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	Fokker-Planck equation - Wikipedia, the free encyclopedia
		The Fokker-Planck equation (also known as the Kolmogorov Forward equation) describes the time evolution of the probability density function of position and velocity of a particle.
		The first use of the Fokker-Planck equation was the statistical description of Brownian motion of a particle in a fluid.
		Brownian motion follows the Langevin equation, which can be solved for many different stochastic forcings with results being averaged (the Monte Carlo Method).
	en.wikipedia.org /wiki/Fokker-Planck_equation (152 words)

	Fokker-Planck equation -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-22)
		The Fokker-Planck equation describes the (The continuum of experience in which events pass from the future through the present to the past) time evolution of the (Click link for more info and facts about probability density function) probability density function of position and (Distance travelled per unit time) velocity of a particle.
		The first use of the Fokker-Planck equation was the statistical description of (The random motion of small particles suspended in a gas or liquid) Brownian motion of a particle in a (A continuous amorphous substance that tends to flow and to conform to the outline of its container: a liquid or a gas) fluid.
		However, instead of this computationally intensive approach, one can use the Fokker-Planck equation and consider, that is, the probability density function of the particle having a velocity in the interval, when it starts its motion with at time.
	www.absoluteastronomy.com /encyclopedia/f/fo/fokker-planck_equation1.htm (207 words)

	CPC Licence Alert (Site not responding. Last check: 2007-10-22)
		A code is presented that solves numerically the full non-relativistic Fokker-Planck equation using the IMSL package TWODEPEP, for the runaway electron distribution function in the presence of a dc electric field.
		To achieve these features, a set of partial integro-differential equations derived from a Legendre expansion of the Fokker-Planck equation is solved simultaneously for the electron distribution parts up to f3 with f0 non-Maxwellian and including the full electron-electron collision operator.
		Besides making amenable the treatment of the full integro-differential equation, calculations based on this expansion, being a series of one-dimensional equations, are easier to solve and require less computer time than a solution of the two- dimensional Fokker-Planck equation.
	www.cpc.cs.qub.ac.uk /summaries/ACJA.html (317 words)

	The Variational Formulation of the Fokker--Planck Equation
		The Fokker--Planck equation, or forward Kolmogorov equation, describes the evolution of the probability density for a stochastic process associated with an Ito stochastic differential equation.
		In this paper, we are concerned with Fokker--Planck equations for which the drift term is given by the gradient of a potential.
		Namely, we demonstrate that the dynamics may be regarded as a gradient flux, or a steepest descent, for the free energy with respect to the Wasserstein metric.
	epubs.siam.org /sam-bin/dbq/article/30335 (210 words)

	Relations Between Markov Processes Via Local Time and Coordinate Transformations
		Examples for the former are the small noise expansion and the adiabatic elimination procedure of fast random variables, for the latter the eigenfunction expansion and the continued-fraction method applied to periodically driven systems [6].
		Some years ago, the DK-method was also applied to the stochastic theory of Markov processes [11, 12], thereby relating the Fokker-Planck equation of Markov processes to other stochastic differential equations.
		With standard methods [6], the Fokker-Planck equation of the Schenzle-Brand process with (38) and (42) can be transformed to the Schrödinger equation of the Morse oscillator.
	www.physik.fu-berlin.de /~kleinert/kleiner_re249/markov.html (1344 words)

	Numerical Methods for Fokker-Planck Equations (Site not responding. Last check: 2007-10-22)
		If the acceleration region is homogeneous and the scattering mean free path is much smaller than both the energy change mean free path and the size of the acceleration region, then the Fokker-Planck equation reduces to a simple form involving only the time and energy variables.
		In this paper we study the numerical methods which must be used to solve more general forms of the equation.
		As discussed in Paper 1, Fokker-Planck equations derived under the above approximations are singular, causing problems with boundary conditions and numerical overflow and underflow.
	www.stanford.edu /dept/astro/parkb/paper2.html (301 words)

	Multipole expansions for the Fokker-Planck equation - LEMOU (ResearchIndex)
		11 On Boltzmann and Landau equations (context) - LIONS - 1994
		6 Kinetic Equations of the Landau type as a model of the Boltz..
		The Linear Boltzmann Equation For Long-Range Forces: A..
	citeseer.ist.psu.edu /363013.html (547 words)

