Over the last thirty years, the study of liquids containing polymers, surfactants, or colloidal particles has developed from a loose assembly of facts into a coherent discipline with substantial predictive power. These liquids expand our conception of what condensed matter can do. Such structured-fluid phenomena dominate the physical environment within living cells. This book teaches how to think of these fluids from a unified point of view, showing the far-reaching effects of thermal fluctuations in producing forces and motions. Keeping mathematics to a minimum, the book seeks the simplest explanations that account for the distinctive scaling properties of these fluids. An example is the growth of viscosity of a polymer solution as the cube of the molecular weight of the constituent polymers. Another is the hydrodynamic radius of a colloidal aggregate, which remains comparable to its geometrical radius even though the density of particles in the aggregate becomes arbitrarily small. The book aims for a simplicity, unity and depth not found in previous treatments. The text is supplemented by numerous figures, tables and problems to aid the student.
This book presents the (to date) most general approach to combinatorial constructions of topological quantum field theories (TQFTs) in three dimensions. The authors describe extended TQFTs as double functors between two naturally defined double categories: one of topological nature, made of 3-manifolds with corners, the other of algebraic nature, made of linear categories, functors, vector spaces and maps. Atiyah's conventional notion of TQFTs as well as the notion of modular functor from axiomatic conformal field theory are unified in this concept. A large class of such extended modular catergory is constructed, assigning a double functor to every abelian modular category, which does not have to be semisimple.
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