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Journal articles on the topic 'Fokker-Planck'

Author: Grafiati

Published: 4 June 2021

Last updated: 26 July 2025

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1

Portegies Zwart, Simon F., and Koji Takahashi. "Escape from a Crisis in Fokker-Planck Models." International Astronomical Union Colloquium 172 (1999): 179–86. http://dx.doi.org/10.1017/s0252921100072535.

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AbstractRecent N-body simulations have shown that there is a serious discrepancy between the results of N-body simulations and the results of Fokker-Planck simulations for the evolution of globular and rich open clusters under the influence of the galactic tidal field. In some cases, the lifetime obtained from Fokker-Planck calculations is more than an order of magnitude smaller than those from N-body simulations. In this paper we show that the principal cause for this discrepancy is an oversimplified treatment of the tidal field used in previous Fokker-Planck simulations. We performed new Fok

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2

POMRANING, G. C. "THE FOKKER-PLANCK OPERATOR AS AN ASYMPTOTIC LIMIT." Mathematical Models and Methods in Applied Sciences 02, no. 01 (1992): 21–36. http://dx.doi.org/10.1142/s021820259200003x.

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It is shown that the Fokker-Planck operator describing a highly peaked scattering process in the linear transport equation is a formal asymptotic limit of the exact integral operator. It is also shown that such peaking is a necessary, but not sufficient, condition for the Fokker-Planck operator to be a legitimate description of such scattering. In particular, the widely used Henyey-Greenstein scattering kernel does not possess a Fokker-Planck limit.

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3

Liu, Chang, Chuo Chang, and Zhe Chang. "Distribution of Return Transition for Bohm-Vigier Stochastic Mechanics in Stock Market." Symmetry 15, no. 7 (2023): 1431. http://dx.doi.org/10.3390/sym15071431.

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The Bohm-Vigier stochastic model is assumed as a natural generalization of the Black-Scholes model in stock market. The behavioral factor of stock market recognizes as a hidden sector in Bohmian mechanics. A Fokker-Planck equation description for the Bohm-Vigier stochastic model is presented. We find the familiar Boltzmann distribution is a stationary solution of the Fokker-Planck equation for the Bohm-Vigier model. The return transition distribution of stock market, which corresponds with a time-dependent solution of the Fokker-Planck equation, is obtained.

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4

Muyassaroh, Siti. "Penyelesaian Persamaan Diferensial Parsial Fokker-Planck Dengan Metode Garis." CAUCHY 3, no. 3 (2014): 169. http://dx.doi.org/10.18860/ca.v3i3.2943.

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Persamaan Fokker-Planck merupakan persamaan diferensial parsial yang menggambarkan fungsi distribusi partikel dalam suatu sistem yang berisi banyak partikel yang saling bertumbukan. Digunakan metode garis untuk menyelesaikan solusi numerik pada persamaan Fokker-Planck. Metode ini merepresentasikan bentuk persamaan diferensial parsial ke dalam bentuk sistem persamaan diferensial biasa yang ekuivalen pada bentuk persamaan diferensial parsialnya. langkah pertama yang dilakukan untuk menyelesaikan persamaan Fokker-Planck dengan metode garis yaitu mengganti turunan ruang dengan metode beda hingga p

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5

Baumann, Gerd, and Frank Stenger. "Fractional Fokker-Planck Equation." Mathematics 5, no. 1 (2017): 12. http://dx.doi.org/10.3390/math5010012.

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6

SUCCI, S., S. MELCHIONNA, and J. P. HANSEN. "LATTICE FOKKER–PLANCK EQUATION." International Journal of Modern Physics C 17, no. 04 (2006): 459–70. http://dx.doi.org/10.1142/s0129183106008613.

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A lattice version of the Fokker–Planck equation is introduced. The resulting numerical method is illustrated through the calculation of the electric conductivity of a one-dimensional charged fluid at zero and finite-temperature.

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7

Olemskoi, A. I. "The Fokker-Planck equation." Uspekhi Fizicheskih Nauk 168, no. 4 (1998): 475. http://dx.doi.org/10.3367/ufnr.0168.199804h.0475.

