415-4833-ba29-65e250e1f7bf,
  abstract     = {We study the role of strong particle/particle interactions and stochastic fluctuations<br/><br>
emanating from the micro-/sub-grid scale, in the context of a simple prototype hybrid system con-<br/><br>
sisting of a scalar linear ordinary differential equation (ODE), coupled to a microscopic spin flip<br/><br>
Ising lattice system. Due to the presence of strong interactions in the lattice model, the mean-field<br/><br>
approximation of this system is a Fitzhugh-Nagumo-type system of ODEs. However, microscopic<br/><br>
noise and local interactions will significantly alter the deterministic and spatially homogeneous<br/><br>
mean-field Fitzhugh-Nagumo behaviours (excitable, bistable and oscillatory) and will yield cor-<br/><br>
responding regimes with phenomena driven by the interaction of nonlinearity and noise across<br/><br>
scales, such as strong intermittency, metastability and random oscillations. Motivated by these<br/><br>
observations we consider a class of stochastic numerical approximations based on systematic<br/><br>
coarse-grainings of stochastic lattice dynamics. The resulting stochastic closures give rise to com-<br/><br>
putationally inexpensive reduced hybrid models that capture correctly the transient and long-time<br/><br>
behaviour of the full system; this is demonstrated by detailed time series analysis that includes<br/><br>
comparisons of power spectra and auto- and cross-correlations in time and space, especially in<br/><br>
examples dominated by strong interactions between scales and fluctuations, such as nucleation,<br/><br>
intermittent and random oscillation regimes.},
  author       = {Katsoulakis, M.A. and Majda, A.J. and Sopasakis, Alexandros},
  issn         = {0951-7715},
  language     = {eng},
  number       = {5},
  pages        = {1021--1047},
  publisher    = {London Mathematical Society / IOP Science},
  series       = {Nonlinearity},
  title        = {Intermittency, metastability and coarse graining for coupled deterministic-stochastic lattice systems},
  url          = {http://dx.doi.org/10.1088/0951-7715/19/5/002},
  volume       = {19},
  year         = {2006},
}