Generalized Fokker–Planck equation for non‐Markovian processes

1983 ◽  
Vol 24 (2) ◽  
pp. 267-270 ◽  
Author(s):  
V. S. Volkov ◽  
V. N. Pokrovsky
Keyword(s):  
Planck Equation ◽  
Fokker Planck Equation ◽  
Markovian Processes ◽  
Fokker Planck

BOLTZMANN–ARRHENIUS–ZHURKOV (BAZ) MODEL IN PHYSICS-OF-MATERIALS PROBLEMS

2013 ◽  
Vol 27 (13) ◽  
pp. 1330009 ◽  
Author(s):  
E. SUHIR ◽  
S.-M. KANG
Keyword(s):  
Steady State ◽  
Planck Equation ◽  
Steady State Solution ◽  
Degradation Process ◽  
Material Degradation ◽  
Fokker Planck Equation ◽  
Markovian Processes ◽  
Transient Period ◽  
The Given ◽  
Fokker Planck

Boltzmann–Arrhenius–Zhurkov (BAZ) model enables one to obtain a simple, easy-to-use and physically meaningful formula for the evaluation of the probability of failure (PoF) of a material after the given time in operation at the given temperature and under the given stress (not necessarily mechanical). It is shown that the material degradation (aging, damage accumulation, flaw propagation, etc.) can be viewed, when BAZ model is considered, as a Markovian process, and that the BAZ model can be obtained as the steady-state solution to the Fokker–Planck equation in the theory of Markovian processes. It is shown also that the BAZ model addresses the worst and a reasonably conservative situation, when the highest PoF is expected. It is suggested therefore that the transient period preceding the condition addressed by the steady-state BAZ model need not be accounted for in engineering evaluations. However, when there is an interest in understanding the physics of the transient degradation process, the obtained solution to the Fokker–Planck equation can be used for this purpose.

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.

Milne problem for a hard-sphere Rayleigh gas: A study based on the Fokker-Planck equation

1983 ◽  
Vol 28 (3) ◽  
pp. 1659-1661 ◽  
Author(s):  
S. Waldenstrøm ◽  
K. J. Mork ◽  
K. Razi Naqvi
Keyword(s):  
Hard Sphere ◽  
Planck Equation ◽  
Milne Problem ◽  
Fokker Planck Equation ◽  
Rayleigh Gas ◽  
Fokker Planck
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