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8

Olemskoi, A. I. "The Fokker–Planck equation." Physics-Uspekhi 41, no. 4 (1998): 411–16. http://dx.doi.org/10.1070/pu1998v041n04abeh000388.

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9

Ho, C. L., and R. Sasaki. "Deformed Fokker-Planck Equations." Progress of Theoretical Physics 118, no. 4 (2007): 667–74. http://dx.doi.org/10.1143/ptp.118.667.

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10

El-Wakil, S. A., and M. A. Zahran. "Fractional Fokker–Planck equation." Chaos, Solitons & Fractals 11, no. 5 (2000): 791–98. http://dx.doi.org/10.1016/s0960-0779(98)00205-7.

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11

Cohn, Haldan. "Direct Fokker-Planck Calculations." Symposium - International Astronomical Union 113 (1985): 161–78. http://dx.doi.org/10.1017/s0074180900147369.

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The past decade has seen the development of powerful numerical methods for studying star cluster evolution by direct integration of the Fokker-Planck equation. Cohn's basic algorithm for spherical systems of identical point masses and its application to the study of core collapse is reviewed. Merritt's extension of this method to treat systems containing a mass spectrum, and Goodman's extensions to include strong scattering and rotation are discussed. Results from direct Fokker-Planck computations of core collapse in single mass and multi-mass isotropic clusters and single mass anisotropic clu

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12

Chang, L. D., and D. Waxman. "Quantum Fokker-Planck equation." Journal of Physics C: Solid State Physics 18, no. 31 (1985): 5873–79. http://dx.doi.org/10.1088/0022-3719/18/31/019.

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13

Tristani, Isabelle. "Fractional Fokker–Planck equation." Communications in Mathematical Sciences 13, no. 5 (2015): 1243–60. http://dx.doi.org/10.4310/cms.2015.v13.n5.a8.

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14

van Kampen, N. G. "Die Fokker-Planck-Gleichung." Physik Journal 53, no. 10 (1997): 1012–13. http://dx.doi.org/10.1002/phbl.19970531016.

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15

Shizgal, Bernie, and Lucio Demeio. "Comparison of WKB (Wentzel–Kramers–Brillouin) and SWKB solutions of Fokker–Planck equations with exact results; application to electron thermalization." Canadian Journal of Physics 69, no. 6 (1991): 712–19. http://dx.doi.org/10.1139/p91-119.

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A comparison of WKB (Wentzel–Kramers–Brillouin) and SWKB eigenfunctions of the Schrödinger equation for potentials in the class encountered in supersymmetric quantum mechanics is presented. The potentials that are studied are those that result from the transformation of a Fokker–Planck eigenvalue problem to a Schrödinger equation. Linear Fokker–Planck equations of the type considered in this paper give the probability distribution function for a large number of physical situations. The time-dependent solutions can be expressed as a sum of exponential terms with each term characterized by an ei

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16

Luo, Lan, and Hongjun Yu. "Spectrum analysis of the linear Fokker–Planck equation." Analysis and Applications 15, no. 03 (2017): 313–31. http://dx.doi.org/10.1142/s0219530515500219.

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In this work, we show the spectrum structure of the linear Fokker–Planck equation by using the semigroup theory and the linear operator perturbation theory. As an application, we show the large time behavior of the solutions to the linear Fokker–Planck equation.

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17

Hong, Deog Ki, Jie Jiang, and Dong-han Yeom. "Numerical investigation of two-dimensional Fokker-Planck equation in inflationary models: importance of slow-roll parameters." Journal of Cosmology and Astroparticle Physics 2024, no. 05 (2024): 008. http://dx.doi.org/10.1088/1475-7516/2024/05/008.

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Abstract In this study, we generalize the Fokker-Planck equation to two-dimensional cases, including potential functions with periodic boundary conditions and piecewise-defined structures, to analyze the probability distribution in multi-field inflationary models. We employ the spectral method for spatial derivatives and the Crank-Nicolson method for the time evolution to solve the equation numerically for the slow-roll inflation. We find that the distribution in the Fokker-Planck equation was determined by the two-dimensional potential combined slow-roll parameters. And the volume weighting e

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18

Du, Zhongzhou, Dandan Wang, Yi Sun, Yuki Noguchi, Shi Bai, and Takashi Yoshida. "Empirical Expression for AC Magnetization Harmonics of Magnetic Nanoparticles under High-Frequency Excitation Field for Thermometry." Nanomaterials 10, no. 12 (2020): 2506. http://dx.doi.org/10.3390/nano10122506.

