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The purpose of the present article is to compare different phase-space sampling methods, such as purely stochastic methods (Rejection method, Metropolized independence sampler, Importance Sampling), stochastically perturbed Molecular Dynamics methods (Hybrid Monte Carlo, Langevin Dynamics, Biased Random Walk), and purely deterministic methods (Nosé-Hoover… (More)

We consider numerical methods for thermodynamic sampling, i.e., computing sequences of points distributed according to the Gibbs–Boltzmann distribution, using Langevin dynamics and overdamped Langevin dynamics (Brownian dynamics). A wide variety of numerical methods for Langevin dynamics may be constructed based on splitting the stochastic differential… (More)

- Tony Lelièvre, Mathias Rousset, Gabriel Stoltz
- The Journal of chemical physics
- 2007

We propose a formulation of an adaptive computation of free energy differences, in the adaptive biasing force or nonequilibrium metadynamics spirit, using conditional distributions of samples of configurations which evolve in time. This allows us to present a truly unifying framework for these methods, and to prove convergence results for certain classes of… (More)

- Alessandra Iacobucci, Frédéric Legoll, Stefano Olla, Gabriel Stoltz
- Physical review. E, Statistical, nonlinear, and…
- 2011

We consider chains of rotors subjected to both thermal and mechanical forcings in a nonequilibrium steady state. Unusual nonlinear profiles of temperature and velocities are observed in the system. In particular, the temperature is maximal in the center, which is an indication of the nonlocal behavior of the system. Despite this uncommon behavior, local… (More)

- Tony Lelièvre, Mathias Rousset, Gabriel Stoltz
- J. Comput. Physics
- 2007

- Tony Lelièvre, Mathias Rousset, Gabriel Stoltz
- Math. Comput.
- 2012

In this paper, we consider Langevin processes with mechanical constraints. The latter are a fundamental tool in molecular dynamics simulation for sampling purposes and for the computation of free energy differences. The results of this paper can be divided into three parts. (i) We propose a simple discretization of the constrained Langevin process based on… (More)

We present some applications of an Interacting Particle System (IPS) methodology to the field of Molecular Dynamics. This IPS method allows several simulations of a switched random process to keep closer to equilibrium at each time, thanks to a selection mechanism based on the relative virtual work induced on the system. It is therefore an efficient… (More)

- Anthony Scemama, Tony Lelièvre, Gabriel Stoltz, Eric Cancès, Michel Caffarel
- The Journal of chemical physics
- 2006

We propose a new algorithm for sampling the N-body density mid R:Psi(R)mid R:(2)R(3N)mid R:Psimid R:(2) in the variational Monte Carlo framework. This algorithm is based upon a modified Ricci-Ciccotti discretization of the Langevin dynamics in the phase space (R,P) improved by a Metropolis-Hastings accept/reject step. We show through some representative… (More)

- Bradley M Dickson, Frédéric Legoll, Tony Lelièvre, Gabriel Stoltz, Paul Fleurat-Lessard
- The journal of physical chemistry. B
- 2010

We develop an efficient sampling and free energy calculation technique within the adaptive biasing potential (ABP) framework. By mollifying the density of states we obtain an approximate free energy and an adaptive bias potential that is computed directly from the population along the coordinates of the free energy. Because of the mollifier, the bias… (More)

- Rémi Joubaud, Gabriel Stoltz
- Multiscale Modeling & Simulation
- 2012