Sensitivity analysis of the non-linear Fokker–Planck equations with uncertainty

2022 ◽  
Vol 64 ◽  
pp. 103450
Author(s):  
Jie Liao ◽  
Hui Liu
Keyword(s):  
Sensitivity Analysis ◽  
Non Linear ◽  
Fokker Planck Equations ◽  
Fokker Planck

scholarly journals Non-Linear Langevin and Fractional Fokker–Planck Equations for Anomalous Diffusion by Lévy Stable Processes

Entropy ◽  
2018 ◽  
Vol 20 (10) ◽  
pp. 760 ◽  
Author(s):  
Johan Anderson ◽  
Sara Moradi ◽  
Tariq Rafiq
Keyword(s):  
Anomalous Diffusion ◽  
Transport Coefficient ◽  
Numerical Solutions ◽  
Distribution Functions ◽  
Space Distribution ◽  
Non Linear ◽  
Non Local ◽  
Local Transport ◽  
Fokker Planck Equations ◽  
Fokker Planck

The numerical solutions to a non-linear Fractional Fokker–Planck (FFP) equation are studied estimating the generalized diffusion coefficients. The aim is to model anomalous diffusion using an FFP description with fractional velocity derivatives and Langevin dynamics where Lévy fluctuations are introduced to model the effect of non-local transport due to fractional diffusion in velocity space. Distribution functions are found using numerical means for varying degrees of fractionality of the stable Lévy distribution as solutions to the FFP equation. The statistical properties of the distribution functions are assessed by a generalized normalized expectation measure and entropy and modified transport coefficient. The transport coefficient significantly increases with decreasing fractality which is corroborated by analysis of experimental data.

Stability of Global Maxwellian For Non-Linear Vlasov-Poisson-Fokker-Planck Equations

2019 ◽  
Vol 39 (1) ◽  
pp. 127-138
Author(s):  
Jie Liao ◽  
Qianrong Wang ◽  
Xiongfeng Yang
Keyword(s):  
Non Linear ◽  
Fokker Planck Equations ◽  
Fokker Planck

scholarly journals Gevrey hypoellipticity for linear and non-linear Fokker–Planck equations

2009 ◽  
Vol 246 (1) ◽  
pp. 320-339 ◽  
Author(s):  
Hua Chen ◽  
Wei-Xi Li ◽  
Chao-Jiang Xu
Keyword(s):  
Non Linear ◽  
Fokker Planck Equations ◽  
Fokker Planck
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