This IMA Volume in Mathematics and its Applications AMORPHOUS POLYMERS AND NON-NEWTONIAN FLUIDS is in part the proceedings of a workshop which was an integral part of the 1984-85 IMA program on CONTINUUM PHYSICS AND PARTIAL DIFFERENTIAL EQUATIONS We are grateful to the Scientific Committee: Haim Brezis Constantine Dafermos Jerry Ericksen David Kinderlehrer for planning and implementing an exciting and stimulating year-long program. We espe cially thank the Program Organizers, Jerry Ericksen, David Kinderlehrer, Stephen Prager and Matthew Tirrell for organizing a workshop which brought together scientists and mathematicians in a variety of areas for a fruitful exchange of ideas. George R. Sell Hans Weinberger Preface Experiences with amorphous polymers have supplied much of the motivation for developing novel kinds of molecular theory, to try to deal with the more significant features of systems involving very large molecules with many degrees offreedom. Similarly, the observations of many unusual macroscopic phenomena has stimulated efforts to develop linear and nonlinear theories of viscoelasticity to describe them. In either event, we are confronted not with a well-established, specific set of equations, but with a variety of equations, conforming to a loose pattern and suggested by general kinds of reasoning. One challenge is to devise techniques for finding equations capable of delivering definite and reliable predictions. Related to this is the issue of discovering ways to better grasp the nature of solutions ofthose equations showing some promise.

These two volumes contain chapters written by experts in such areas as bio and food rheology, polymer rheology, flow of suspensions, flow in porous media, electrorheological fluids, etc. Computational as well as analytical mathematical descriptions, involving appropriate constitutive equations deal with complex flow situations of industrial importance. This work is unique in that it brings together state of the art reviews and recent advances in a variety of areas, involving viscoelastic materials, in a desirable and timely manner.

This IMA Volume in Mathematics and its Applications AMORPHOUS POLYMERS AND NON-NEWTONIAN FLUIDS is in part the proceedings of a workshop which was an integral part of the 1984-85 IMA program on CONTINUUM PHYSICS AND PARTIAL DIFFERENTIAL EQUATIONS We are grateful to the Scientific Committee: Haim Brezis Constantine Dafermos Jerry Eri cksen David Kinderlehrer for planning and implementing an exciting and stimulating year-long program. We espe cially thank the Program Organizers, Jerry Ericksen, David Kinderlehrer, Stephen Prager and Matthew Tirrell for organizing a workshop which brought together scientists and mathematicians in a variety of areas for a fruitful exchange of ideas. George R. Sell Hans Weinberger Preface The diversity of experimental phenomena and the range of applications of liquid crystals present timely and challenging questions for experimentalists, mechanists, and mathematicians. The scope of this workshop was to bring together research workers and practitioners in these areas from laboratories, industry, and universities to explore common issues. The contents of this volume vary from descriptions of experimental phenomena, of which our understanding is insufficient, to questions of a mathematical nature and of efficient computation.

Awarded the Literature Prize of the VCI This comprehensive textbook describes the synthesis, characterization and technical and engineering applications of polymers. Polymers are unique molecules and have properties different from any other class of materials. We encounter them in everyday life, not only in the form of the well-known, large-volume plastics such as PE or PP or the many other special polymers, some of which are very specifically modified but also in nature as polymeric biomolecules, such as DNA. Our life, as we know it, would not only be completely different without macromolecules but it would also be biologically impossible. This textbook provides a broad knowledge of the basic concepts of macromolecular chemistry and the unique properties of this class of materials. Environmentally relevant topics, such as biopolymers and microplastic, which should not be missing in a contemporary textbook are also covered. Building on basic knowledge of organic chemistry and thermodynamics, the book presents an easy-to-understand yet in-depth picture of this very dynamic and increasingly important interdisciplinary science that involves elements of chemistry, physics, engineering, and the life sciences. Readers of this work can confirm their understanding of the text at the end of each chapter by working through a selection of exercises. In writing the book, great importance was attached to good readability despite the necessary depth of detail. It is a book that is just as suitable for students of chemistry and related courses as it is for the applied scientist in an industrial environment. The first edition of this work is so far the only textbook on polymer chemistry to be awarded the Literature Prize of the Fund of the German Chemical Industry Association in 2015.

The material included in this book was first presented in a series of lectures de livered at the University of Minnesota in June 1983 in connection with the con ference "Thermodynamics and Phase Transitions". This conference was one of the principal events in the first year of operation of the Institute for Mathematics and its Applications (lMA) at the University of Minnesota. The Institute was founded under the auspices of the National Science Foun dation of the United States and the University of Minnesota and is devoted to strengthening and fostering the relation of mathematics with its various applica tions to problems of the real world. The present volume constitutes an important element in the continuing pub lication program of the Ipstitute. Previous publications in this program have ap peared as lecture notes in the well-known Springer series, and future ones will be part of a new series "IMA Volumes in Applied Mathematics". Preface Until recently it was believed that thermodynamics could be given a rigorous foundation only in certain restricted circumstances, particularly those involving reversible and quasi-static processes. More general situations, commonly arising in continuum theories, have therefore been treated on the assumption that inter nal energy, entropy and absolute temperature are a priori given quantities, or have been dealt with on a more or less ad hoc basis, with emphasis for example on various types of variational formulations and maximization rules.

This volume represents a continuation of the Polymer Science and Technology series edited by Dr. D. M. Brewis and Professor D. Briggs. The theme of the series is the production of a number of stand alone volumes on various areas of polymer science and technology. Each volume contains short articles by a variety of expert contributors outlining a particular topic and these articles are extensively cross referenced. References to related topics included in the volume are indicated by bold text in the articles, the bold text being the title of the relevant article. At the end of each article there is a list of bibliographic references where interested readers can obtain further detailed information on the subject of the article. This volume was produced at the invitation of Derek Brewis who asked me to edit a text which concentrated on the mechanical properties of polymers. There are already many excellent books on the mechanical properties of polymers, and a somewhat lesser number of volumes dealing with methods of carrying out mechanical tests on polymers. Some of these books are listed in Appendix 1. In this volume I have attempted to cover basic mechanical properties and test methods as well as the theory of polymer mechanical deformation and hope that the reader will find the approach useful.

This volume developed from a Workshop on Natural Locomotion in Fluids and on Surfaces: Swimming, Flying, and Sliding which was held at the Institute for Mathematics and its Applications (IMA) at the University of Minnesota, from June 1-5, 2010. The subject matter ranged widely from observational data to theoretical mechanics, and reflected the broad scope of the workshop. In both the prepared presentations and in the informal discussions, the workshop engaged exchanges across disciplines and invited a lively interaction between modelers and observers. The articles in this volume were invited and fully refereed. They provide a representative if necessarily incomplete account of the field of natural locomotion during a period of rapid growth and expansion. The papers presented at the workshop, and the contributions to the present volume, can be roughly divided into those pertaining to swimming on the scale of marine organisms, swimming of microorganisms at low Reynolds numbers, animal flight, and sliding and other related examples of locomotion.