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The Fokker–Planck equation accurately describes AC magnetization dynamics of magnetic nanoparticles (MNPs). However, the model for describing AC magnetization dynamics of MNPs based on Fokker-Planck equation is very complicated and the numerical calculation of Fokker-Planck function is time consuming. In the stable stage of AC magnetization response, there are differences in the harmonic phase and amplitude between the stable magnetization response of MNPs described by Langevin and Fokker–Planck equation. Therefore, we proposed an empirical model for AC magnetization harmonics to compensate th

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19

Takahashi, Koji. "Two-Dimensional Fokker-Planck Models." Symposium - International Astronomical Union 174 (1996): 91–100. http://dx.doi.org/10.1017/s007418090000142x.

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The evolution of spherical single-mass star clusters was followed by numerically solving the orbit-averaged two-dimensional Fokker-Planck equation in energy-angular momentum space. Velocity anisotropy is allowed in the two-dimensional Fokker-Planck model. The development of the anisotropy is discussed in detail.

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20

HO, CHOON-LIN, and YAN-MIN DAI. "A PERTURBATIVE APPROACH TO A CLASS OF FOKKER–PLANCK EQUATIONS." Modern Physics Letters B 22, no. 07 (2008): 475–81. http://dx.doi.org/10.1142/s0217984908015000.

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In this paper, we present a direct perturbative method to solving certain Fokker–Planck equations, which have constant diffusion coefficients and some small parameters in the drift coefficients. The method makes use of the connection between the Fokker–Planck and Schrödinger equations. Two examples are used to illustrate the method. In the first example, the drift coefficient depends only on time but not on space. In the second example, we consider the Uhlenbeck–Ornstein process with a small drift coefficient. These examples show that such perturbative approach can be a useful tool to obtain a

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21

Liu, Li-wei. "Interval Wavelet Numerical Method on Fokker-Planck Equations for Nonlinear Random System." Advances in Mathematical Physics 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/651357.

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The Fokker-Planck-Kolmogorov (FPK) equation governs the probability density function (p.d.f.) of the dynamic response of a particular class of linear or nonlinear system to random excitation. An interval wavelet numerical method (IWNM) for nonlinear random systems is proposed using interval Shannon-Gabor wavelet interpolation operator. An FPK equation for nonlinear oscillators and a time fractional Fokker-Planck equation are taken as examples to illustrate its effectiveness and efficiency. Compared with the common wavelet collocation methods, IWNM can decrease the boundary effect greatly. Comp

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22

Romadani, Arista, and Muhammad Farchani Rosyid. "Proses difusi relativistik melalui persamaan langevin dan fokker-planck." Jurnal Teknosains 11, no. 2 (2022): 101. http://dx.doi.org/10.22146/teknosains.63229.

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Brownian motion theory is always challenging how to describe diffusion phenomena with the main issue is how to extend the classical theory of Brownian motion to the special relativity framework. In this study, we formulated dynamics and distribution of a Brownian particle in relativistic framework by using Langevin and Fokker-Planck equation. By representing Brownian particle dynamics by Langevin equation, the velocity curves were dependent on the presence of viscous friction coefficient (heat bath), and were used generalized in special relativity theory, A relativistic Langevin equation reduc

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23

Yamagishi, O. "An alternative expression for ad hoc field collision model." Physics of Plasmas 29, no. 10 (2022): 102507. http://dx.doi.org/10.1063/5.0104611.

