# Numerical aspects of nonequilibrium dynamics

25-28 April 2017
IHP
Europe/Paris timezone

## Posters

A poster session will be held during the workshop. If you want to participate, send an email to Gabriel Stoltz (gabriel.stoltz.AT.enpc.fr) with a tentative title.

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Manon Baudel (University Orléans)
Spectral theory for random Poincaré maps

See the summary (pdf file).

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Deepat Bhak (ICTS Bangalore)
Dynamics of a piston pushed by a single particle gas as a microscopic model for Szilard engine

See the summary (pdf file).

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Peter Embacher (Cardiff University)
Computing Transport Coefficients from Particle Models out of Equilibrium

A new method is proposed to numerically extract the diffusivity from stochastic particle systems which are macroscopically described by a possibly non-linear diffusion equation. The method allows for the system to be out of equilibrium and is motivated by the fact that finite, yet large, particle systems formally obey a stochastic partial differential equation of gradient-flow type satisfying a fluctuation-dissipation relation. The method is showcased over two zero-range-processes, a symmetric simple-exclusion-process and a Kawasaki-type dynamic model.

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Grégoire Ferré (Ecole des Ponts)
Discretization of Feynman-Kac semi-groups

We study the discretization of continuous Feynman-Kac semi-groups. These semi-groups appear for example in large deviation theory, and can be used as a probabilistic representation of Schrödinger ground states. In particular, we focus on their long time behavior and the comparison between the continuous process and its time discretization. We show that, using a Talay-Tubaro expansion of a non-Markovian dynamics, it is possible to obtain error estimates on the invariant measure depending on the time step. We use this procedure to construct second order schemes that provide a better numerical accuracy.

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Nikolas Nüsken (Imperial College London)
Optimal perturbations of Langevin dynamics to sample from probability distributions

Computing expectations with respect to high-dimensional probability distributions is a recurring task both in statistical methodology and molecular dynamics simulations. A powerful and general approach is to consider long-time averages of a Markov chain that is ergodic with respect to a given target measure. Finding appropriate Markovian dynamics that are optimal in terms of convergence characteristics (spectral gap and asymptotic variance) therefore represents an interesting and challenging inverse problem. The poster shows recent results on optimal perturbations of overdamped and underdamped Langevin dynamics.

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Priyanka Priyanka (ICTS Bangalore)

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Julien Roussel (Ecole des Ponts)
Variance reduction for non-equilibrium steady states

Transport properties in materials, such as the thermal conductivity in atom chains, can be studied by using the linear response of the system to an external perturbation. To speed up the empirical means estimated on the simulated trajectories, standard variance reduction techniques cannot be used. Indeed the invariant measure of the non-equilibrium system is unknown, so straightforward stratification or importance sampling techniques are impossible. We propose here a control variate technique and present numerical results in two cases: a one-dimensional system and an atom chain.