Effective dynamics for slow (and not so slow) reaction coordinates
Frederic Legoll (ENPC)
From Atomistics to Reality: Spanning Scales in Simulations and Experiments Symposium A
Mon 4:20 - 5:40
CIT 165
The question of coarse-graining is ubiquitous in materials science. In this work, we are interested in deriving effective properties for the dynamics of a coarse-grained variable $\xi(X)$, where $X$ describes the configuration of the system, and $\xi$ is a smooth scalar function. Typically, $X$ is a high-dimensional variable (representing the positions of all the atoms in the system), whereas $\xi(X)$ is a coarse-grained information, that evolves more slowly. We assume that the configuration $X_t$ of the complete system evolves according to the Langevin stochastic differential equation, and we propose an effective closed dynamics that approximates the evolution of $\xi(X_t)$. The relation between that dynamics and the free energy is explored. Numerical simulations illustrate the accuracy of the proposed dynamics. We next turn to the case when the time scale separation between slow and fast components is not large enough so that the approximation of infinite time scale separation, used above, is not accurate enough. In that case, we show that we can still use the effective dynamics obtained above as a predictor to compute more efficiently the true dynamics. Based on joint works with T. Lelievre and G. Samaey.