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An alternative form of ad hoc collision model to the Fokker–Planck field collision operator is proposed. The model is so constructed that the results of exact Fokker–Planck field collision, applied to the low-order Legendre and associated Laguerre polynomials, are used to impose self-adjointness first and then collisional conservation laws. The model is shown to be actually identical to the conventional ad hoc model in the l = 0 and 1 parts in Legendre polynomial expansion in an isothermal case, while it is not limited to extend to the higher order, in contrast to the conventional ad hoc model

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24

Furioli, Giulia, Ada Pulvirenti, Elide Terraneo, and Giuseppe Toscani. "Non-Maxwellian kinetic equations modeling the dynamics of wealth distribution." Mathematical Models and Methods in Applied Sciences 30, no. 04 (2020): 685–725. http://dx.doi.org/10.1142/s0218202520400023.

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We introduce a class of new one-dimensional linear Fokker–Planck-type equations describing the dynamics of the distribution of wealth in a multi-agent society. The equations are obtained, via a standard limiting procedure, by introducing an economically relevant variant to the kinetic model introduced in 2005 by Cordier, Pareschi and Toscani according to previous studies by Bouchaud and Mézard. The steady state of wealth predicted by these new Fokker–Planck equations remains unchanged with respect to the steady state of the original Fokker–Planck equation. However, unlike the original equation

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25

Iollo, Angelo, and Tommaso Taddei. "Point-set registration in bounded domains via the Fokker–Planck equation." Comptes Rendus. Mathématique 363, G8 (2025): 809–24. https://doi.org/10.5802/crmath.753.

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We present a point set registration method in bounded domains based on the solution to the Fokker–Planck equation. Our approach leverages (i) density estimation based on Gaussian mixture models; (ii) a stabilized finite element discretization of the Fokker–Planck equation; (iii) a specialized method for the integration of the particles. We review relevant properties of the Fokker–Planck equation that provide the foundations for the numerical method. We discuss two strategies for the integration of the particles and we propose a regularization technique to control the distance of the particles

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26

Cao, Xue-Nian, Jiang-Li Fu, and Hu Huang. "Numerical Method for The Time Fractional Fokker-Planck Equation." Advances in Applied Mathematics and Mechanics 4, no. 06 (2012): 848–63. http://dx.doi.org/10.4208/aamm.12-12s13.

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AbstractIn this paper, a new numerical algorithm for solving the time fractional Fokker-Planck equation is proposed. The analysis of local truncation error and the stability of this method are investigated. Theoretical analysis and numerical experiments show that the proposed method has higher order of accuracy for solving the time fractional Fokker-Planck equation.

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27

Khalili Golmankhaneh, Ali, Saleh Ashrafi, Dumitru Baleanu, and Arran Fernandez. "Brownian Motion on Cantor Sets." International Journal of Nonlinear Sciences and Numerical Simulation 21, no. 3-4 (2020): 275–81. http://dx.doi.org/10.1515/ijnsns-2018-0384.

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AbstractIn this paper, we have investigated the Langevin and Brownian equations on fractal time sets using Fα-calculus and shown that the mean square displacement is not varied linearly with time. We have also generalized the classical method of deriving the Fokker–Planck equation in order to obtain the Fokker–Planck equation on fractal time sets.

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28

Dolbeault, Jean, та Xingyu Li. "φ-Entropies: convexity, coercivity and hypocoercivity for Fokker–Planck and kinetic Fokker–Planck equations". Mathematical Models and Methods in Applied Sciences 28, № 13 (2018): 2637–66. http://dx.doi.org/10.1142/s0218202518500574.

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This paper is devoted to [Formula: see text]-entropies applied to Fokker–Planck and kinetic Fokker–Planck equations in the whole space, with confinement. The so-called [Formula: see text]-entropies are Lyapunov functionals which typically interpolate between Gibbs entropies and [Formula: see text] estimates. We review some of their properties in the case of diffusion equations of Fokker–Planck type, give new and simplified proofs, and then adapt these methods to a kinetic Fokker–Planck equation acting on a phase space with positions and velocities. At kinetic level, since the diffusion only ac

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29

Delettrez, J. "Thermal electron transport in direct-drive laser fusion." Canadian Journal of Physics 64, no. 8 (1986): 932–43. http://dx.doi.org/10.1139/p86-162.

