1. Modeling and simulation, different scales

The terms modeling and simulation are often used interchangeably. However, these terms cover very different realities, even if they are linked in some way. The aim of both is to provide a mathematical representation of physical phenomena or behavioral laws.

Modeling consists in putting a physical phenomenon or a set of physical phenomena into simple analytical form (as far as possible), using physical laws. Since the mathematical representation is derived from a rigorous physical theory, it is referred to as a model, because in this case it has a real physical meaning (e.g. Newton's laws of gravitation, Maxwell's equations of electromagnetism, Navier Stokes' equations of fluid mechanics, Schrödinger's equation for the electronic structure of matter, etc.).

When the mathematical representation is derived from observation or experiment, the...