Ritz method for transition paths and quasipotentials of rare diffusive events

Sampling diffusive transition paths.

The authors address the problem of sampling double-ended diffusive paths. The ensemble of paths is expressed using a symmetric version of the Onsager-Machlup formula, which only requires evaluation of the force field and which, upon direct time discretization, gives rise to a symmetric integrator that is accurate to second order. Efficiently sampling this ensemble requires avoiding the well-kno...

Title Sampling diffusive transition paths

How rare are diffusive rare events?

We study the time until first occurrence, the first-passage time, of rare density fluctuations in diffusive systems. We approach the problem using a model consisting of many independent random walkers on a lattice. The existence of spatial correlations makes this problem analytically intractable. However, for a mean-field approximation in which the walkers can jump anywhere in the system, we ob...

Transition paths, diffusive processes, and preequilibria of protein folding.

Fundamental relationships between the thermodynamics and kinetics of protein folding were investigated using chain models of natural proteins with diverse folding rates by extensive comparisons between the distribution of conformations in thermodynamic equilibrium and the distribution of conformations sampled along folding trajectories. Consistent with theory and single-molecule experiment, dur...

Modeling Rare Transition Events

Dynamics in nature often proceed in the form of rare transition events: The system under study spends very long periods of time at various metastable states; only very rarely it hops from one metastable state to another. Understanding the dynamics of such systems requires us to study the ensemble of transition paths between the different metastable states. Transition path theory is a general ma...