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The experimental and theoretical aspects of electron thermal transport in direct-drive laser-fusion are reviewed. The Fokker–Planck equation and the flux-limited diffusion model, which is widely used in laser-fusion simulation codes, are described. After a discussion on the limitation of planar-target transport experiments, results of spherical experiments are surveyed. Solutions of the Fokker–Planck equations for cathode problems and for cases with stationary and moving ion density profiles are presented. Limitations of the flux-limited diffusion model are discussed in light of the Fokker–Pla

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30

Younas, H., Muhammad Mustahsan, Tareq Manzoor, Nadeem Salamat, and S. Iqbal. "Dynamical Study of Fokker-Planck Equations by Using Optimal Homotopy Asymptotic Method." Mathematics 7, no. 3 (2019): 264. http://dx.doi.org/10.3390/math7030264.

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In this article, Optimal Homotopy Asymptotic Method (OHAM) is used to approximate results of time-fractional order Fokker-Planck equations. In this work, 3rd order results obtained through OHAM are compared with the exact solutions. It was observed that results from OHAM have better convergence rate for time-fractional order Fokker-Planck equations. The solutions are plotted and the relative errors are tabulated.

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31

Shin, Jihye, and Sungsoo S. Kim. "Dynamical Evolution of the Mass Function of the Globular Cluster System from Fokker-Planck Calculations: Preliminary Results." Proceedings of the International Astronomical Union 2, S235 (2006): 110. http://dx.doi.org/10.1017/s1743921306005424.

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AbstractUsing anisotropic Fokker-Planck models, we calculate the evolution of mass and luminosity functions of the Galactic globular cluster system. Our models include two-body relaxation, binary heating, tidal shocks, dynamical friction, and stellar evolution. We perform Fokker-Planck simulations for a large number of virtual globular clusters and synthesize these results to study the relation between the initial and present GCMFs.

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32

RENNER, CHRISTOPH, J. PEINKE, and R. FRIEDRICH. "Experimental indications for Markov properties of small-scale turbulence." Journal of Fluid Mechanics 433 (April 25, 2001): 383–409. http://dx.doi.org/10.1017/s0022112001003597.

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We present a stochastic analysis of a data set consisting of 1.25 × 107 samples of the local velocity measured in the turbulent region of a round free jet. We find evidence that the statistics of the longitudinal velocity increment v(r) can be described as a Markov process. This new approach to characterize small-scale turbulence leads to a Fokker–Planck equation for the r-evolution of the probability density function (p.d.f.) of v(r). This equation for p(v, r) is completely determined by two coefficients D1(v, r) and D2(v, r) (drift and diffusion coefficient, respectively). It is shown how th

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33

Liu, Shu, Wuchen Li, Hongyuan Zha, and Haomin Zhou. "Neural Parametric Fokker--Planck Equation." SIAM Journal on Numerical Analysis 60, no. 3 (2022): 1385–449. http://dx.doi.org/10.1137/20m1344986.

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34

Pomraning, G. C. "Higher Order Fokker-Planck Operators." Nuclear Science and Engineering 124, no. 3 (1996): 390–97. http://dx.doi.org/10.13182/nse96-a17918.

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35

Abe, Sumiyoshi. "Invariants of Fokker-Planck equations." European Physical Journal Special Topics 226, no. 3 (2017): 529–32. http://dx.doi.org/10.1140/epjst/e2016-60215-1.

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36

Ho, Choon-Lin, and Ryu Sasaki. "Deformed multivariable Fokker-Planck equations." Journal of Mathematical Physics 48, no. 7 (2007): 073302. http://dx.doi.org/10.1063/1.2748375.

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37

Rosu, Haret C. "Supersymmetric Fokker-Planck strict isospectrality." Physical Review E 56, no. 2 (1997): 2269–71. http://dx.doi.org/10.1103/physreve.56.2269.

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38

Coghi, Michele, and Benjamin Gess. "Stochastic nonlinear Fokker–Planck equations." Nonlinear Analysis 187 (October 2019): 259–78. http://dx.doi.org/10.1016/j.na.2019.05.003.

