Publications
35 results found
Duncan AB, Kalliadasis S, Pavliotis GA, et al., 2016, Noise-induced transitions in rugged energy landscapes, Physical Review E, Vol: 94, ISSN: 1539-3755
We consider the problem of an overdamped Brownian particle moving in multiscale potential with N+1 characteristic length scales: the macroscale and N separated microscales. We show that the coarse-grained dynamics is given by an overdamped Langevin equation with respect to the free energy and with a space-dependent diffusion tensor, the calculation of which requires the solution of N fully coupled Poisson equations. We study in detail the structure of the bifurcation diagram for one-dimensional problems, and we show that the multiscale structure in the potential leads to hysteresis effects and to noise-induced transitions. Furthermore, we obtain an explicit formula for the effective diffusion coefficient for a self-similar separable potential, and we investigate the limit of infinitely many small scales.
Duncan AB, Pavliotis GA, Lelievre T, 2016, Variance reduction using nonreversible Langevin samplers, Journal of Statistical Physics, Vol: 163, Pages: 457-491, ISSN: 1572-9613
A standard approach to computing expectations with respect to a given target measure is to introduce an overdamped Langevin equation which is reversible with respect to the target distribution, and to approximate the expectation by a time-averaging estimator. As has been noted in recent papers, introducing an appropriately chosen nonreversiblecomponent to the dynamics is beneficial, both in terms of reducing the asymptotic variance and of speeding up convergence to the target distribution. In this paper we present a detailed study of the dependence of the asymptotic variance on the deviation from reversibility. Our theoretical findings are supported by numerical simulations.
Duncan A, Liao S, Vejchodský T, et al., 2015, Noise-induced multistability in chemical systems: Discrete versus continuum modeling, Physical Review E, Vol: 91, ISSN: 1539-3755
Duncan AB, Elliott CM, Pavliotis GA, et al., 2015, A Multiscale Analysis of Diffusions on Rapidly Varying Surfaces, JOURNAL OF NONLINEAR SCIENCE, Vol: 25, Pages: 389-449, ISSN: 0938-8974
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Duncan AB, 2015, Homogenization of Lateral Diffusion on a Random Surface, Multiscale Modeling & Simulation, Vol: 13, Pages: 1478-1506, ISSN: 1540-3459
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