scholarly journals Mean field games in the weak noise limit : A WKB approach to the Fokker–Planck equation

2019 ◽  
Vol 523 ◽  
pp. 310-325 ◽  
Author(s):  
Thibault Bonnemain ◽  
Denis Ullmo
Keyword(s):  
Mean Field ◽  
Planck Equation ◽  
Mean Field Games ◽  
Weak Noise ◽  
Fokker Planck Equation ◽  
Noise Limit ◽  
Fokker Planck

scholarly journals Active matter in infinite dimensions: Fokker–Planck equation and dynamical mean-field theory at low density

2021 ◽  
Vol 155 (17) ◽  
pp. 174106
Author(s):  
Thibaut Arnoulx de Pirey ◽  
Alessandro Manacorda ◽  
Frédéric van Wijland ◽  
Francesco Zamponi
Keyword(s):  
Field Theory ◽  
Mean Field Theory ◽  
Mean Field ◽  
Planck Equation ◽  
Dynamical Mean Field Theory ◽  
Low Density ◽  
Active Matter ◽  
Infinite Dimensions ◽  
Fokker Planck Equation ◽  
Fokker Planck

scholarly journals Semi-Dilute Dumbbells: Solutions of the Fokker–Planck Equation

J ◽  
2021 ◽  
Vol 4 (3) ◽  
pp. 341-355
Author(s):  
Stephen Chaffin ◽  
Julia Rees
Keyword(s):  
Constitutive Equation ◽  
Mean Field ◽  
Planck Equation ◽  
Intermolecular Forces ◽  
Concentration Effects ◽  
Fokker Planck Equation ◽  
Dynamics Simulations ◽  
Nonlinear Elastic ◽  
Background Shear ◽  
Fokker Planck

Spring bead models are commonly used in the constitutive equations for polymer melts. One such model based on kinetic theory—the finitely extensible nonlinear elastic dumbbell model incorporating a Peterlin closure approximation (FENE-P)—has previously been applied to study concentration-dependent anisotropy with the inclusion of a mean-field term to account for intermolecular forces in dilute polymer solutions for background profiles of weak shear and elongation. These investigations involved the solution of the Fokker–Planck equation incorporating a constitutive equation for the second moment. In this paper, we extend this analysis to include the effects of large background shear and elongation beyond the Hookean regime. Further, the constitutive equation is solved for the probability density function which permits the computation of any macroscopic variable, allowing direct comparison of the model predictions with molecular dynamics simulations. It was found that if the concentration effects at equilibrium are taken into account, the FENE-P model gives qualitatively the correct predictions, although the over-shoot in extension in comparison to the infinitely dilute case is significantly underpredicted.

scholarly journals Emergence of network structure in models of collective evolution and evolutionary dynamics

2008 ◽  
Vol 464 (2096) ◽  
pp. 2207-2217 ◽  
Author(s):  
Henrik Jeldtoft Jensen
Keyword(s):  
Degree Distribution ◽  
Evolutionary Dynamics ◽  
Mean Field ◽  
Planck Equation ◽  
Fixed Number ◽  
Fokker Planck Equation ◽  
Degree Correlations ◽  
Approximate Treatment ◽  
Mean Field Equation ◽  
Fokker Planck

We consider an evolving network of a fixed number of nodes. The allocation of edges is a dynamical stochastic process inspired by biological reproduction dynamics, namely by deleting and duplicating existing nodes and their edges. The properties of the degree distribution in the stationary state is analysed by use of the Fokker–Planck equation. For a broad range of parameters, exponential degree distributions are observed. The mechanism responsible for this behaviour is illuminated by use of a simple mean field equation and reproduced by the Fokker–Planck equation. The latter is treated exactly, except for an approximate treatment of the degree–degree correlations. In the limit of 0 mutations, the degree distribution becomes a power law with exponent 1.

AN APPLICATION OF FOKKER–PLANCK EQUATION TO JOSEPHSON JUNCTION

1989 ◽  
Vol 9 (1) ◽  
pp. 109-120
Author(s):  
G. Liao ◽  
A.F. Lawrence ◽  
A.T. Abawi
Keyword(s):  
Josephson Junction ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
Fokker Planck
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