“Strange” Fermi processes and power-law nonthermal tails from a self-consistent fractional kinetic equation

2001 ◽  
Vol 64 (5) ◽  
Author(s):  
Alexander V. Milovanov ◽  
Lev M. Zelenyi
Author(s):  
Aleksander Stanislavsky ◽  
Karina Weron

AbstractWe present a probabilistic model of the microscopic scenario of dielectric relaxation relating to the atypical case of two-power-law responses.The surveyed approach extends the cluster model concept used for the description of the typical, Havriliak-Negami (HN) law. Within the proposed framework, all empirical two-power-law relaxation patterns may be derived. Their relaxation functions are expressed in terms of the three-parameter Mittag-Leffler function, and the kinetic equation takes the pseudodifferential form generalizing the Riemann-Louiville fractional calculus. This provides a clue to explain the universality observed in relaxation phenomena.


2021 ◽  
Vol 10 (5) ◽  
pp. 2593-2610
Author(s):  
Wagdi F.S. Ahmed ◽  
D.D. Pawar ◽  
W.D. Patil

In this study, a new and further generalized form of the fractional kinetic equation involving the generalized V$-$function has been developed. We have discussed the manifold generality of the generalized V$-$function in terms of the solution of the fractional kinetic equation. Also, the graphical interpretation of the solutions by employing MATLAB is given. The results are very general in nature, and they can be used to generate a large number of known and novel results.


Author(s):  
Vladimir Kolobov ◽  
Juan Alonso Guzmán ◽  
R R Arslanbekov

Abstract A self-consistent hybrid model of standing and moving striations was developed for low-current DC discharges in noble gases. We introduced the concept of surface diffusion in phase space (r,u) (where u denotes the electron kinetic energy) described by a tensor diffusion in the nonlocal Fokker-Planck kinetic equation for electrons in the collisional plasma. Electrons diffuse along surfaces of constant total energy ε=u-eφ(r) between energy jumps in inelastic collisions with atoms. Numerical solutions of the 1d1u kinetic equation for electrons were obtained by two methods and coupled to ion transport and Poisson solver. We studied the dynamics of striation formation in Townsend and glow discharges in Argon gas at low discharge currents using a two-level excitation-ionization model and a “full-chemistry” model, which includes stepwise and Penning ionization. Standing striations appeared in Townsend and glow discharges at low currents, and moving striations were obtained for the discharge currents exceeding a critical value. These waves originate at the anode and propagate towards the cathode. We have seen two types of moving striations with the 2-level and full-chemistry models, which resemble the s and p striations previously observed in the experiments. Simulations indicate that processes in the anode region could control moving striations in the positive column plasma. The developed model helps clarify the nature of standing and moving striations in DC discharges of noble gases at low discharge currents and low gas pressures.


2003 ◽  
Vol 208 ◽  
pp. 449-450
Author(s):  
Koji Takahashi ◽  
Tomohiro Sensui ◽  
Yoko Funato ◽  
Junichiro Makino

We investigate the dynamical evolution of clusters of galaxies in virial equilibrium by using Fokker–Planck models and self-consistent N-body models. In particular we focus on the growth of the common halos and the development of the central density cusps in the clusters. We find good agreement between the Fokker–Planck and N-body models. At the cluster center the cusp approximated by a power law, ρ(r) ∝ r-α (α ∼ 1), develops. We conclude that this shallow cusp results from the combined effects of two-body relaxation and tidal stripping. The cusp steepness α weakly depends on the relative importance of tidal stripping.


2005 ◽  
Vol 37 (2) ◽  
pp. 366-392 ◽  
Author(s):  
J. M. Angulo ◽  
V. V. Anh ◽  
R. McVinish ◽  
M. D. Ruiz-Medina

In this paper, we consider a certain type of space- and time-fractional kinetic equation with Gaussian or infinitely divisible noise input. The solutions to the equation are provided in the cases of both bounded and unbounded domains, in conjunction with bounds for the variances of the increments. The role of each of the parameters in the equation is investigated with respect to second- and higher-order properties. In particular, it is shown that long-range dependence may arise in the temporal solution under certain conditions on the spatial operators.


1994 ◽  
Vol 09 (07) ◽  
pp. 1153-1180 ◽  
Author(s):  
Y. YAMANAKA ◽  
H. UMEZAWA ◽  
K. NAKAMURA ◽  
T. ARIMITSU

Making use of the thermo field dynamics (TFD) we formulate a calculable method for time-dependent nonequilibrium systems in a time representation (t-representation) rather than in the k0-Fourier representation. The corrected one-body propagator in the t-representation has the form of B−1 (diagonal matrix) B (B being a thermal Bogoliubov matrix). The number parameter in B here is the observed number (the Heisenberg number) with a fluctuation. With the usual definition of the on-shell self-energy a self-consistent renormalization condition leads to a kinetic equation for the number parameter. This equation turns out to be the Boltzmann equation, from which the entropy law follows.


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