A stabilized finite volume element method for solving Poisson-Nernst-Planck equations.
Sign Up to like & getrecommendations! Published in 2021 at "International journal for numerical methods in biomedical engineering"
DOI: 10.1002/cnm.3543
Abstract: One difficulty in solving the Poisson-Nernst-Planck (PNP) equations used for studying the ion transport in channel proteins is the possible convection-dominant problem in the Nernst-Planck equations. In this paper, to overcome this issue, considering the… read more here.
Keywords: nernst planck; stabilized finite; solving poisson; planck ... See more keywords
Coercivity, hypocoercivity, exponential time decay and simulations for discrete Fokker–Planck equations
Sign Up to like & getrecommendations! Published in 2020 at "Numerische Mathematik"
DOI: 10.1007/s00211-019-01094-y
Abstract: In this article, we propose and study several discrete versions of homogeneous and inhomogeneous one-dimensional Fokker–Planck equations. In particular, for these discretizations of velocity and space, we prove the exponential convergence to the equilibrium of… read more here.
Keywords: fokker planck; time; coercivity hypocoercivity; planck equations ... See more keywords
Structure Preserving Schemes for Nonlinear Fokker–Planck Equations and Applications
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Scientific Computing"
DOI: 10.1007/s10915-017-0510-z
Abstract: In this paper we focus on the construction of numerical schemes for nonlinear Fokker–Planck equations that preserve the structural properties, like non negativity of the solution, entropy dissipation and large time behavior. The methods here… read more here.
Keywords: fokker planck; schemes nonlinear; nonlinear fokker; planck equations ... See more keywords
Nonlinear Fokker-Planck equations in super-diffusive and sub-diffusive regimes
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Mathematical Physics"
DOI: 10.1063/1.5001189
Abstract: Anomalous-diffusion phenomena are very common in nature and may be suitably described by means of nonlinear Fokker-Planck equations, characterized by specific types of nonlinear diffusion contributions. The most explored situations in the literature consist in… read more here.
Keywords: fokker planck; diffusion; nonlinear fokker; planck equations ... See more keywords
Solving Non-local Fokker-Planck Equations by Deep Learning
Sign Up to like & getrecommendations! Published in 2022 at "Chaos"
DOI: 10.1063/5.0128935
Abstract: Physics-informed neural networks (PiNNs) recently emerged as a powerful solver for a large class of partial differential equations (PDEs) under various initial and boundary conditions. In this paper, we propose trapz-PiNNs, physics-informed neural networks incorporated… read more here.
Keywords: physics; planck equations; fokker planck; solving non ... See more keywords
Physically consistent numerical solver for time-dependent Fokker-Planck equations.
Sign Up to like & getrecommendations! Published in 2019 at "Physical review. E"
DOI: 10.1103/physreve.99.032117
Abstract: We present a simple thermodynamically consistent method for solving time-dependent Fokker-Planck equations (FPE) for overdamped stochastic processes, also known as Smoluchowski equations. It yields both transition and steady-state behavior and allows for computations of moment-generating… read more here.
Keywords: fokker planck; time; planck equations; dependent fokker ... See more keywords
Fractional-View Analysis of Fokker-Planck Equations by ZZ Transform with Mittag-Leffler Kernel
Sign Up to like & getrecommendations! Published in 2022 at "Symmetry"
DOI: 10.3390/sym14081513
Abstract: This work combines a ZZ transformation with the Adomian decomposition method to solve the fractional-order Fokker-Planck equations. The fractional derivative is represented in the Atangana-Baleanu derivative. It is looked at with graphs that show that… read more here.
Keywords: fractional view; planck equations; fokker planck; view analysis ... See more keywords