Document Detail


Scaling theory for the quasideterministic limit of continuous bifurcations.
MedLine Citation:
PMID:  23004734     Owner:  NLM     Status:  Publisher    
Abstract/OtherAbstract:
Deterministic rate equations are widely used in the study of stochastic, interacting particles systems. This approach assumes that the inherent noise, associated with the discreteness of the elementary constituents, may be neglected when the number of particles N is large. Accordingly, it fails close to the extinction transition, when the amplitude of stochastic fluctuations is comparable with the size of the population. Here we present a general scaling theory of the transition regime for spatially extended systems. We demonstrate this through a detailed study of two fundamental models for out-of-equilibrium phase transitions: the Susceptible-Infected-Susceptible (SIS) that belongs to the directed percolation equivalence class and the Susceptible-Infected-Recovered (SIR) model belonging to the dynamic percolation class. Implementing the Ginzburg criteria we show that the width of the fluctuation-dominated region scales like N^{-κ}, where N is the number of individuals per site and κ=2/(d_{u}-d), d_{u} is the upper critical dimension. Other exponents that control the approach to the deterministic limit are shown to be calculable once κ is known. The theory is extended to include the corrections to the front velocity above the transition. It is supported by the results of extensive numerical simulations for systems of various dimensionalities.
Authors:
David A Kessler; Nadav M Shnerb
Related Documents :
22957554 - Transition path sampling for discrete master equations with absorbing states.
4058874 - Congenital optic disc deformities. a clinical approach.
23485274 - Extension of the kli approximation toward the exact optimized effective potential.
24572314 - On physical property tensors invariant under line groups.
15979084 - On the lagrangian/eulerian modeling of dispersed droplet inertia: internal circulation ...
16609174 - The historical development of cryogenically cooled monochromators for third-generation ...
Publication Detail:
Type:  JOURNAL ARTICLE     Date:  2012-5-29
Journal Detail:
Title:  Physical review. E, Statistical, nonlinear, and soft matter physics     Volume:  85     ISSN:  1550-2376     ISO Abbreviation:  Phys Rev E Stat Nonlin Soft Matter Phys     Publication Date:  2012 May 
Date Detail:
Created Date:  2012-9-25     Completed Date:  -     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  101136452     Medline TA:  Phys Rev E Stat Nonlin Soft Matter Phys     Country:  -    
Other Details:
Languages:  ENG     Pagination:  051138     Citation Subset:  -    
Affiliation:
Department of Physics, Bar-Ilan University, Ramat-Gan 52900 Israel.
Export Citation:
APA/MLA Format     Download EndNote     Download BibTex
MeSH Terms
Descriptor/Qualifier:

From MEDLINE®/PubMed®, a database of the U.S. National Library of Medicine


Previous Document:  Surface-directed spinodal decomposition: A molecular dynamics study.
Next Document:  Estimation of the entropy based on its polynomial representation.