### From molecular to Langevin dynamics

Most of the physical mechanisms which control material evolution can be described with kinetic based approaches at the atomic scale: phase transformations, diffusion of vacancies, deformation, dislocation nucleation and propagation, microcavities, microcracks. Classical methods like molecular dynamics are however limited by high frequencies phonons. Currently, the time scale reached by these methods is of the order of several nanoseconds. Different approaches have been investigated to go beyond this limit (Diffusive Molecular Dynamics, ART Monte Carlo, Phase Field Crystal) but neither emerged as being clearly the most appropriated. In that context, we would like to develop a new approach, still at the atomic scale, but based on a Langevin dynamics, which is of first order in time. This is equivalent to remove kinetic energy. The main interest is to keep a discrete description of matter and a continuous description of atomic positions without having to follow fast oscillations caused by phonons. Accessible time scales should be therefore several orders of magnitude larger than those reached by classical methods. A noise term must be however introduced in the kinetics, and has to be controlled to guaranty the convergence towards to the thermodynamical equilibrium. First results tend to show that this method is promising to study materials subjected to different thermal and mechanical loadings.

The main objective of the present work is to validate the conditions in which the Langevin dynamics correctly reproduces kinetics at the atomic scale. Using molecular dynamics codes, the first step will be to identify concentration and temperature regimes where the time scales between atomic vibrations and thermally activated processes are separated. Then, a numerical method which proceeds to the change of scale will be developed to derive the correct Langevin equations.

**Job:** Internship (4-6 months)

**Academic level : **Master degree

**Location:** LEM, Châtillon

**Expertise:** **:** Solid state physics, Materials Science. Interest in theoretical physics and numerical simulations

**Contacts: **Mathieu Fèvre, Alphonse Finel