Atomistic simulation of materials

This course lays the foundations for using 'atomistic' simulation tools, i.e. based on microscopic interactions between constituents. Mainly, it lays the foundations for the so-called 'Molecular Dynamics' and 'Monte Carlo' simulations.

It addresses the underlying theoretical notions, in order to build a good understanding of the methods, as well as the practical implementation of the corresponding codes.

The critical and reasoned use of data is also discussed.

Understand the classical Molecular Dynamics approach and know how to use it; understand the Monte Carlo approach and know how to use it; know how to implement these approaches for interacting particle systems, with periodic conditions at the edges; appreciate the issues of generating pseudo-random numbers; know how to interpret statistical physics type data for simple static observables or structural properties from simulations, including the appreciation of statistical errors; be aware of the difficulties of equilibration, correlations, etc.; know how to implement all these methods using a compiled language (C, C++ or Fortran).To be aware of the difficulties of balancing, correlations, etc.; to know how to implement all these methods with the help of a compiled language (C, C++ or Fortran).

knowledge of a programming language; a course in Statistical Physics

Recommended Prerequisites:

a compiled programming language (C, C++ or Fortran) in imperative programming

Integral Continuous Control

Awareness of the atomistic approach and interaction modeling; Overview of Molecular Dynamics and Monte Carlo methods; Foundations of the Molecular Dynamics method; Integration algorithms and criteria to evaluate them; Verification of an implementation by conservation of energy; Handling periodic conditions at the edges; Adaptation of pair potentials: truncation, offset and associated corrections; Using periodic conditions at edges and the nearest periodic image convention; Simple static thermodynamic observables (temperature, pressure, chemical potential); Appreciation of statistical uncertainties; Structure analysis in terms of the density-density correlation function g(r) and the static structure factor S(q); Pseudo-random numbers on the computer : Generators, subtleties, non-uniform distributions; Theory supporting the Monte Carlo method: Markov chains and detailed balance; Metropolis algorithm; Thermodynamic ensembles in Molecular Dynamics and Monte Carlo: thermostats and barostats.

Practical implementation of the methods seen in class, for simple models (Lennard Jones, hard spheres, Ising models, etc.) by implementing them in a compiled language.