There is currently considerable mathematical interest and very real potential for applications in using geometry in the design, identification and control of technological processes. Geometry plays the role of a design variable in the shape optimization of mechanical parts. It also appears as a control variable in optimal swimming, shape control of aircraft wings or stabilization of membranes and plates by periodic variations of the boundary. As it is used as a design or control variable, it often undergoes "mutations" as in the microstructures of materials, crystal growth, image processing or the texture of objects which involve relaxations of classical geometry and geometrical entities. In other areas, such as free and moving boundary problems, the understanding of the underlying phenomena is very much related to the geometric properties of the fronts and the nature of the nonlinearities involved.

This book brings together tools that have been developed in a priori distant areas of mathematics, mechanics and physics. It provides coverage of selected contemporary problems in the areas of optimal design, mathematical models in material sciences, hysteresis, superconductivity, phase transition, crystal growth, moving boundary problems, thin shells and some of the associated numerical issues.

Titles in this series are co-published with the Centre de Recherches Mathématiques.

Readership

Graduate students, researchers and applied mathematicians working in partial differential equations.

Table of Contents

• K. Coughlin -- The transition to turbulence via turbulent bursts
• M. C. Delfour -- Intrinsic differential geometric methods in the asymptotic analysis of linear thin shells
• M. C. Delfour and J.-P. Zolésio -- Shape analysis via distance functions: Local theory
• I. Müller -- Six lectures on shape memory
• J. Rubinstein -- Six lectures on superconductivity
• H. M. Soner -- Front propagation
• A. Visintin -- Six talks on hysteresis
• M. J. Ward -- Dynamic metastability and singular perturbations
• J.-J. Xu -- Dendrites, fingers, interfaces and free boundaries