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39

Wei, Jinlong, and Bin Liu. "-solutions of Fokker–Planck equations." Nonlinear Analysis: Theory, Methods & Applications 85 (July 2013): 110–24. http://dx.doi.org/10.1016/j.na.2013.02.022.

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40

Karney, Charles F. F. "Fokker-Planck and quasilinear codes." Computer Physics Reports 4, no. 3-4 (1986): 183–244. http://dx.doi.org/10.1016/0167-7977(86)90029-8.

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41

Yano, Ryosuke. "On Quantum Fokker–Planck Equation." Journal of Statistical Physics 158, no. 1 (2014): 231–47. http://dx.doi.org/10.1007/s10955-014-1123-7.

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42

Chavanis, Pierre-Henri. "Generalized Stochastic Fokker-Planck Equations." Entropy 17, no. 5 (2015): 3205–52. http://dx.doi.org/10.3390/e17053205.

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43

Ligou, Jacques. "The Boltzmann-Fokker-Planck equation." Transport Theory and Statistical Physics 15, no. 6-7 (1986): 985–1005. http://dx.doi.org/10.1080/00411458608212727.

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44

Frisch, H. L., and Bogdan Nowakowski. "The thermalized Fokker–Planck equation." Journal of Chemical Physics 98, no. 11 (1993): 8963–69. http://dx.doi.org/10.1063/1.464455.

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45

Yau, Stephen S. T. "Computation of Fokker-Planck equation." Quarterly of Applied Mathematics 62, no. 4 (2004): 643–50. http://dx.doi.org/10.1090/qam/2104266.

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46

Kolwankar, Kiran M., and Anil D. Gangal. "Local Fractional Fokker-Planck Equation." Physical Review Letters 80, no. 2 (1998): 214–17. http://dx.doi.org/10.1103/physrevlett.80.214.

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47

Bogachev, Vladimir Igorevich, and Stanislav Valer'evich Shaposhnikov. "Nonlinear Fokker-Planck-Kolmogorov equations." Russian Mathematical Surveys 79, no. 5 (2024): 751–805. https://doi.org/10.4213/rm10202e.

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This paper gives a survey of recent investigations on nonlinear Fokker-Planck-Kolmogorov equations of elliptic and parabolic types and contains a number of new results. We discuss in detail the problems of existence and uniqueness of solutions, various estimates of solutions, connections with linear equations, and the convergence of solutions of parabolic equations to stationary solutions. Bibliography: 116 items.

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48

Chow, C. W., and K. L. Liu. "Fokker–Planck equation and subdiffusive fractional Fokker–Planck equation of bistable systems with sinks." Physica A: Statistical Mechanics and its Applications 341 (October 2004): 87–106. http://dx.doi.org/10.1016/j.physa.2004.04.114.

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49

Weber, Piotr, Piotr Bełdowski, Martin Bier, and Adam Gadomski. "Entropy Production Associated with Aggregation into Granules in a Subdiffusive Environment." Entropy 20, no. 9 (2018): 651. http://dx.doi.org/10.3390/e20090651.

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We study the entropy production that is associated with the growing or shrinking of a small granule in, for instance, a colloidal suspension or in an aggregating polymer chain. A granule will fluctuate in size when the energy of binding is comparable to k B T , which is the “quantum” of Brownian energy. Especially for polymers, the conformational energy landscape is often rough and has been commonly modeled as being self-similar in its structure. The subdiffusion that emerges in such a high-dimensional, fractal environment leads to a Fokker–Planck Equation with a fractional time derivative. We

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50

LUO, DEJUN. "WELL-POSEDNESS OF FOKKER–PLANCK TYPE EQUATIONS ON THE WIENER SPACE." Infinite Dimensional Analysis, Quantum Probability and Related Topics 13, no. 02 (2010): 273–304. http://dx.doi.org/10.1142/s0219025710004061.

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We consider Fokker–Planck type equations on the abstract Wiener space. Under the assumptions that the coefficients have a certain Sobolev regularity and they, together with their gradients and divergences, are exponentially integrable, we establish the existence of solutions to these equations, based on the estimates for solutions to Fokker–Planck equations in the finite-dimensional case. Moreover, the solution is unique if it belongs to the first-order Sobolev space.

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