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Full Description
Inthecourseofthelast?ftyyears, developmentsinnonsmoothana- sisandnonsmoothmechanicshaveoftenbeencloselylinked. Thepresent book acts as an illustration of this. Its objective is two-fold. It is of course intended to help to di?use the recent results obtained by various renownedspecialists. ButthereisanequaldesiretopayhomagetoJean Jacques Moreau, who is undoubtedly the most emblematic ?gure in the correlated, not to say dual, advances in these two ?elds. Jean Jacques Moreau appears as a rightful heir to the founders of di?erential calculus and mechanics through the depth of his thinking in the ?eld of nonsmooth mechanics and the size of his contribution to the development of nonsmooth analysis. His interest in mechanics has focused on a wide variety of subjects: singularities in ?uid ?ows, the initiation of cavitation, plasticity, and the statics and dynamics of gr- ular media. The 'Ariadne's thread' running throughout is the notion of unilateral constraint. Allied to this is his investment in mathematics in the ?elds of convex analysis, calculus of variations and di?erential m- sures.
When considering these contributions, regardless of their nature, one cannot fail to be struck by their clarity, discerning originality and elegance. Precision and rigor of thinking, clarity and elegance of style are the distinctive features of his work.
Contents
Convex and Nonsmooth Analysis.- Moreau's Proximal Mappings and Convexity in Hamilton-Jacobi Theory.- Three Optimization Problems in Mass Transportation Theory.- Some Geometrical and Algebraic Properties of Various Types of Convex Hulls.- A Note on the Legendre-Fenchel Transform of Convex Composite Functions.- What Is to be a Mean?.- Nonsmooth Mechanics.- Thermoelastic Contact with Frictional Heating.- A Condition for Statical Admissibility in Unilateral Structural Analysis.- Min-Max Duality and Shakedown Theorems in Plasticity.- Friction and Adhesion.- The Clausius-Duhem Inequality, an Interesting and Productive Inequality.- Unilateral Crack Identification.- Penalty Approximation of Painlevé Problem.- Discrete Contact Problems with Friction: A Stress-Based Approach.- Fluid Mechanics.- A Brief History of Drop Formation.- Semiclassical Approach of the "Tetrad Model" of Turbulence.- Multibody Dynamics: Numerical Aspects.- The Geometry Of Newton's Cradle.- Using Nonsmooth Analysis for Numerical Simulation of Contact Mechanics.- Numerical Simulation of a Multibody Gas.- Granular Media and Ballasted Railway Tracks Milieux Granulaires Et Voies Ballastées.- Scaling Behaviour of Velocity Fluctuations in Slow Granular Flows.- Topics in Nonsmooth Science.- Morphological Equations and Sweeping Processes.- Higher Order Moreau's Sweeping Process.- An Existence Result in Non-Smooth Dynamics.- Finite Time Stabilization of Nonlinear Oscillators Subject to dry Friction.- Canonical Duality in Nonsmooth, Constrained Concave Minimization.
