Related papers: A Concerted Variational Strategy for Investigating…
We introduce a path sampling method for obtaining statistical properties of an arbitrary stochastic dynamics. The method works by decomposing a trajectory in time, estimating the probability of satisfying a progress constraint, modifying…
A method for locating first order saddle points on the energy surface of a magnetic system is described and several applications presented where the mechanism of various magnetic transitions is identified. The starting point for the…
This article reviews the concepts and methods of variational path sampling. These methods allow computational studies of rare events in systems driven arbitrarily far from equilibrium. Based upon a statistical mechanics of trajectory space…
Global dynamics in nonlinear stochastic systems is often difficult to analyze rigorously. Yet, many excellent numerical methods exist to approximate these systems. In this work, we propose a method to bridge the gap between computation and…
Transition path sampling is a method for estimating the rates of rare events in molecular systems based on the gradual transformation of a path distribution containing a small fraction of reactive trajectories into a biased distribution in…
We study counting statistics of number of transitions in a stochastic process. For mesoscopic systems, a path integral formulation for the counting statistics has already been derived. We here show that it is also possible to derive the…
Analysing stationary point databases to extract phenomenological rate constants can become time-consuming for systems with large potential energy barriers. In the present contribution we analyse several different approaches to this problem.…
How systems transit between different stable states under external perturbation is an important practical issue. We discuss here how a recently-developed energy optimization method for identifying the minimal disturbance necessary to reach…
We present a numerical method for computing optimal transition pathways and transition rates in systems of stochastic differential equations (SDEs). In particular, we compute the most probable transition path of stochastic equations by…
We develop a non-empirical scheme to search for the minimum-energy escape paths from the minima of the potential surface to unknown saddle points nearby. A stochastic algorithm is constructed to move the walkers up the surface through the…
The probability of trajectories of weakly diffusive processes to remain in the tubular neighbourhood of a smooth path is given by the Freidlin-Wentzell-Graham theory of large deviations. The most probable path between two states (the…
This article studies the existence of long-time solutions to the Hamiltonian boundary value problem, and their consistent numerical approximation. Such a boundary value problem is, for example, common in Molecular Dynamics, where one aims…
We review the development and practical uses of a generalized Maupertuis least action principle in classical mechanics, in which the action is varied under the constraint of fixed mean energy for the trial trajectory. The original…
Hamiltonian Flow Monte Carlo(HFMC) methods have been implemented in engineering, biology and chemistry. HFMC makes large gradient based steps to rapidly explore the state space. The application of the Hamiltonian dynamics allows to estimate…
Fluctuational transitions between two co-existing chaotic attractors, separated by a fractal basin boundary, are studied in a discrete dynamical system. It is shown that the mechanism for such transitions is determined by a hierarchy of…
We consider the dynamics of a Hamiltonian particle forced by a rapidly oscillating potential in $\dim$-dimensional space. As alternative to the established approach of averaging Hamiltonian dynamics by reformulating the system as…
Hamilton variational principle for special type of statistical ensemble of deterministic dynamical systems is derived. Thie form of variational principle allows one to describe the statistical ensemble in terms of wave functions and…
By means of a novel variational approach and using dual maps techniques and general ideas of dynamical system theory we derive exact results about several models of transport flows, for which we also obtain a complete description of their…
We investigate the theoretical and numerical computation of rare transitions in simple geophysical turbulent models. We consider the barotropic quasi-geostrophic and two-dimensional Navier-Stokes equations in regimes where bistability…
Transition probabilities for stochastic systems can be expressed in terms of a functional integral over paths taken by the system. Evaluating the integral by the saddle point method in the weak-noise limit leads to a remarkable mapping…