For the purpose of these lectures, a microstructure is any structure on a scale between the
macroscopic scale (on which we usually make observations) and the atomic scale. Such …

Microstructure is a feature of crystals with multiple symmetry-related energy-minimizing
states. Continuum models have been developed explaining microstructure as the mixture of …

The main purpose of this chapter is to give a derivation, which is mathematically precise,
physically natural, and conceptually simple, of the quasilinear system of partial differential …

This book is developed for the study of vectorial problems in the calculus of variations. The
subject is a very active one and almost half of the book consists of new material. This is a …

1. Introduction.............................. 13 2. Internally Twinned Martensite...................... 15 3. The
Free Energy Functional and Minima................. 17 4. Compatibility, Almost Compatibility and …

The purpose of this book is to explain systematically and clearly many of the most important
techniques set forth in recent years for using weak convergence methods to study nonlinear …

Weak convergence is a basic tool of modern nonlinear analysis because it enjoys the same
compactness properties that finite dimensional spaces do: basically, bounded sequences …

Plastically deformed crystals are often observed to develop intricate dislocation patterns
such as the labyrinth, mosaic, fence and carpet structures. In this paper, such dislocation …

Martensitic transformations are diffusionless, solid-to-solid phase transitions, and have been
observed in metals, alloys, ceramics and proteins,. They are characterized by a rapid …

The goal of this book is to present some modern aspects of nonlinear analysis. Some of the
material introduced is classical, some more exotic. We have tried to emphasize simple cases …