Atomistic simulation of materials

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

It covers the underlying theoretical concepts, 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 involved in producing pseudo-random numbers; know how to interpret statistical physics-type data for simple static observables or structural properties derived from simulations, including appreciation of statistical errors; become aware of the difficulties of balancing, correlations, etc.; know how to implement all these methods using a compiled language (C,C++ or Fortran).to be able to implement all these methods using 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) for 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 for evaluating them; Verification of an implementation through conservation of energy; Managing periodic conditions at the edges; Adapting pair potentials : truncation, offset and associated corrections; Use of periodic edge conditions and nearest periodic image convention; Simple static thermodynamic observables (temperature, pressure, chemical potential); Assessment of statistical uncertainties; Structure analysis in terms of density-density correlation function g(r) and static structure factor S(q); Pseudo-random numbers on 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.