A nonlinear Fokker–Planck equation approach for interacting systems: Anomalous diffusion and Tsallis statistics

Marin, Diana; Ribeiro, Maurício A.; Ribeiro, Haroldo V.; Lenzi, E. K.

doi:10.1016/j.physleta.2018.05.009

Cited by 15 publications

(13 citation statements)

References 27 publications

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“…The results we present here have as particular cases those presented in ref. [42]. In the second situation, we have dealt with the presence of only a sink term in a way that one of the walkers (e.g.…”

Section: Discussionmentioning

confidence: 99%

“…, where the function C 1(2) [ρ 1(2) (x, t)] determines how the interaction between systems 1 and 2 (see ref. [42] for a particular case) is. By using equations (2.37) and (2.38), we can write the nonlinear equations as…”

Section: Random Walk and Nonlinear Diffusion Equationmentioning

confidence: 99%

“…Particles can also interact in different forms so that only the process of relaxation of a given part of a system is altered. An example of the former situation appears when part of the particles acts as a thermal bath to the other during the relaxation process [42].…”

Section: Introductionmentioning

confidence: 99%

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Extensions and solutions for nonlinear diffusion equations and random walks

Lenzi

Ribeiro

et al. 2019

Proc. R. Soc. A.

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We investigate a connection between random walks and nonlinear diffusion equations within the framework proposed by Einstein to explain the Brownian motion. We show here how to properly modify that framework in order to handle different physical scenarios. We obtain solutions for nonlinear diffusion equations that emerge from the random walk approach and analyse possible connections with a generalized thermostatistics formalism. Finally, we conclude that fractal and fractional derivatives may emerge in the context of nonlinear diffusion equations, depending on the choice of distribution functions related to the spreading of systems.

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Section: Discussionmentioning

confidence: 99%

Section: Random Walk and Nonlinear Diffusion Equationmentioning

confidence: 99%

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Extensions and solutions for nonlinear diffusion equations and random walks

Lenzi

Ribeiro

et al. 2019

Proc. R. Soc. A.

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“…The correlated unsteady diffusion of self-interacting particles has been investigated over the years by a number of authors [36][37][38]. Because of its complexity from the theoretical and computational side, it is useful to introduce some approximation s that clarify the underlying physics of the coupled transport.…”

Section: Physical Setup and Mathematical Modelmentioning

confidence: 99%

Anomalous sorption kinetics of self-interacting particles by a spherical trap

Raudino,

Grassi,

Lombardo

et al. 2022

Preprint

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“…Another aspect we want to model is the saturation effect when high concentrations 'stuck' to the surface of the trap ( [8,9]). Standard expressions for the flux satisfies a Fermi-Dirac form for the mixing entropy [10][11][12] :…”

Section: Introductionmentioning

confidence: 99%

Multiscale Modeling of Sorption Kinetics

Astuto¹,

Raudino²,

Russo³

2022

Preprint

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In this paper we propose and validate a multiscale model for the description of particle diffusion in presence of trapping boundaries. We start from a driftdiffusion equation in which the drift term describes the effect of bubble traps, and is modeled by a short range potential with an attractive term and a repulsive core. The interaction of the particles attracted by the bubble surface is simulated by the Lennard-Jones potential that simplifies the capture due to the hydrophobic properties of the ions. In our model the effect of the potential is replaced by a suitable boundary condition derived by mass conservation and asymptotic analysis. The potential is assumed to have a range of small size ε.An asymptotic expansion in the ε is considered, and the boundary conditions are obtained by retaining the lowest order terms in the expansion.Another aspect we investigate is saturation effect coming from high concentrations in the proximity of the bubble surface. Various studies show that these reactions lead to a modification of the model, including also non linear terms.The validity of the model is carefully checked with several tests in 1D, 2D and different geometries.

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A nonlinear Fokker–Planck equation approach for interacting systems: Anomalous diffusion and Tsallis statistics

Cited by 15 publications

References 27 publications

Extensions and solutions for nonlinear diffusion equations and random walks

Extensions and solutions for nonlinear diffusion equations and random walks

Anomalous sorption kinetics of self-interacting particles by a spherical trap

Multiscale Modeling of Sorption Kinetics

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