	On The Trend To Equilibrium For The Fokker-Planck Equation: An Interplay Between Physics And Functional Analysis - ...
		We present connections between the problem of trend to equilibrium for the Fokker-Planck equation of statistical physics, and several inequalities from functional analysis, like logarithmic Sobolev or Poincare inequalities, together with some inequalities arising in the context of concentration of measures, introduced by Talagrand, or in the study of Gaussian isoperimetry.
		P.A. Markowich, C. Villani, On the trend to equilibrium for the Fokker-Planck equation : an interplay between physics and functional analysis, Preprint 1999.
		41 The geometry of dissipative evolution equations: the porous..
	citeseer.ist.psu.edu /markowich99trend.html (695 words)

	CAMCOS: 2002-present
		We were therefore able to extend the techniques previously developed for the diffusion equation case to this case of the Fokker-Planck equation.
		We added various types of noise to several parts of the Fokker-Planck equation, including initial conditions and parameters in the equation; and we measured the effect of noise by calculating the Mean Squared Error (MSE) in comparing the noisy solutions with the original un-noisy solutions.
		The goal of this project was to estimate the three parameters by minimizing the errors between the equation and the data.
	www.math.sjsu.edu /camcos/history.hsu.html (1972 words)

	Singular Perturbation Analysis of the Fokker--Planck Equation: Kramers' Underdamped Problem
		Singular Perturbation Analysis of the Fokker--Planck Equation: Kramers' Underdamped Problem:SIAM Journal on Applied Mathematics Vol.
		The one-dimensional Fokker--Planck equation for a bistable potential is considered in the "underdamped" limit.
		Using singular perturbation analysis, an asymptotic series solution is constructed in the parameter associated with the small viscosity.
	epubs.siam.org /sam-bin/dbq/article/25511 (133 words)

	Hide Cateau, Math. Biol. Seminar (Site not responding. Last check: 2007-10-22)
		The Fokker-Planck equation provides neuroscience with a powerful tool to analyze macroscopically how states of a population change as well as how strengths of numerous synapse on one neuron change.
		In our next application of the Fokker-Planck equation to an in vitro feedforward synchronization (Reyes, 2003), however, we find that the 1+1 dim Fokker-Planck equation fails to describe the system even in the fast synapse limit.
		We demonstrate that 2+1 dim Fokker-Planck equation based on this unique form of the autocovariance reproduces the feedforward synchronization very well.
	cams.njit.edu /tao/mathbio/cateau.html (133 words)

	Talk Abstract: Remarks about the dynamics of the Fokker-Planck Equation (Site not responding. Last check: 2007-10-22)
		Nonlinear systems which are active across disparate length and time scales are among the most intriguing ones we encounter in nature.
		This is the competition between the thermodynamic energy and nearness in the appropriate sense for the distribution of microscopic variables, the `averages' that describe the evolution of the macroscopic system.
		The result is a new derivation of the Fokker-Planck Equation as the gradient flux or steepest descent of the ordinary thermodynamic energy (e.g., minus the entropy in the case of ordinary diffusion or Brownian motion.).
	www.ima.umn.edu /dynsys/wkshp_abstracts/kinder1.html (179 words)

	ANS : Store : Electronic Articles
		The Fokker-Planck equation is often used to approximate the description of particle transport processes with highly forward-peaked scattering.
		Pomraning has shown that if the physical scattering kernel is sufficiently dominated by small-angle scattering, then the Fokker-Planck equation is an asymptotic approximation to the linear Boltzmann equation.
		Numerical experiments demonstrate that the resulting GFP equations are much more accurate than the standard Fokker-Planck equation.
	www.ans.org /store/index.cgi?i=E110000-nse-137-3-236-250 (165 words)

	Re: Probability current in Fokker-Planck equation (Site not responding. Last check: 2007-10-22)
		The equilibrium solution of the > Fokker-Planck equation has a nonzero probability current.
		I would > be particularly interested in papers where the probability current is > used to deduce something about the underlying physical system.
		It's been a few years since I worked with Fokker-Planck equations, but the main texts I used were: H. Risken, "The Fokker Planck Equation", (Springer, Berlin, 1984) C. Gardiner, "Handbook of Stochastic methods", (Springer, Berlin, 1983).
	www.lns.cornell.edu /spr/2001-03/msg0031630.html (160 words)

	Welcome to Cedric's Homepage (Site not responding. Last check: 2007-10-22)
		Time dependent simulations for Maxwell's equations (electromagnetism), in collaboration with Prof.
		Lozinski A. and Chauvière C., A fast solver for Fokker-Planck equation applied to viscoelastic flows calculations: 2D FENE model, J. of Computational Physics, 189(2) pp607-625 (2003).
		Owens R. On the numerical simulation of flows of polymer solutions using high-order methods based on the Fokker-Planck equation, Int.
	wwwlma.univ-bpclermont.fr /~chauvier (366 words)

