Advanced

Hybrid deterministic stochastic systems with microscopic look-ahead dynamics

Katsoulakis, M.A.; Majda, A.J. and Sopasakis, Alexandros LU (2010) In Communications in Mathematical Sciences 8(2). p.409-437
Abstract
We study the impact of stochastic mechanisms on a coupled hybrid system consisting of a general advection-diffusion-reaction partial differential equation and a spatially distributed stochastic lattice noise model. The stochastic dynamics include both spin-flip and spin-exchange type interparticle interactions. Furthermore, we consider a new, asymmetric, single exclusion pro- cess, studied elsewhere in the context of traffic flow modeling, with an one-sided interaction potential which imposes advective trends on the stochastic dynamics. This look-ahead stochastic mechanism is responsible for rich nonlinear behavior in solutions. Our approach relies heavily on first deriving approximate differential mesoscopic equations. These... (More)
We study the impact of stochastic mechanisms on a coupled hybrid system consisting of a general advection-diffusion-reaction partial differential equation and a spatially distributed stochastic lattice noise model. The stochastic dynamics include both spin-flip and spin-exchange type interparticle interactions. Furthermore, we consider a new, asymmetric, single exclusion pro- cess, studied elsewhere in the context of traffic flow modeling, with an one-sided interaction potential which imposes advective trends on the stochastic dynamics. This look-ahead stochastic mechanism is responsible for rich nonlinear behavior in solutions. Our approach relies heavily on first deriving approximate differential mesoscopic equations. These approximations become exact either in the long range, Kac interaction partial differential equation case, or, given sufficient time separation con- ditions, between the partial differential equation and the stochastic model giving rise to a stochastic averaging partial differential equation. Although these approximations can in some cases be crude, they can still give a first indication, via linearized stability analysis, of the interesting regimes for the stochastic model. Motivated by this linearized stability analysis we choose particular regimes where interacting nonlinear stochastic waves are responsible for phenomena such as random switching, convective instability, and metastability, all driven by stochasticity. Numerical kinetic Monte Carlo simulations of the coarse grained hybrid system are implemented to assist in producing solutions and understanding their behavior. (Less)
Please use this url to cite or link to this publication:
author
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Monte Carlo, critical phenomena, look-ahead dynamics, multiscale interactions, stochastic closures, Coupled hybrid systems
in
Communications in Mathematical Sciences
volume
8
issue
2
pages
409 - 437
publisher
International Press
external identifiers
  • scopus:77954651244
ISSN
1945-0796
language
English
LU publication?
no
id
81fd6049-340f-42cb-bee3-98028f9a11e5 (old id 2201569)
alternative location
http://www.intlpress.com/CMS/p/2010/issue8-2/CMS-8-2-A6.pdf
date added to LUP
2011-12-29 19:04:36
date last changed
2018-05-29 09:39:43
@article{81fd6049-340f-42cb-bee3-98028f9a11e5,
  abstract     = {We study the impact of stochastic mechanisms on a coupled hybrid system consisting of a general advection-diffusion-reaction partial differential equation and a spatially distributed stochastic lattice noise model. The stochastic dynamics include both spin-flip and spin-exchange type interparticle interactions. Furthermore, we consider a new, asymmetric, single exclusion pro- cess, studied elsewhere in the context of traffic flow modeling, with an one-sided interaction potential which imposes advective trends on the stochastic dynamics. This look-ahead stochastic mechanism is responsible for rich nonlinear behavior in solutions. Our approach relies heavily on first deriving approximate differential mesoscopic equations. These approximations become exact either in the long range, Kac interaction partial differential equation case, or, given sufficient time separation con- ditions, between the partial differential equation and the stochastic model giving rise to a stochastic averaging partial differential equation. Although these approximations can in some cases be crude, they can still give a first indication, via linearized stability analysis, of the interesting regimes for the stochastic model. Motivated by this linearized stability analysis we choose particular regimes where interacting nonlinear stochastic waves are responsible for phenomena such as random switching, convective instability, and metastability, all driven by stochasticity. Numerical kinetic Monte Carlo simulations of the coarse grained hybrid system are implemented to assist in producing solutions and understanding their behavior.},
  author       = {Katsoulakis, M.A. and Majda, A.J. and Sopasakis, Alexandros},
  issn         = {1945-0796},
  keyword      = {Monte Carlo,critical phenomena,look-ahead dynamics,multiscale interactions,stochastic closures,Coupled hybrid systems},
  language     = {eng},
  number       = {2},
  pages        = {409--437},
  publisher    = {International Press},
  series       = {Communications in Mathematical Sciences},
  title        = {Hybrid deterministic stochastic systems with microscopic look-ahead dynamics},
  volume       = {8},
  year         = {2010},
}