# Time dependent nucleation. II. A semiclassical approach

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- Asymptotic eigenvalue degeneracy for a class of one-dimensional Fokkerâ€“Planck operators. Angeletti, Angelo; Castagnari, Cinzia; Zirilli, Francesco // Journal of Mathematical Physics;Apr85, Vol. 26 Issue 4, p678
Let f(x), xâˆˆR, be a fourth-degree polynomial with lira f(x) = + âˆž with two minima, and let L[sub âˆˆ](Â·) = âˆˆsup2;/2âˆ‚Â²(Â·)/âˆ‚xÂ² + (âˆ‚/âˆ‚x)((Â·)(âˆ‚f/âˆ‚x)) be the corresponding Fokker-Planck operator. We study the spectrum of L[sub...

- Microscopic effects and kinetics of binary nucleation beyond the confines of the Fokker-Planck approximation. Djikaev, Y. S.; Grinin, A. P.; Kuni, F. M. // AIP Conference Proceedings;2000, Vol. 534 Issue 1, p131
The kinetic equation of isothermal binary nucleation is derived from the discrete equation of balance. It is shown that under some circumstances the Fokker-Planck approximation in the kinetic equation is not applicable. For such a case, we establish the hierarchy of the time scales of binary...

- Eigenfunctions and eigenvalues of the Dougherty collision operator. Anderson, M. W.; O'Neil, T. M. // Physics of Plasmas;May2007, Vol. 14 Issue 5, p052103
The Dougherty collision operator is a simplified Fokker-Planck collision operator that conserves particle number, momentum, and energy. In this paper, a complete set of orthogonal eigenfunctions of the linearized Dougherty operator is obtained. Five of the eigenfunctions have zero eigenvalue and...

- Outflow Probability for Drift—Diffusion Dynamics. Hinkel, Julia; Mahnke, Reinhard // International Journal of Theoretical Physics;Jun2007, Vol. 46 Issue 6, p1542
The proposed explanations are provided for the oneâ€“dimensional diffusion process with constant drift by using forward Fokkerâ€“Planck technique. We present the exact calculations and numerical evaluation to get the outflow probability in a finite interval, i.e. first passage time...

- Distributed approximating functional approach to the Fokker-Planck equation: Eigenfunction... Zhang, D.S.; Wei, G.W. // Journal of Chemical Physics;3/22/1997, Vol. 106 Issue 12, p5216
Applies the distributed approximating functional method to the solution of the Fokker-Planck equations. Limitation of the approach to the standard eigenfunction expansion method; Consideration of three typical examples in the numerical testing; Agreement of the results with those of established...

- Kinetics of activated processes from nonstationary solutions of the Fokkerâ€“Planck equation for a bistable potential. Cartling, Bo // Journal of Chemical Physics;9/1/1987, Vol. 87 Issue 5, p2638
The kinetics of thermally activated processes are studied by the nonstationary solutions of the Fokkerâ€“Planck equation, or Kramersâ€™ equation, for a particle moving in a bistable potential and coupled to a heat bath. An alternate direction implicit method is formulated and used to...

- Nonexponential magnetization thermal decay of a single-domain particle: Numerical computations using the dynamic Fokkerâ€“Planck equation. Zhang, Kezhao // Journal of Applied Physics;Apr2009, Vol. 105 Issue 7, p07D307
Nonexponential thermal decay of magnetization in a single-domain particle has been studied by numerically solving the Fokkerâ€“Planck equation as an initial value problem as well as an eigenvalue problem. The probability of not switching and switching time distribution is calculated for a...

- Does variational transition state theory provide an upper bound to the rate in dissipative systems? Drozdov, Alexander N.; Drodzov, Alexander N.; Tucker, Susan C. // Journal of Chemical Physics;3/22/2000, Vol. 112 Issue 12
By comparing variational transition state theory (VTST) against exact numerical calculations for the Brownian motion of a reactive particle, we uncover the unexpected result that VTST does not provide a rigorous upper bound to the least nonvanishing eigenvalue of the corresponding Fokker-Planck...

- Time dependent nucleation. Shizgal, B.; Barrett, J. C. // Journal of Chemical Physics;11/15/1989, Vol. 91 Issue 10, p6505
Continuum approximations to the discrete birth and death equations for classical nucleation are investigated. The discrete equations are parametrized by rate coefficients Î±i and Î²i for a cluster of size i to lose or gain a monomer, respectively. The continuum equations considered for the...