	Amazon.co.uk: Books: The Fokker-Planck Equation: Methods of Solutions and Applications (Springer Series in Synergetics) (Site not responding. Last check: 2007-10-22)
		This book deals with the derivation of the Fokker-Planck equation, methods of solving it and some of its applications.
		This is the first time that this last method, which is very effective in dealing with simple Fokker-Planck equations having two variables, appears in a textbook.
		It is shown that the solution of the equation for Brownian motion in a variety of potentials can be expressed in terms suitable for evaluation on a computer.
	www.amazon.co.uk /exec/obidos/ASIN/354061530X (432 words)

	Global optimization using the Fokker-Planck machine
		The method follows from the fact that a forward Kolmogorov (or Fokker-Planck) equation can be associated with the evolution of a stochastic differential equation.
		The transition density which satisfies the Fokker-Planck equation is parametrized by means of a Radial Basis Function (RBF) neural network.
		By sampling the search space, a learning rule for the RBF network is obtained.
	www.esat.kuleuven.ac.be /sista/yearreport97/node16.html (252 words)

	fp-num (Site not responding. Last check: 2007-10-22)
		Inject a distribution of electrons into the loop and calculate, using the Fokker-Planck Equation, the distributions at several subsequent time steps.
		Process these images to simulate the fourier synthesis imaging of real hard X-ray telescopes.
		The Fokker-Planck equation can be used to describe how a distribution of electrons propagate in a coronal loop.
	physics.open.ac.uk /~ajconway/fp-num.html (389 words)

	No Title
		Master equation approach considered time evolution of probability distribution.
		For additive white Gaussian noise Langevin equation equivalent to Fokker-Planck equation.
		Can transform equation with Ito interpretation into one with Stratanovich interpretation or vice versa.
	www.physics.ubc.ca /~birger/lect9/lect9.html (270 words)

	Probability current in Fokker-Planck equation (Site not responding. Last check: 2007-10-22)
		I am looking at some stochastic dynamical systems in the context of the Fokker-Planck equation.
		The equilibrium solution of the Fokker-Planck equation has a nonzero probability current.
		I am trying to understand the physical implications of this nonzero current.
	www.lns.cornell.edu /spr/2001-02/msg0031442.html (119 words)

	The Fokker-Planck Equation (Site not responding. Last check: 2007-10-22)
		The Fokker-Planck formalism [ Gurevich 1978] starts by taking the spatially homogeneous Boltzmann equation
		For a weekly ionized plasma in the presence of an oscillating field, the distribution of electrons is mainly governed by the interaction with neutrals, therefore, giving the Fokker-Planck equation
		The Fokker-Planck equation, given by Eq.(2), is solved numerically.
	macul.ciencias.uchile.cl /~alejo/sprites/fokker/fokker.html (155 words)

	510n5
		Time dependent Fokker-Planck equation can be solved explicitly for linear processes (Malthus-Verhulst problem example).
		Considered a more general form of Fokker-Planck equation.
		Interpreted terms in equation in terms of probability current, drift and diffusion.
	www.phas.ubc.ca /~birger/510n5 (135 words)

	The Fokker-Planck equation (Site not responding. Last check: 2007-10-22)
		We shall not treat this equation any further here, except for one quick remark.
		The probability to find the particle at time t with velocity
		We may easily obtain the solution to this equation by using the results of the previous section.
	www.tn.utwente.nl /cdr/PolymeerDictaat/node30.html (176 words)

	books
		Ablowitz, M.J. and Clarkson, P.A. Solitons, Nonlinear Evolution Equations and Inverse Scattering,
		Qualitative Problems for Differential Equations and Control Theory
		Dodd, R.K.; Eilbeck, J.C.; Gibbon, J.D.; Morris, H.C. Solitons and Nonlinear Wave Equations
	www.camtp.uni-mb.si /camtp/books (3064 words)

	Best Book Buys - Fokker-Planck equation Books (Site not responding. Last check: 2007-10-22)
		Books > Browse > Subject Category > Mathematics > General > Fokker-Planck equation
		The Fokker-Planck Equation: Methods of Solution and Applications
		All trademarks are owned by the respective company or Best Web Buys.
	www.bestwebbuys.com /Mathematics-General-N_10020697-books.html (52 words)

	No Title
		Fokker-Planck equations commonly referred to as linear if A(x) linear and
		Stationary processes governed by linear Fokker Planck equation
		Found steady state probability distribution in Malthus-Verhulst problem.
	www.physics.ubc.ca /~birger/lect3 (113 words)

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