Synopses & Reviews
This volume contains a selection of the invited papers presented at a LMS Durham Symposium on modern developments in non-classical continuum mechanics. A major aim was to bring together workers in both the abstract and practical aspects of the subject in order to achieve enhanced appreciation of each others' approach and hence of the mathematical techniques and physical intuition essential for successful research in this field. As a result, the present collection consists of a series of concise articles which are introductions to, and succinct accounts of, current activity in many branches of non-classical continuum mechanics. Research workers in applied mathematics, physics, theoretical mechanics, and structural and aeronautical engineering will find much of interest in this collection.
Table of Contents
Part I. Principal Lectures: 1. Pulse reflection by a random medium R. Burridge, G. C. Papanicolaou, P. Sheng and B. White; 2. Shape memory alloys - phenomenology and simulation I. Muller; 3. Relativistic extended thermodynamics I. Muller; 4. Spectra of singularly perturbed operators O. A. Oleinik; 5. Conservation laws in continuum mechanics P. J. Oliver; 6. On geometric and modeling perturbations in partial differential equations L. E. Payne; 7. The appearance of oscillations in optimization problems L. Tartar; Part II. Single Invited Lectures: 8. Some mathematical problems arising from the oil service industry C. Atkinson, P. S. Hammond, M. Sheppard and I. J. Sobey; 9. Randomly diluted inhomogeneous elastic networks near the percolation threshold D. J. Bergman; 10. Adaptive anisotropy: an example in living bone S. C. Cowin; 11. Stability of elastic crystals I. Fonseca; 12. Optimal bounds for conduction in two-dimensional, two-phase, anisotropic media G. A. Francfort and F. Murat; 13. Rapid flows of granular materials J. T. Jenkins; 14. The constrained least gradient problem R. Kohn and G. Strang; 15. The fusion of physical and continuum-mechanical concepts in the formulation of constitutive relations for elastic-plastic materials E. H. Lee and A. Agah-Tehrani; 16. Singularities in elliptic non-smooth problems. Applications to elasticity D. Leguillon and E. Sanchez-Palencia; 17. Solitons in elastic solids exhibiting phase transitions G. A. Maugin; 18. On the dynamics of structural phase transitions in shape memory alloy M. Niezgodka and J. Sprekels; 19. On the homogenization of some free boundary problems J. R. Rodrigues; 20. The point interaction approximation, viscous flow through porous media, and related topics J. Rubinstein; 21. The vanishing viscosity-capillarity approach to the Riemann problem for a Van Der Waals fluid M. Slemrod.