Analytical and Numerical Approaches to Asymptotic Problems in Analysis

Markedly apart from elementary particle physics, another current has been building up and cont i nuous ly growi ng within contemporary phys i cs for severa 1 decades, and even expanding into many other disciplines, especially chemistry, biology and, quite recently, economics. Several reasons account for this: presumably the most impor tant one lies in the fact that, whatever the specific problem, model or material concerned, the same basic mathematical features are always involved. In this way, a general phenomenology has emerged which, unlike thermodynamics, is no longer depen dent upon the details or specifics: what largely prevails is the nonlinear charac ter of the underlying dynamics. Perhaps we are witnessing the emergence of a "non linear physics"--In a way similar to the birth of "quantum physics" in the twen ties - a physics which deals with the general behaviour of systems, whatever they are or may be. Over the past fifteen years, chemical systems evolving sufficiently far from equilibrium have proved to be particularly well fitted to experimental research on nonlinear behaviour: oscillation, multistability, birhythmicity, chaotic evolution, spatial self-organization and hysteresis are displayed by chemical reactions whose number is growing each year. In this volume are collected the lectures, communica tions and posters (abstracts) presented at an international meeting entitled: "Non-Equilibrium Dynamics in Chemical Systems", held in Bordeaux (France), Septem ber 3 rd-lth, 1984.

Improving our understanding of friction, lubrication, and fatigue, Modeling and Analytical Methods in Tribology presents a fresh approach to tribology that links advances in applied mathematics with fundamental problems in tribology related to contact elasticity, fracture mechanics, and fluid film lubrication. The authors incorporate the classical tenets of tribology while providing new mathematical solutions that address various shortcomings in existing theories. From contact interactions to contact fatigue life, the book connects traditionally separate areas of tribology research to create a coherent modeling methodology that encompasses asymptotic and numerical techniques. The authors often demonstrate the efficacy of the models by comparing predictions to experimental data. In most cases, they derive equations from first principles. They also rigorously prove problem formulations and derive certain solution properties. Solutions to problems are presented using simple analytical formulas, graphs, and tables. In addition, the end-of-chapter exercises highlight points important for comprehending the material and mastering the appropriate skills. Unlocking the secrets that govern the physics of lubricated and dry contacts, this book helps tribologists on their quest to reduce friction, minimize wear, and extend the operating life of mechanical equipment. It provides a real-world industrial perspective so that readers can attain a practical understanding of the material.

This volume contains the lectures and invited seminars pre sented at the NATO Advanced Study Institute on NON-EQUILIBRIUM COOPERATIVE PHENOMENA IN PHYSICS AND RELATED FIELDS that was held at EL ESCORIAL (MADRID), SPAIN, on August 1-11, 1983. Most nonlinear problems in dissipative systems, i . e . , most mathematical models in SYNERGETICS are highly trans disciplinary in practice and the list of lecturers and participants at the ASI reflects this di versi ty both in background and interest. The presentation of the material fell into two main categories: tutopia~ Zectures on some basic ideas and methods, both experimental and theoretical, intended to lay a common base for all participants, and a series of more specific lectures and seminars, serving the purpose of exemplying selected but typical applications in their current state of development. Topics were chosen for their basic interest as well as for their potential for applications (laser, hydrodynamics, liquid crystals, EHD, combustion, thermoelasticity, etc. ). We had more seminars and some of the oral presentations were supported or complemented with 16 mm films and on occasion with experimental demonstrations including a special seminar, a social one on broken symmetries in Art and Music. There is here no record of these non-standard acti vi ties. We had, indeed, quite a heavy load for which I was fully responsible. However, the reader and, above all, the participants at the ASI ought to be aware of the fact that in Spain, with.