System-size expansion of the moments of a master equation

2018 ◽  
Vol 28 (10) ◽  
pp. 106303 ◽  
Author(s):  
A. F. Peralta ◽  
R. Toral
Keyword(s):  
Master Equation ◽  
System Size ◽  
System Size Expansion

scholarly journals System size expansion for systems with an absorbing state

2011 ◽  
Vol 83 (1) ◽  
Author(s):  
Francesca Di Patti ◽  
Sandro Azaele ◽  
Jayanth R. Banavar ◽  
Amos Maritan
Keyword(s):  
System Size ◽  
Absorbing State ◽  
System Size Expansion

scholarly journals A new modelling framework for statistical cumulus dynamics

2012 ◽  
Vol 370 (1962) ◽  
pp. 1041-1060 ◽  
Author(s):  
Robert S. Plant
Keyword(s):  
Large Scale ◽  
System Size ◽  
Time Dependent ◽  
Basic Character ◽  
Statistical Dynamics ◽  
Convective Systems ◽  
Modelling Framework ◽  
Natural Extensions ◽  
Simplifying Assumptions ◽  
System Size Expansion

We propose a new modelling framework suitable for the description of atmospheric convective systems as a collection of distinct plumes. The literature contains many examples of models for collections of plumes in which strong simplifying assumptions are made, a diagnostic dependence of convection on the large-scale environment and the limit of many plumes often being imposed from the outset. Some recent studies have sought to remove one or the other of those assumptions. The proposed framework removes both, and is explicitly time dependent and stochastic in its basic character. The statistical dynamics of the plume collection are defined through simple probabilistic rules applied at the level of individual plumes, and van Kampen's system size expansion is then used to construct the macroscopic limit of the microscopic model. Through suitable choices of the microscopic rules, the model is shown to encompass previous studies in the appropriate limits, and to allow their natural extensions beyond those limits.

scholarly journals System size expansion using Feynman rules and diagrams

2014 ◽  
Vol 47 (45) ◽  
pp. 455007 ◽  
Author(s):  
Philipp Thomas ◽  
Christian Fleck ◽  
Ramon Grima ◽  
Nikola Popović
Keyword(s):  
System Size ◽  
Feynman Rules ◽  
System Size Expansion

scholarly journals An alternative route to the system-size expansion

2017 ◽  
Vol 50 (39) ◽  
pp. 395003 ◽  
Author(s):  
Claudia Cianci ◽  
David Schnoerr ◽  
Andreas Piehler ◽  
Ramon Grima
Keyword(s):  
System Size ◽  
Alternative Route ◽  
System Size Expansion
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