| The minimum resistance path of Berkowitz et al (1983) is a simple way of specifying a "representative" finite-temperature transition path between two given molecular conformations. (An implementation, MaxFlux, is proposed by Huo & Straub (1997).) Starting from the transition path theory of E & Vanden-Eijnden (2006), a generalization of the MaxFlux concept from Cartesian coordinates to generalized coordinates, especially coarse-grained collective variables, is derived in Zhao et (2010). The numerical calculation of involves 3 components: discretization, sampling, and the solution of a system of nonlinear equations, each presenting significant challenges. An effective method that addresses discretization and solution of equations is the semi-implicit simplified string method of Vanden-Eijnden, Ren, E, & Heymann. Its discretization is a nonstandard upwinding scheme, and its solution method is a novel nonlinear 2-stage process. Presented as an alternative discretization is a finite element scheme having higher accuracy and continuous dependence on problem parameters. Presented as an alternative solution method is a 1-stage variable step size process. |
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