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About this book
About this book
Physical and biological systems driven out of equilibrium may spontaneously evolve to form spatial structures. In some systems molecular constituents may self-assemble to produce complex ordered structures. This book describes how such pattern formation processes occur and how they can be modeled. Experimental observations are used to introduce the diverse systems and phenomena leading to pattern formation. The physical origins of various spatial structures are discussed, and models for their formation are constructed.
In contrast to many treatments, pattern-forming processes in nonequilibrium systems are treated in a coherent fashion. The book shows how near-equilibrium and far-from-equilibrium modeling concepts are often combined to describe physical systems. This inter-disciplinary book can form the basis of graduate courses in pattern formation and self-assembly. It is a useful reference for graduate students and researchers in a number of disciplines, including condensed matter science, nonequilibrium statistical mechanics, nonlinear dynamics, chemical biophysics, materials science, and engineering.
Preface; 1. Self-organized and self-assembled structures; 2. Order parameter, free energy and phase transitions; 3. Free energy functional; 4. Phase separation kinetics; 5. Langevin model for nonconserved order parameter systems; 6. Langevin model for conserved order parameter systems; 7. Interface dynamics at late times; 8. Domain growth and structure factor for model B; 9. Order parameter correlation function; 10. Vector order parameter and topological defects; 11. Liquid crystals; 12. Lifshitz-Slyozov-Wagner theory; 13. Systems with long-range repulsive interactions; 14. Kinetics of systems with competing interactions; 15. Competing interactions and defect dynamics; 16. Diffusively-rough interfaces; 17. Morphological instability in solid films; 18. Propagating chemical fronts; 19. Transverse front instabilities; 20. Cubic autocatalytic fronts; 21. Competing interactions and front repulsion; 22. Labyrinthine patterns in chemical systems; 23. Turing patterns; 24. Excitable media; 25. Oscillatory media and complex Ginzburg-Landau equation; 26. Spiral waves and defect turbulence; 27. Complex-oscillatory media; 28. Resonantly-forced oscillatory media; 29. Nonequilibrium patterns in laser-induced melting; 30. Reaction dynamics and phase segregation; 31. Active materials; References; Index.
Rashmi C. Desai is Professor Emeritus of Physics at the University of Toronto. Raymond Kapral is Professor of Chemistry at the University of Toronto.
342 pages, 60 tones
'I recommend this book. It is a practical no-nonsense cookbook which should be on the bookshelves of graduate students in this area.' Martin Grant, Physics in Canada 'The authors made a significant effort to describe the main principles of pattern formatio in a transparent manner ... The book is generously illustrated and has a useful index ... a useful reference for graduate students and researchers in many fields including nonlinear dynamics, engineering, biophysics [and] statistical mechanics ...' Zentralblatt MATH 'I enthusiastically recommend this book to graduate students and young researchers entering the exciting and truly interdisciplinary field of self-organization and self-assembly in complex systems. The book is very useful, provides an excellent source of reference material, and is clearly a valuable asset and excellent introduction not only for graduate students, but also for professors looking to build a course on pattern formation and self-assembly.' Igor Aranson, Argonne National Laboratory 'This book is a practical collection of topics in pattern formation, worked through step by step. Each topic is given a brief, even breezy discussion; the 31 chapters whip by five or ten pages each. Overall, I recommend this book. It is a practical, no-nonsense cookbook which should be on the bookshelves of graduate students in this area.' Martin Grant, McGill University