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This IMA Volume in Mathematics and its Applications SHOCK INDUCED TRANSITIONS AND PHASE STRUCTURES IN GENERAL MEDIA is based on the proceedings of a workshop that was an integral part of the 1990-91 IMA program on "Phase Transitions and Free Boundaries." The workshop focused on the thermodynamics and mechanics of dynamic phase transitions that are mainly inertially driven and brought together physicists, metallurgists, mathematicians, engineers, and molecular dynamicists with interests in these problems. Financial support of the National Science Foundation made the meeting pos sible. We are grateful to J .E. Dunn, Roger Fosdick, and Marshall Slemrod for organizing the meeting and editing the proceedings. A vner Friedman Willard Miller, .Jr. PREFACE When a body is subjected to a strong shock the material may suffer severe local structural changes. Rapid solidification, liquification, or vaporization can oc cur, and, moreover, complex structural heterogeneity is often left in the wake of the passing wave. Thus, inertially driven shock waves raise fundamental questions involving experiment, theory, and mathematics which bear on phase stability and metastability, as well as on reaction kinetics and appropriate measures of phase structure.
List of contents
Nucleation, kinetics and admissibility criteria for propagating phase boundaries.- On a combustion-like model for plastic strain localization.- Shear waves and phase transformations.- The Riemann problem for stystems of conservation laws of mixed type.- On the evolutionary condition for stationary plane waves in inert and reactive substances.- Dynamic effects in gradient theory for fluid mixtures.- Continuum limits of discrete gases II.- Nonequilibrium molecular dynamics.- Nonlinear stability and instability of overcompressive shock waves.- The dissipation topography associated with solutions to a Riemann problem involving elastic materials undergoing phase transitions.- Kinks versus shocks.- Shear strain localization in plastic deformations.
