Diffusion in a bistable potential: a comparative study of different methods of solution

Indira, R. ; Valsakumar, M. C. ; Murthy, K. P. N. ; Ananthakrishna, G. (1983) Diffusion in a bistable potential: a comparative study of different methods of solution Journal of Statistical Physics, 33 (1). pp. 181-194. ISSN 0022-4715

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Official URL: http://www.springerlink.com/content/n41r020n101m38...

Related URL: http://dx.doi.org/10.1007/BF01009755


The problem of diffusion in a bistable potential is studied by considering the associated nonlinear Langevin equation and its equivalent Fokker-Planck equation. Two numerically exact methods of solution, namely, the Monte Carlo solution of the nonlinear Langevin equation and the solution of the Fokker-Planck equation via the finite difference technique, are considered. The latter method has the advantage that it directly gives the evolution of the probability distribution function. Approximate analyses of the fluctuations using the system size expansion, the Gaussian decoupling procedure, and the scaling approach are also carried out. These investigations are performed on a representative problem for two specific cases: (1) evolution from intrinsically unstable states and (2) evolution from extensive regime. The fluctuations obtained using these approximate methods are compared with those obtained via the numerically exact methods. The study brings out the advantages and limitations of each of the methods considered.

Item Type:Article
Source:Copyright of this article belongs to Springer.
Keywords:Diffusion in Bistable Potential; Numerical Solution of the Nonlinear F. P. Equation; Scaling Theory; Generalized Statistical Linearization; System Size Expansion; Monte Carlo Solution of the Nonlinear Langevin Equation
ID Code:72022
Deposited On:28 Nov 2011 05:13
Last Modified:28 Nov 2011 05:13

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