Conservation, dissemination and propagation CPES S4

This course discusses the theoretical tools for describing distributed and conserved quantities, such as a density, an energy or a charge density.

The first introductory chapter presents the general conservation equation, and the vector analysis tools necessary to understand it, as well as the different fields where this equation comes into play (practically all physics but also chemistry, economics, etc.).

The following chapters are mainly devoted to the case of a dimension of space and a dimension of time (1+1 D). In Chapter 2, we discuss convective transport, and we present the method of characteristics to solve the corresponding first-order quasilinear partial differential equation. Diffusive transport is then studied in Chapter 3, with the heat equation and the Fourier solution method. Finally, chapter 4 devoted to reaction-diffusion equations considers the case of convective and diffusive transport with the Smoluchowsky equation, and the derivation of the famous Einstein equation for diffusion.

The course is accompanied by theoretical and numerical tutorials, for example on road traffic and queue modelling.

Physics courses in the first year of CPES and the first semester of the second year of CPES