Nose-Hoover dynamics in a shaker.

We introduce a new class of systems based on the Nose-Hoover equations. We show that we can add time-dependent terms without destroying the measure and energy conservation properties of the initial system. These "shakers" are typically pseudoperiodic in time, i.e., depend on a collection of harmonic oscillators. We show by numerical examples that it strengthens the sampling properties of the initial system with respect to the Gibbs measure and helps the computation of averages in the canonical ensemble.

High-order averaging schemes with error bounds for thermodynamical properties calculations by molecular dynamics simulations.

We introduce high-order formulas for the computation of statistical averages based on the long-time simulation of molecular dynamics trajectories. In some cases, this allows us to significantly improve the convergence rate of time averages toward ensemble averages. We provide some numerical examples that show the efficiency of our scheme. When trajectories are approximated using symplectic integration schemes (such as velocity Verlet), we give some error bounds that allow one to fix the parameters of the computation in order to reach a given desired accuracy in the most efficient manner.