Journal ArticleDOI
Eigenvalues of a diffusion process with a critical point
H. Dekker,N.G. Van Kampen +1 more
TLDR
In this article, the eigenvalues of a Fokker-Planck equation involving a critical point have been computed by means of a simple discretization technique, which smoothly connects the monostable case above the critical point with the bistable case below it.About:
This article is published in Physics Letters A.The article was published on 1979-10-15. It has received 41 citations till now. The article focuses on the topics: Critical point (thermodynamics) & Discretization.read more
Citations
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Journal ArticleDOI
Discrete singular convolution for the solution of the Fokker–Planck equation
TL;DR: In this paper, a discrete singular convolution algorithm for solving the Fokker-Planck equation is presented, where singular kernels of the Hilbert-type and the delta type are presented for numerical computations.
Journal ArticleDOI
Bifurcations in fluctuating systems: The center-manifold approach
Edgar Knobloch,Kurt Wiesenfeld +1 more
TL;DR: In this article, the authors studied center-manifold reduction of fluctuating dynamical systems and proposed a classification scheme for the different kinds of dynamical behavior possible near bifurcation points.
Book ChapterDOI
Microscopic simulations of chemical instabilities
Journal ArticleDOI
Solutions and applications of tridiagonal vector recurrence relations
Hannes Risken,H. D. Vollmer +1 more
TL;DR: A general method is presented by which the initial value problem can be solved by iteration and the applicability of the method is demonstrated by calculating the eigenvalues of the laser Fokker-Planck operator.
Journal ArticleDOI
New unified formulation of transient phenomena near the instability point on the basis of the fokker-planck equation
TL;DR: In this article, a unified theory of transient phenomena is proposed to treat the passage from an initially unstable state to a final stable state, and for t → ∞ it gives a correct fluctuation asymptotically.
References
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Journal ArticleDOI
a Power Series Expansion of the Master Equation
TL;DR: In this paper, an expansion in powers of some parameter is needed in order to solve the master equation by a systematic approximation method, and the appropriate parameter is the reciprocal size of the system.
Journal ArticleDOI
A soluble model for diffusion in a bistable potential
TL;DR: In this article, an explicit solution is obtained for a special form of the potential, where the diffusing particle is initially at an arbitrary point near the potential maximum and various suggested approximation schemes are tested, with the following conclusions, (i) in linear approximation around the maximum the probability distribution is Gaussian.
Journal ArticleDOI
Kramers’s theory of chemical kinetics: Eigenvalue and eigenfunction analysis
R. S. Larson,M. D. Kostin +1 more
TL;DR: In this article, the Smoluchowski equation for a double minimum potential is studied as a means of calculating rate constants for chemical reactions, and the expression for the rate constant is seen to be a generalization of earlier results, and its range of validity is determined by solving the appropriate equations numerically.
Journal ArticleDOI
Scaling theory of transient phenomena near the instability point
TL;DR: In this paper, a scaling theory of transient phenomena is formulated near the instability point for the moments of the relevant macrovariable, for the generating function, and for the probability distribution function.