Atomistic simulation of materials

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

He addresses the underlying theoretical concepts in order to build a solid 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 boundary conditions; appreciate the challenges of pseudo-random number generation; know how to interpret statistical physics data for simple static observables or structural properties from simulations, including the assessment of statistical errors; be aware of the difficulties of equilibration, correlations, etc.; know how to implement all of 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) in imperative programming

Continuous Integral Control

Introduction to the atomistic approach and interaction modeling; Overview of Molecular Dynamics and Monte Carlo methods; Fundamentals of the Molecular Dynamics method; Integration algorithms and criteria for evaluating them; Verification of implementation through energy conservation; Managing periodic boundary conditions; Adaptation of pair potentials: truncation, shifting, and associated corrections; Use of periodic boundary conditions and nearest periodic image convention; Simple static thermodynamic observables (temperature, pressure, chemical potential); Assessment of statistical uncertainties; Analysis of structure in terms of the density-density correlation function g(r) and the static structure factor S(q); Pseudo-random numbers on computers: 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 methods seen in class for simple models (Lennard Jones, hard spheres, Ising models, etc.) by implementing them in a compiled language.