Eric Vanden-Eijnden

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We present an efficient numerical algorithm for simulating chemical kinetic systems with multiple time scales. This algorithm is an improvement of the traditional stochastic simulation algorithm (SSA), also known as Gillespie's algorithm. It is in the form of a nested SSA and uses an outer SSA to simulate the slow reactions with rates computed from(More)
We investigate thermally-activated phenomena in micromagnetics using large deviation theory and concepts from stochastic resonance. We give a natural mathematical definition of finite-temperature as-troids, finite-temperature hysteresis loops, etc. Generically, these objects emerge when the (generalized) Arrhenius timescale governing the thermally-activated(More)
The framework of transition path theory (TPT) is developed in the context of continuous-time Markov chains on discrete state-spaces. Under assumption of ergodicity, TPT singles out any two subsets in the state-space and analyzes the statistical properties of the associated reactive trajectories, i.e. these trajectories by which the random walker transits(More)
Construction of stochastic models that describe the effective dynamics of observ-ables of interest is an useful instrument in various fields of application, such as physics, climate science, and finance. We present a new technique for the construction of such models. From the timeseries of an observable, we construct a discrete-in-time Markov chain and(More)
A few recent techniques to calculate free energies in the context of molecular dynamics simulations are discussed: temperature-accelerated molecular dynamics, which is a method to explore fast the important regions in the free energy landscape associated with a set of continuous collective variables without having to know where these regions are beforehand;(More)
This paper is devoted to the theoretical analysis of the zero-temperature string method, a scheme for identifying minimum energy paths (MEP's) on a given energy landscape. By definition , MEP's are curves connecting critical points on the energy landscape which are everywhere tangent to the gradient of the potential except possibly at critical points. In(More)
A variational approach to the estimation of generators for Markov jump processes from discretely sampled data is discussed and generalized. In this approach, one first calculates the spectrum of the discrete maximum likelihood estimator for the transition matrix consistent with the discrete data. Then the generator that best matches the spectrum is(More)
Keywords: Molecular dynamics Metropolis–Hastings Verlet RATTLE RESPA a b s t r a c t This paper extends the results in [8] to stochastic differential equations (SDEs) arising in molecular dynamics. It implements a patch to explicit integrators that consists of a Metropolis–Hastings step. The 'patched integrator' preserves the SDE's equilibrium distribution(More)
In this paper we present a new procedure for the estimation of diffusion processes from discretely sampled data. It is based on the close relation between eigenpairs of the diffusion operator L and those of the conditional expectation operator Pt, a relation stemming from the semigroup structure Pt = exp(tL) for t ≥ 0. It allows for estimation without(More)