Intermittency, metastability and coarse graining for coupled deterministic-stochastic lattice systems
(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:
https://lup.lub.lu.se/record/2201814
- author
- Katsoulakis, M.A. ; Majda, A.J. and Sopasakis, Alexandros LU
- publishing date
- 2006
- 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}}, }