| Title | Intermittency, metastability and coarse graining for coupled deterministic-stochastic lattice systems |
| Authors | M.A. Katsoulakis, A.J. Majda, Alexandros Sopasakis |
| Alternative Location | http://dx.doi.org/10.1088/0..., Restricted Access |
| Publication | Nonlinearity |
| Year | 2006 |
| Volume | 19 |
| Issue | 5 |
| Pages | 1021 - 1047 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | London Mathematical Society / IOP Science |
| Abstract English | We study the role of strong particle/particle interactions and stochastic fluctuations<br> emanating from the micro-/sub-grid scale, in the context of a simple prototype hybrid system con-<br> sisting of a scalar linear ordinary differential equation (ODE), coupled to a microscopic spin flip<br> Ising lattice system. Due to the presence of strong interactions in the lattice model, the mean-field<br> approximation of this system is a Fitzhugh-Nagumo-type system of ODEs. However, microscopic<br> noise and local interactions will significantly alter the deterministic and spatially homogeneous<br> mean-field Fitzhugh-Nagumo behaviours (excitable, bistable and oscillatory) and will yield cor-<br> responding regimes with phenomena driven by the interaction of nonlinearity and noise across<br> scales, such as strong intermittency, metastability and random oscillations. Motivated by these<br> observations we consider a class of stochastic numerical approximations based on systematic<br> coarse-grainings of stochastic lattice dynamics. The resulting stochastic closures give rise to com-<br> putationally inexpensive reduced hybrid models that capture correctly the transient and long-time<br> behaviour of the full system; this is demonstrated by detailed time series analysis that includes<br> comparisons of power spectra and auto- and cross-correlations in time and space, especially in<br> examples dominated by strong interactions between scales and fluctuations, such as nucleation,<br> intermittent and random oscillation regimes. |
| ISBN/ISSN/Other | ISSN: 1361-6544 (online) |
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