Continuous and discrete modeling

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Goal
Scaling devices down to the nanoscale allows generating new physical properties and functionalities.  Modeling the physics at this intermediate scale between atoms and macroscopic world is therefore a prerequisite as it strongly deviates from that of bulk material: size, shape, composition and environment are as many parameters which have to be controlled in order to taylor their properties. The aim of the course is therefore to introduce concepts, methods and tools required to simulate the physical properties of systems from the nanoscopic to the macroscopic scale, and to describe their coupling to the environment.

Content
The course will address three main subjects in exercice classes (about 10h):

  • Finite elements methods for partial derivative equations applied to the modeling of continuous media. The main concepts will be illustrated by examples of numerical simulations with Comsol sofware.
  • Monte-Carlo approaches and simulations
  • Molecular dynamics modeling of microscopic systems
Students will then performed a numerical project on one of these three topics.

Pré-requisites
A first course in physics of continuous media, and in statistical physics.

Published on April 11, 2019
Updated on September 2, 2021