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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)
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author
; and
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
2016-04-01 11:53:58
date last changed
2022-01-26 19:53:52
@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}},
  doi          = {{10.1088/0951-7715/19/5/002}},
  volume       = {{19}},
  year         = {{2006}},
}