CORRELATION FUNCTIONS IN THE THEORY OF THE BROWNIAN MOTION GENERALIZATION OF THE FOKKER-PLANCK EQUATION**Zh. eksp. teor. fiz. (With acknowledgements to John Crerar Library, SLA Translation Center, Chicago.)

1965 ◽  
pp. 77-100 ◽  
Author(s):  
P.I. KUZNETSOV ◽  
R.L. STRATONOVICH ◽  
V.I. TIKHONOV
Keyword(s):  
Brownian Motion ◽  
Correlation Functions ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
Fokker Planck

Brownian Motion on Cantor Sets

2020 ◽  
Vol 21 (3-4) ◽  
pp. 275-281
Author(s):  
Ali Khalili Golmankhaneh ◽  
Saleh Ashrafi ◽  
Dumitru Baleanu ◽  
Arran Fernandez
Keyword(s):  
Brownian Motion ◽  
Classical Method ◽  
Mean Square Displacement ◽  
Planck Equation ◽  
Cantor Sets ◽  
Mean Square ◽  
Fokker Planck Equation ◽  
Fractal Time ◽  
The Mean ◽  
Fokker Planck

AbstractIn this paper, we have investigated the Langevin and Brownian equations on fractal time sets using Fα-calculus and shown that the mean square displacement is not varied linearly with time. We have also generalized the classical method of deriving the Fokker–Planck equation in order to obtain the Fokker–Planck equation on fractal time sets.

Brownian Motion of Rotating Particles

1968 ◽  
Vol 23 (4) ◽  
pp. 597-609 ◽  
Author(s):  
Siegfried Hess
Keyword(s):  
Brownian Motion ◽  
Angular Velocity ◽  
Brownian Particle ◽  
Planck Equation ◽  
Transverse Force ◽  
Particle Collision ◽  
Fokker Planck Equation ◽  
Rotational Motions ◽  
Transport Relaxation ◽  
Fokker Planck

A kinetic theory for the Brownian motion of spherical rotating particles is given starting from a generalized Fokker-Planck equation. The generalized Fokker-Planck collision operator is a sum of two ordinary Fokker-Planck differential operators in velocity and angular velocity space respectively plus a third term which provides a coupling of translational and rotational motions. This term stems from a transverse force proportional to the cross product of velocity and angular velocity of a Brownian particle. Collision brackets pertaining to the generalized Fokker-Planck operator are defined and their general properties are discussed. Application of WALDMANN'S moment method to the Fokker-Planck equation yields a set of coupled linear differential equations (transport-relaxation equations) for certain local mean values. The constitutive laws for diffusion, heat conduction by Brownian particles and spin diffusion are deduced from the transport-relaxation equations. The transport-relaxations coefficients appearing in them are given in terms of the two friction coefficients for the damping of translational and rotational motions and a third coefficient which is a measure of the transverse force. By the coupling of translational and rotational motions a diffusion flow gives rise to a correlation of linear and angular velocities.

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