scholarly journals Simulating the Dynamics of Entangled Polymers Using the Kinetic Theory Description of the Doi-Edwards Model

2006 ◽  
Author(s):  
B. Mokdad ◽  
A. Ammar ◽  
F. Chinesta
Keyword(s):  
Kinetic Theory ◽  
Planck Equation ◽  
Computation Time ◽  
Unit Vector ◽  
Time Interval ◽  
Problem Resolution ◽  
Simulation Techniques ◽  
Fokker Planck Equation ◽  
Edwards Model ◽  
Fokker Planck

In this work, the model of Doi-Edwards with independant alignment approximation describing the dynamics of polymer melts is simulated. The main aim of this work is the analysis of some new simulation techniques operating on the Fokker-Planck equation related to that model. For this purpose we consider the kinetic theory description of the Doi-Edwards model, implemented in the 2D and 3D cases under shear and elongational flows. The Fokker Planck equation which governs the evolution of the distribution function involves two variables: the tube orientation (described by a unit vector defining the unit surface in 3D and the unit circle in 2D) and the coordinate that locates the segment tube on the molecular chain, taking values in the unit interval. To separate both variables during the problem resolution we make use of the Alternating Direction Implicit method (ADI) which allows reducing the computation time and efforts. A model reduction technique is also proposed and analyzed. It consists of considering an optimal representation basis which is constructed during the problem resolution. Thus, a reduced number of approximation functions, now defined in the whole domain, are enough to describe the solution evolution during the entire time interval considered in the simulation, with significant CPU time savings.

scholarly journals On a relativistic Fokker-Planck equation in kinetic theory

2011 ◽  
Vol 4 (2) ◽  
pp. 401-426 ◽  
Author(s):  
José Antonio Alcántara ◽  
◽  
Simone Calogero ◽  
Keyword(s):  
Kinetic Theory ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
Fokker Planck

Kinetic theory of a two-dimensional magnetized plasma. Part 2. Balescu-Lenard limit

1972 ◽  
Vol 8 (3) ◽  
pp. 357-374 ◽  
Author(s):  
George Vahala
Keyword(s):  
Kinetic Theory ◽  
Plasma Parameter ◽  
Planck Equation ◽  
Large Integer ◽  
Collision Term ◽  
Two Dimensional ◽  
Fokker Planck Equation ◽  
Long Time ◽  
Time Average ◽  
Fokker Planck

The kinetic theory of a two-dimensional one-species plasma in a uniform d.c. magnetic field is investigated in the small plasma parameter limit. The plasma consists of charged rods interacting through the logarithmic Coulomb potential. Vahala & Montgomery earlier derived a Fokker –;Planck equation for this system, but it contained a divergent integral, which had to be cut-off on physical grounds. This cut-off is compared to the standard cut-off introduced in the two-dimensional unmagnetized Fokker –;Planck equation. In the small plasma parameter limit, it is shown (under the assumption that for large integer n, γn/γn+1 = O(np), with p < 2, where γn = ωn −nΩ. with ωn the nth. Bernstein mode and Q the electron gyro frequency) that the Balescu-Lenard collision term is zero in the long time average limit if one considers only two-body interactions. The energy transfer from a test particle to an equilibrium plasma is discussed and also shown to be zero in the long time average limit. This supports the unexpected result of zero Balescu-Lenard collision term.

scholarly journals Classical Model of Quons

Entropy ◽  
2019 ◽  
Vol 21 (9) ◽  
pp. 841 ◽  
Author(s):  
Giorgio Kaniadakis ◽  
Antonio M. Scarfone
Keyword(s):  
Kinetic Theory ◽  
Classical Model ◽  
Planck Equation ◽  
Exclusion Principle ◽  
Type I ◽  
Type Ii ◽  
Fokker Planck Equation ◽  
Kinetic Interaction ◽  
Fokker Planck

By using the kinetic interaction principle, the quons statistics in the framework of kinetic theory is introduced. This is done by properly generalizing the inclusion/exclusion principle of standard boson and fermion statistics within a nonlinear classical model. The related nonlinear Fokker-Planck equation is introduced and the corresponding steady distribution describing quons statistics of type I and type II is derived.

A covariant Fokker-Planck equation for a simple gas from relativistic kinetic theory

2010 ◽  
Author(s):  
Guillermo Chacón-Acosta ◽  
Leonardo Dagdug ◽  
Hugo A. Morales-Técotl ◽  
Leonardo Dagdug ◽  
A. García-Perciante ◽  
...  
Keyword(s):  
Kinetic Theory ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
Relativistic Kinetic Theory ◽  
Fokker Planck

scholarly journals Non-Normalizable Quasi-Equilibrium Solution of the Fokker–Planck Equation for Nonconfining Fields

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 131
Author(s):  
Celia Anteneodo ◽  
Lucianno Defaveri ◽  
Eli Barkai ◽  
David A. Kessler
Keyword(s):  
Free Particle ◽  
Mean Square Displacement ◽  
Independent Solution ◽  
Planck Equation ◽  
Time Interval ◽  
Escape Time ◽  
Quasi Equilibrium ◽  
Potential Well ◽  
Fokker Planck Equation ◽  
Fokker Planck

We investigate the overdamped Langevin motion for particles in a potential well that is asymptotically flat. When the potential well is deep as compared to the temperature, physical observables, like the mean square displacement, are essentially time-independent over a long time interval, the stagnation epoch. However, the standard Boltzmann–Gibbs (BG) distribution is non-normalizable, given that the usual partition function is divergent. For this regime, we have previously shown that a regularization of BG statistics allows for the prediction of the values of dynamical and thermodynamical observables in the non-normalizable quasi-equilibrium state. In this work, based on the eigenfunction expansion of the time-dependent solution of the associated Fokker–Planck equation with free boundary conditions, we obtain an approximate time-independent solution of the BG form, being valid for times that are long, but still short as compared to the exponentially large escape time. The escaped particles follow a general free-particle statistics, where the solution is an error function, which is shifted due to the initial struggle to overcome the potential well. With the eigenfunction solution of the Fokker–Planck equation in hand, we show the validity of the regularized BG statistics and how it perfectly describes the time-independent regime though the quasi-stationary state is non-normalizable.

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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