Heavy (or large) ions in a fluid in an electric field: The fundamental solution of the Fokker–Planck equation and related questions

2003 ◽  
Vol 118 (24) ◽  
pp. 11092-11099 ◽  
Author(s):  
Leonardo Ferrari
Keyword(s):  
Fundamental Solution ◽  
Electric Field ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
Fokker Planck

scholarly journals A STOCHASTIC DERIVATION OF THE GEODESIC RULE

2006 ◽  
Vol 21 (07) ◽  
pp. 1493-1502 ◽  
Author(s):  
NIKOS KALOGEROPOULOS
Keyword(s):  
Asymptotic Behavior ◽  
Random Walk ◽  
Fundamental Solution ◽  
Heat Kernel ◽  
Continuum Limit ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
The Continuum ◽  
Fokker Planck

We argue that the geodesic rule, for global defects, is a consequence of the randomness of the values of the Goldstone field ϕ in each causally connected volume. As these volumes collide and coalescence, ϕ evolves by performing a random walk on the vacuum manifold [Formula: see text]. We derive a Fokker–Planck equation that describes the continuum limit of this process. Its fundamental solution is the heat kernel on [Formula: see text], whose leading asymptotic behavior establishes the geodesic rule.

scholarly journals A Tandem Cell for Nanopore-based DNA Sequencing with Exonuclease

2014 ◽  
Author(s):  
G Sampath
Keyword(s):  
Electric Field ◽  
Dna Sequencing ◽  
Planck Equation ◽  
Natural Order ◽  
Exit Side ◽  
Tandem Cell ◽  
Fokker Planck Equation ◽  
Dna Strand ◽  
Fokker Planck

A tandem cell is proposed for DNA sequencing in which an exonuclease enzyme cleaves bases (mononucleotides) from a strand of DNA for identification inside a nanopore. It has two nanopores and three compartments with the structure [cis1, upstream nanopore (UNP), trans1=cis2, downstream nanopore (DNP), trans2]. The exonuclease is attached to the exit side of UNP in trans1/cis2. A cleaved base cannot regress into cis1 because of the remaining DNA strand in UNP. A profiled electric field over DNP with positive and negative components slows down base translocation through DNP. The proposed structure is modeled with a Fokker-Planck equation and a piecewise solution presented. Results from the model indicate that with probability approaching 1 bases enter DNP in their natural order, are detected without any loss, and do not regress into DNP after progressing into trans2. Sequencing efficiency with a tandem cell would then be determined solely by the level of discrimination among the base types inside DNP.

scholarly journals Fundamental solution of fractional Kolmogorov–Fokker–Planck equation

2021 ◽  
Vol 1 ◽  
pp. 100031
Author(s):  
Cong He ◽  
Jingchun Chen ◽  
Houzhang Fang ◽  
Huan He
Keyword(s):  
Fundamental 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
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