scholarly journals A Novel High Order Space-Time Spectral Method for the Time Fractional Fokker--Planck Equation

2015 ◽  
Vol 37 (2) ◽  
pp. A701-A724 ◽  
Author(s):  
Minling Zheng ◽  
Fawang Liu ◽  
Ian Turner ◽  
Vo Anh
Keyword(s):  
Spectral Method ◽  
Planck Equation ◽  
Space Time ◽  
High Order ◽  
Fokker Planck Equation ◽  
Time Spectral Method ◽  
Fokker Planck

scholarly journals Space-Time Inversion of Stochastic Dynamics

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 839
Author(s):  
Massimiliano Giona ◽  
Antonio Brasiello ◽  
Alessandra Adrover
Keyword(s):  
Stochastic Dynamics ◽  
Exit Time ◽  
Planck Equation ◽  
Space Time ◽  
Langevin Equations ◽  
Time Inversion ◽  
Stochastic Thermodynamics ◽  
Wiener Processes ◽  
Fokker Planck Equation ◽  
Fokker Planck

This article introduces the concept of space-time inversion of stochastic Langevin equations as a way of transforming the parametrization of the dynamics from time to a monotonically varying spatial coordinate. A typical physical problem in which this approach can be fruitfully used is the analysis of solute dispersion in long straight tubes (Taylor-Aris dispersion), where the time-parametrization of the dynamics is recast in that of the axial coordinate. This allows the connection between the analysis of the forward (in time) evolution of the process and that of its exit-time statistics. The derivation of the Fokker-Planck equation for the inverted dynamics requires attention: it can be deduced using a mollified approach of the Wiener perturbations “a-la Wong-Zakai” by considering a sequence of almost everywhere smooth stochastic processes (in the present case, Poisson-Kac processes), converging to the Wiener processes in some limit (the Kac limit). The mathematical interpretation of the resulting Fokker-Planck equation can be obtained by introducing a new way of considering the stochastic integrals over the increments of a Wiener process, referred to as stochastic Stjelties integrals of mixed order. Several examples ranging from stochastic thermodynamics and fractal-time models are also analyzed.

A Numerical Solution Based on the Fokker-Planck Equation for Dilute Polymer Solutions Using High Order RBF Methods

2014 ◽  
Vol 553 ◽  
pp. 187-192
Author(s):  
H.Q. Nguyen ◽  
C.D. Tran ◽  
N. Pham-Sy ◽  
T. Tran-Cong
Keyword(s):  
Numerical Solutions ◽  
Polymer Solutions ◽  
Planck Equation ◽  
High Order ◽  
Collocation Methods ◽  
Dilute Polymer Solutions ◽  
Fokker Planck Equation ◽  
Start Up ◽  
Nonlinear Elastic ◽  
Fokker Planck

This paper presents a numerical method for the Fokker-Planck Equation (FPE) based on mesoscopic modelling of dilute polymer solutions using Radial Basis Function (RBF) approaches. The stress is determined by the solution of a FPE while the velocity field is locally calculated via the solution of conservation Differential Equations (DEs) [1,2]. The FPE and PDEs are approximated separately by two different Integrated RBF methods. The time implicit discretisation of both FPE and PDEs is carried out using collocation methods where the high order RBF approximants improve significantly the accuracy of the numerical solutions and the convergence rate. As an illustration of the method, the time evolution of a start-up flow is studied for the Finitely Extensible Nonlinear Elastic (FENE) dumbbell model.

Fractional (space-time) Fokker–Planck equation

2001 ◽  
Vol 12 (6) ◽  
pp. 1035-1040 ◽  
Author(s):  
S.A. El-Wakil ◽  
A. Elhanbaly ◽  
M.A. Zahran
Keyword(s):  
Planck Equation ◽  
Space Time ◽  
Fokker Planck Equation ◽  
Fractional Space ◽  
Fokker Planck
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