Pierre-Louis Lions

Claude Le Bris

Isabelle Catto

The thermodynamic limit is a mathematical technique which allows us to consider crystals (or other macroscopic objects) as infinitely sized periodically arranged molecules. This means that we can derive models in solid state physics from models in quantum chemistry. Based on this technique,the book presents established as well as new mathematical results for a large class of models in quantum chemistry.

Thomas-Fermi Type Models

The Mathematical Theory of Thermodynamic Limits

Jean-Frédéric Gerbeau

Tony Lelièvre

Aimed at research mathematicians, engineers and physicists, as well as those in industry, the approach of this text is highly mathematical and based on solid numerical analysis. It focuses on mathematical and numerical techniques for the simulation of magnetohydrodynamic phenomena, with an emphasis on industrial applications.

Mathematical Methods for the Magnetohydrodynamics of Liquid Metals

Xavier Blanc

The book provides a pedagogic and comprehensive introduction to homogenization theory with a special focus on problems set for non-periodic media. The presentation encompasses both deterministic and probabilistic settings. It also mixes the most abstract aspects with some more practical aspects regarding the numerical approaches necessary to simulate such multiscale problems. Based on lecture courses of the authors, the book is suitable for graduate students of mathematics and engineering.

An introduction

Homogenization Theory for Multiscale Problems

Aiming to provide the reader with a general overview of the mathematical and numerical techniques used for the simulation of matter at the microscopic scale, this book lays the emphasis on the numerics, but modelling aspects are also addressed. The contributors come from different scientific communities: physics, theoretical chemistry, mathematical analysis, stochastic analysis, numerical analysis, and the text should be suitable for graduate students in mathematics, sciences and engineering and technology.

Claude Le Bris

Books

Your next favorite book is out there