Shock Induced Transitions and Phase Structures in General Media

1. Front Matter

   Pages i-xv

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2. Nucleation, Kinetics and Admissibility Criteria for Propagating Phase Boundaries

   • Rohan Abeyaratne, James K. Knowles

   Pages 1-33

3. On a Combustion-Like Model for Plastic Strain Localization

   • Timothy J. Burns

   Pages 35-44

4. Shear Waves and Phase Transformations

   • Rodney J. Clifton

   Pages 45-60

5. The Riemann Problem for Systems of Conservation Laws of Mixed Type

   • Haitao Fan, Marshall Slemrod

   Pages 61-91

6. On the Evolutionary Condition for Stationary Plane Waves in Inert and Reactive Substances

   • G. Richard Fowles

   Pages 93-110

7. Dynamic Effects in Gradient Theory for Fluid Mixtures

   • Henri Gouin

   Pages 111-121

8. Continuum Limits of Discrete Gases II

   • J. M. Greenberg, J. Hack

   Pages 123-145

9. Nonequilibrium Molecular Dynamics

   • William G. Hoover

   Pages 147-157

10. Nonlinear Stability and Instability of Overcompressive Shock Waves

    • Tai-Ping Liu

    Pages 159-167

11. The Dissipation Topography Associated with Solutions to a Riemann Problem Involving Elastic Materials Undergoing Phase Transitions

    • Thomas J. Pence

    Pages 169-183

12. Kinks versus Shocks

    • L. Truskinovsky

    Pages 185-229

13. Shear Strain Localization in Plastic Deformations

    • Athanasios E. Tzavaras

    Pages 231-250

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.

• Phase Transition
• Phase Transitions
• dynamics
• evolution
• mathematics
• mechanics
• modeling
• transitions

• Numerical Mathematics Division # 1534, Sandia National Labs, Albuquerque, USA

  J. E. Dunn

• Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, USA

  Roger Fosdick

• Department of Mathematics, University of Wisconsin, Madison, USA

  Marshall Slemrod

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