scholarly journals Fokker-Planck equation with memory: the cross over from ballistic to diffusive processes in many particle systems and incompressible media

2013 ◽  
Vol 16 (1) ◽  
pp. 13004 ◽  
Author(s):  
Ilyin ◽  
Procaccia ◽  
Zagorodny
Keyword(s):  
Planck Equation ◽  
Particle Systems ◽  
Fokker Planck Equation ◽  
Incompressible Media ◽  
The Cross ◽  
Diffusive Processes ◽  
With Memory ◽  
Fokker Planck

scholarly journals Diffusion and Memory Effect in a Stochastic Processes and the Correspondence to an Information Propagation in a Social System

2021 ◽  
Author(s):  
Peng Wang ◽  
Jie Huo ◽  
Xu-Ming Wang
Keyword(s):  
Social System ◽  
Particle System ◽  
Planck Equation ◽  
Generalized Langevin Equation ◽  
Information Propagation ◽  
Fokker Planck Equation ◽  
Social Ideology ◽  
Diffusion Particle ◽  
With Memory ◽  
Fokker Planck

Abstract A generalized Langevin equation is suggested to describe a diffusion particle system with memory. The equation can be transformed into the Fokker-Planck equation by using the Kramers-Moyal expansion. The solution of Fokker-Planck equation can describe not only the diffusion of particles but also that of opinion particles based on the similarities between the two. We find that the memory can restrain some non-equilibrium phenomena of velocity distribution in the system, without memory, induced by correlation between the noise and space[1]. However, the memory can enhance the effective collision among particles as shown by the variation of diffusion coefficients, and changes the diffusion mode between the dissipative and pumping region by comparing with that in the aforementioned system without memory. As the discussions in this physical system is paralleled to a social system, the random diffusion of social ideology, such as the information propagation, can be suppressed by the correlation between the noise and space.

Narrow-Band Excitation of a Nonlinear Oscillator

1976 ◽  
Vol 43 (2) ◽  
pp. 340-344 ◽  
Author(s):  
W. C. Lennox ◽  
Y. C. Kuak
Keyword(s):  
Nonlinear Oscillator ◽  
Narrow Band ◽  
Planck Equation ◽  
Restoring Force ◽  
Narrow Band Noise ◽  
Band Noise ◽  
Fokker Planck Equation ◽  
With Memory ◽  
Fokker Planck

A nonlinear oscillator characterized by a hardening-type restoring force is excited by stationary narrow-band noise. The analysis is based on the concept of quasi-static amplitude and phase values which is exactly opposite to the stochastic or Markov approach with its associated Fokker-Planck equation. The approach, in effect, replaces a system with memory with one without memory. The existence of jumps is demonstrated and an expression for the probability of the occurrence of jumps is derived.

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

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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