Stochastic processes in polymeric fluids. Tools and examples for developing simulation algorithms.

*(English)*Zbl 0995.60098
Berlin: Springer. xxiv, 362 p. (1996).

The book begins with a short introduction to the kinetic theory of polymers, the main body consists of two parts, i.e. Part I called “Stochastic processes” (Chapters 2 and 3) and Part II called “Polymer dynamics” (Chapters 4, 5, and 6). Part I starts with basic concepts of stochastics, covering events and probabilities, random variables and some theory of stochastic processes. Then an introduction to stochastic calculus is presented, first discussing a naive approach to stochastic differential equations, then providing the theory of stochastic integration and stochastic differential equations. A section on numerical integration schemes concludes this part. The necessary brevity for an introduction is achieved by sketching and explaining some of the longer proofs rather than giving them in detail. The presentation is well-balanced between providing background material for applied scientist and maintaining mathematical rigour. In Part II several models for polymer dynamics are discussed in detail. The topics include bead-spring-models for dilute solutions, such as the Rouse or the Zimm model, models with constraints, rigid rod molecules, and reptation models of concentrated solutions and melts, such as the Doi-Edwards and the Curtiss-Bird model. The models are derived, their properties and the possibilities of the application of computer simulations are discussed.

The book contains over 250 references, and more than 100 solved problems. For the mathematical material presented, some background knowledge of basic linear algebra and mathematical analysis, and possibly numerical mathematics, would be useful. Polymer scientists, physicists and engineers will certainly gain from this book. The first part of the book may serve as a concise, yet rigourous introduction to stochastic calculus for mathematicians as well. It can very well be used as a basis for a course on an intermediate level. In addition, it contains many problems which can be used as examples of the application of stochastic numerical methods.

The book contains over 250 references, and more than 100 solved problems. For the mathematical material presented, some background knowledge of basic linear algebra and mathematical analysis, and possibly numerical mathematics, would be useful. Polymer scientists, physicists and engineers will certainly gain from this book. The first part of the book may serve as a concise, yet rigourous introduction to stochastic calculus for mathematicians as well. It can very well be used as a basis for a course on an intermediate level. In addition, it contains many problems which can be used as examples of the application of stochastic numerical methods.

Reviewer: Evelyn Buckwar (Berlin)