In this Course, we shall familiarize with the main computational methods which permit to simulate and analyze the behavior of a wide range of problems involving fluids, solids, soft matter, electromagnetic and quantum systems, as well as the dynamics of (some) biological and social systems. The course consists of three main parts,
Part I : Classical and Quantum Fields on Grids
Part II : Mesoscale Methods
Part III: Statistical Data Analysis and Learning
In Part I, we shall discuss the fundamentals of grid discretization and present concrete applications to a broad variety of problems from classical and quantum physics, such as Advection-Diffusion Reaction transport, Navier-Stokes fluid-dynamics, nonlinear classical and quantum wave propagation. Both regular and complex geometrical grids will be discussed through Finite Differences, Volumes and Elements, respectively.
In Part II we shall discuss mesoscale technique based on the two basic mesoscale descriptions: probability distribution functions, as governed by Boltzmann and Fokker-Planck kinetic equations, and stochastic particle dynamics (Langevin equations). The lattice Boltzmann method will be discussed in great detail, with applications to fluids and soft matter problems.
In addition, we shall provide the opportunity of hands-on on a multi scale codes for X (extreme) simulations at the interface between physics and molecular biology.
Finally, in Part III, we shall present data analysis & learning tools of particular relevance to complex systems with non-gaussian statistics, such as turbulence, fractional transport and extreme events in general. An introduction to Physics-Aware Machine Learning will also be presented.