EPSRC Symposium Capstone Conference

Ruslan Davidchack (Leicester) Discretisation errors in MD simulations with deterministic and stochastic thermostats
We investigate the influence of numerical discretisation errors on computed averages in molecular dynamics simulations with deterministic and stochastic thermostats, and discuss possible approaches to estimating such errors and taking them into account when computing the averages. In most cases this enables the use of larger integration time steps than those typically considered acceptable by the MD practitioners.

Frédéric Legoll (ENPC, Paris)Parareal algorithms and long-time integration of Hamiltonian systems
Time integration schemes for ODEs are naturally sequential in time. The parareal algorithm, proposed in 2001, was one of the first efficient integration schemes that include some parallel computations. Since then, it has been successfully used on many different equations.
Our aim is to get a better understanding of the long-time properties of such an approach, that are of paramount importance when the scheme is used to integrate Hamiltonian systems. We will present several modifications of the original scheme, aiming at improving its long-time behaviour.

Nawaf Bou-Rabee (New York) Metropolized integrators for SDEs
Metropolis adjusted integrators for stochastic differential equations (SDE) are presented which (i) are ergodic with respect to the exact equilibrium distribution of the SDE and (ii) approximate pathwise the solutions of the SDE on finite time intervals. Both these properties are demonstrated and precise strong error estimates are derived. It is also shown that the Metropolized integrator retains these properties even in situations where the drift in the SDE is nonglobally Lipschitz, and vanilla explicit integrators for SDEs typically become unstable and fail to be ergodic. This talk is based on a joint paper with Eric Vanden-Eijnden.

Emad Noorizadeh (Edinburgh) The concept of heat bath in molecular dynamics
A heat bath in molecular dynamics is a perturbation of the Hamiltonian dynamics which enables correct computation of ensemble averages. On the other hand computation of dynamical averages such as autocorrelation functions requires the molecular dynamics trajectory to be close to a microcanonical dynamics. This suggests that, ideally, we would like to have a small growth of the perturbation together with a fast rate of convergence to the Boltzmann-Gibbs measure. In this talk we try to quantify the rate of convergence to equilibrium and the growth of the perturbation for Langevin dynamics and the Hoover-Langevin method (a highly degenerate diffusion). We illustrate our results using numerical experiments. This is joint work with Ben Leimkuhler and Oliver Penrose.

Further details will be added as they become available