Material Theories

Abstract

Physical Sciences and, in particular, Mechanics, have always played an important role as a source of inspiration for Mathematics. They have suggested fundamental problems, and stimulated the development of new techniques and tools. Now it is a particularly exciting time for the interaction of Mathematics and Mechanics: experimental developments in Mechanics and Biophysics at nano scales are posing challenging questions and giving new opportunities to Mathematics. This became very clear at this meeting. A broad spectrum of problems from such diverse fields of applications as biology and biophysics, mechanics of nanostructures, and crystal plasticity was presented. From theoretical physics, recent concepts and paradigms such as self-organized criticality, and non equilibrium statistical mechanics as applied to living systems were discussed. Stochastic processes, calculus of variations, and pde's, up to the theory of Boltzmann equation are the mathematical foundations of the recent results presented at the workshop. A new topic of attention with respect to the glorious tradition of this conference series was the attempt to establish the foundations of engineering theories at the mesoscopic scales from ab-initio calculations (quantum mechanics). An important aspect of the meeting was also the contribution from experimentalists, from wetting and contact angle hysteresis phenomena, to intermittency in plasticity, to electronic transport in semiconductors. The success of the workshop was mostly due to the strong interaction among participants, bridging different fields of expertise, particularly in the discussion on classical fields such as dislocation mechanics, plasticity, kinetic theory and even buckling phenomena in structural mechanics. We have witnessed that several participants were coming out of the meeting with new ideas and new research projects to pursue. Many expressed their appreciation for the open-minded spirit with which problems were presented, and for the constructive spirit of the discussions. The atmosphere at the Institute certainly contributed in a decisive way to the success of the Workshop.