Approximate solution of the Fokker-Planck equation for aerosol particles

1970 ◽  
Vol 5 (2) ◽  
pp. 304-309 ◽  
Author(s):  
V. M. Voloshchuk
Keyword(s):  
Approximate Solution ◽  
Aerosol Particles ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
Fokker Planck

Approximate Solution of the Fokker–Planck Equation for a Multidegree of Freedom Frictionally Damped Bladed Disk Under Random Excitation

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Alwin Förster ◽  
Lars Panning-von Scheidt ◽  
Jörg Wallaschek
Keyword(s):  
Approximate Solution ◽  
Weighting Function ◽  
Gaussian White Noise ◽  
Planck Equation ◽  
Random Excitation ◽  
Stationary Response ◽  
Bladed Disk ◽  
Fokker Planck Equation ◽  
Finite Differences Method ◽  
Fokker Planck

Bladed disks are subjected to different types of excitations, which cannot, in any, case be described in a deterministic manner. Fuzzy factors, such as slightly varying airflow or density fluctuation, can lead to an uncertain excitation in terms of amplitude and frequency, which has to be described by random variables. The computation of frictionally damped blades under random excitation becomes highly complex due to the presence of nonlinearities. Only a few publications are dedicated to this particular problem. Most of these deal with systems of only one or two degrees-of-freedom (DOFs) and use computational expensive methods, like finite element method or finite differences method (FDM), to solve the determining differential equation. The stochastic stationary response of a mechanical system is characterized by the joint probability density function (JPDF), which is driven by the Fokker–Planck equation (FPE). Exact stationary solutions of the FPE only exist for a few classes of mechanical systems. This paper presents the application of a semi-analytical Galerkin-type method to a frictionally damped bladed disk under influence of Gaussian white noise (GWN) excitation in order to calculate its stationary response. One of the main difficulties is the selection of a proper initial approximate solution, which is applicable as a weighting function. Comparing the presented results with those from the FDM, Monte–Carlo simulation (MCS) as well as analytical solutions proves the applicability of the methodology.

An approximate solution of the Fokker—Planck equation for reactions in condensed phases

1992 ◽  
Vol 192 (5-6) ◽  
pp. 472-478 ◽  
Author(s):  
M. Ben-Nun ◽  
R.D. Levine
Keyword(s):  
Approximate Solution ◽  
Planck Equation ◽  
Condensed Phases ◽  
Fokker Planck Equation ◽  
Fokker Planck

Approximate Solution of the Fokker-Planck Equation for a Multi-Degree of Freedom Frictionally Damped Bladed Disk Under Random Excitation

2018 ◽  
Author(s):  
Alwin Förster ◽  
Lars Panning-von Scheidt ◽  
Jörg Wallaschek
Keyword(s):  
Approximate Solution ◽  
Weighting Function ◽  
Gaussian White Noise ◽  
Planck Equation ◽  
Random Excitation ◽  
Stationary Response ◽  
Bladed Disk ◽  
Fokker Planck Equation ◽  
Finite Differences Method ◽  
Fokker Planck

Bladed Disks are subjected to different types of excitations, which cannot in any case be described in a deterministic manner. Fuzzy factors, such as slightly varying airflow or density fluctuation, can lead to an uncertain excitation in terms of amplitude and frequency, which has to be described by random variables. The computation of frictionally damped blades under random excitation becomes highly complex due to the presence of nonlinearities. Only a few publications are dedicated to this particular problem. Most of these deal with systems of only one or two degrees of freedom and use computational expensive methods, like finite element method (FEM) or finite differences method (FDM), to solve the determining differential equation. The stochastic stationary response of a mechanical system is characterized by the joint probability density function (JPDF), which is driven by the Fokker-Planck equation (FPE). Exact stationary solutions of the FPE only exist for a few classes of mechanical systems. This paper presents the application of a semi-analytical Galerkin-type method to a frictionally damped bladed disk under influence of Gaussian white noise (GWN) excitation in order to calculate its stationary response. One of the main difficulties is the selection of a proper initial approximate solution, which is applicable as a weighting function. Comparing the presented results with those from the FDM, Monte-Carlo Simulation (MCS) as well as analytical solutions proves the applicability of the methodology.

scholarly journals Approximate solution for Fokker-Planck equation

2015 ◽  
Vol 18 (4) ◽  
pp. 43003 ◽  
Author(s):  
Araujo ◽  
Drigo Filho
Keyword(s):  
Approximate Solution ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
Fokker Planck

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

The Fokker-Planck equation

1998 ◽  
Vol 168 (4) ◽  
pp. 475 ◽  
Author(s):  
A.I. Olemskoi
Keyword(s):  
Planck Equation ◽  
Fokker Planck Equation ◽  
Fokker Planck

Numerical Solution of the Fokker-Planck Equation by Spectral Collocation and Finite-Element Methods for Stochastic Magnetization Dynamics

2021 ◽  
pp. 1-1
Author(s):  
Valentino Scalera ◽  
Patrizio Ansalone ◽  
Salvatore Perna ◽  
Claudio Serpico ◽  
Massimiliano d'Aquino
Keyword(s):  
Finite Element ◽  
Numerical Solution ◽  
Finite Element Methods ◽  
Planck Equation ◽  
Magnetization Dynamics ◽  
Spectral Collocation ◽  
Fokker Planck Equation ◽  
Fokker Planck

scholarly journals Time-changed fractional Ornstein-Uhlenbeck process

2020 ◽  
Vol 23 (2) ◽  
pp. 450-483 ◽  
Author(s):  
Giacomo Ascione ◽  
Yuliya Mishura ◽  
Enrica Pirozzi
Keyword(s):  
Planck Equation ◽  
Uhlenbeck Process ◽  
Fokker Planck Equation ◽  
Ornstein Uhlenbeck Process ◽  
Fokker Planck

AbstractWe define a time-changed fractional Ornstein-Uhlenbeck process by composing a fractional Ornstein-Uhlenbeck process with the inverse of a subordinator. Properties of the moments of such process are investigated and the existence of the density is shown. We also provide a generalized Fokker-Planck equation for the density of the process.

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