Self-similar characteristics of neural networks based on Fokker–Planck equation

2004 ◽  
Vol 20 (2) ◽  
pp. 329-335 ◽  
Author(s):  
Yoshinobu Kamitani ◽  
Ikuo Matsuba
Keyword(s):  
Neural Networks ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
Self Similar ◽  
Fokker Planck

scholarly journals Entropy Production Associated with Aggregation into Granules in a Subdiffusive Environment

Entropy ◽  
2018 ◽  
Vol 20 (9) ◽  
pp. 651 ◽  
Author(s):  
Piotr Weber ◽  
Piotr Bełdowski ◽  
Martin Bier ◽  
Adam Gadomski
Keyword(s):  
Entropy Production ◽  
Colloidal Suspension ◽  
Time Derivative ◽  
Planck Equation ◽  
Small Granule ◽  
Fokker Planck Equation ◽  
Self Similar ◽  
Set Up ◽  
Fractional Time Derivative ◽  
Fokker Planck

We study the entropy production that is associated with the growing or shrinking of a small granule in, for instance, a colloidal suspension or in an aggregating polymer chain. A granule will fluctuate in size when the energy of binding is comparable to k B T , which is the “quantum” of Brownian energy. Especially for polymers, the conformational energy landscape is often rough and has been commonly modeled as being self-similar in its structure. The subdiffusion that emerges in such a high-dimensional, fractal environment leads to a Fokker–Planck Equation with a fractional time derivative. We set up such a so-called fractional Fokker–Planck Equation for the aggregation into granules. From that Fokker–Planck Equation, we derive an expression for the entropy production of a growing granule.

scholarly journals STOCHASTIC ELECTRON ACCELERATION IN SNR RX J1713.7-3946

2013 ◽  
Vol 23 ◽  
pp. 319-323 ◽  
Author(s):  
ZHONGHUI FAN ◽  
SIMING LIU
Keyword(s):  
Diffusion Coefficients ◽  
Planck Equation ◽  
Plasma Waves ◽  
Numerical Code ◽  
Model Parameters ◽  
Similar Model ◽  
Fokker Planck Equation ◽  
Self Similar ◽  
Time And Energy ◽  
Fokker Planck

Stochastic acceleration of charged particles due to their interactions with plasma waves may be responsible for producing superthermal particles in a variety of astrophysical systems. This process can be described as a diffusion process in the energy space with the Fokker-Planck equation. In this paper, a time-dependent numerical code is used to solve the reduced Fokker-Planck equation involving only time and energy variables with general forms of the diffusion coefficients. We also propose a self-similar model for particle acceleration in Sedov explosions and use the TeV SNR RX J1713.7-3946 as an example to demonstrate the model characteristics. Markov Chain Monte Carlo method is utilized to constrain model parameters with observations.

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
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