The physics of soft matter - materials such as elastomers, gels, foams and liquid crystals - is an area of intense interest and contemporary study. Moreover, soft matter plays a role in a wide variety of important processes and application. For example, gel swelling and dynamics are an essential part of many biological and individual processes, such as motility mechanisms in bacteria and the transport and absorption of drugs. Ferroelectrics, liquid crystals, and elastomers are being used to design ever faster switching devices. Experimental studies, such as scattering, optical and electron microscopy, have provided a great deal of detailed information on structures. But the integration of mathematical modeling and analysis with experimental approaches promises to greatly increase our understanding of structure-property relationships and constitutive equations. The workshop on Modeling of Soft Matter has taken such an integrated approach. It brought together researchers in applied and computational mathematical fields such as differential equations, dynamical systems, analysis, and fluid and solid mechanics, and scientists and engineers from a variety of disciplines relevant to soft matter physics. An important outcome of the workshop has been to identify beautiful and novel scientific problems arising in soft matter that are in need of mathematical modeling and appear amenable to it and so to set the stage for further research. This volume presents a collection of papers representing the key aspects of the topics discussed at depth in the course of the workshop.

This IMA Volume in Mathematics and its Applications MODELING OF SOFT MATTER contains papers presented at a very successful workshop with the same ti tle. The event, which was held on September 27-October 1, 2004, was an integral part of the 2004-2005 IMA Thematic Year on "Mathematics of Ma terials and Macromolecules: Multiple Scales, Disorder, and Singularities. " We would like to thank Maria-Carme T. Calderer (School of Mathematics, University of Minnesota) and Eugene M. Terentjev (Cavendish Laboratory, University of Cambridge) for their superb role as workshop organizers and editors of the proceedings. We take this opportunity to thank the National Science Foundation for its support of the IMA. Series Editors Douglas N. Arnold, Director of the IMA Arnd Scheel, Deputy Director of the IMA PREFACE The physics of soft matter in particular, focusing on such materials as complex fluids, liquid crystals, elastomers, soft ferroelectrics, foams, gels and particulate systems is an area of intense interest and contemporary study. Soft matter plays a role in a wide variety of important processes and application, as well as in living systems. For example, gel swelling is an essential part of many biological processes such as motility mecha nisms in bacteria and the transport and absorption of drugs. Ferroelectrics, liquid crystals, and elastomers are being used to design ever faster switch ing devices. Experiments of the last decade have provided a great deal of detailed information on structures and properties of soft matter.

Soft condensed matter is a relatively new topic. Condensed matter has typically referred to more traditional liquids, which have a long history of study, or to solids, which have focused more commonly on hard materials, driven in large measure by the importance of structural materials or the metals and semiconductors which drove the rapid evolution of microelectronics. It is only relatively recently, over the past 20 to 30 years, that soft condensed matter has matured into its own identifiable field. However, the field is an amalgam of many subfields, and many of these have themselves much longer histories. This handbook serves as an overview of many of these topics. Because of the great breadth, it is impossible to include them all; nevertheless, the key subjects of soft condensed matter are represented here. Together, they form both an introduction and an overview of the field. Each topic, and its representing Chapter, could have been a full size book - in fact, there are a number of such books on many of the topics covered in the handbook. Our aim here was to give a current snapshot of the field, identify the key principles at play and the most prominent (and promising) ways of its further development, provide essential references for anyone to follow the subject, but not necessarily go into a lot of detail on each topic.

Soft condensed matter is a relatively new topic. Condensed matter has typically referred to more traditional liquids, which have a long history of study, or to solids, which have focused more commonly on hard materials, driven in large measure by the importance of structural materials or the metals and semiconductors which drove the rapid evolution of microelectronics. It is only relatively recently, over the past 20 to 30 years, that soft condensed matter has matured into its own identifiable field. However, the field is an amalgam of many subfields, and many of these have themselves much longer histories. This handbook serves as an overview of many of these topics. Because of the great breadth, it is impossible to include them all; nevertheless, the key subjects of soft condensed matter are represented here. Together, they form both an introduction and an overview of the field. Each topic, and its representing Chapter, could have been a full size book - in fact, there are a number of such books on many of the topics covered in the handbook. Our aim here was to give a current snapshot of the field, identify the key principles at play and the most prominent (and promising) ways of its further development, provide essential references for anyone to follow the subject, but not necessarily go into a lot of detail on each topic.