Pattern Formation and Dynamics in Nonequilibrium Systems

Many exciting frontiers of science and engineering require understanding the spatiotemporal properties of sustained nonequilibrium systems such as fluids, plasmas, reacting and diffusing chemicals, crystals solidifying from a melt, heart muscle, and networks of excitable neurons in brains. This introductory textbook for graduate students in biology, chemistry, engineering, mathematics, and physics provides a systematic account of the basic science common to these diverse areas. This book provides a careful pedagogical motivation of key concepts, discusses why diverse nonequilibrium systems often show similar patterns and dynamics, and gives a balanced discussion of the role of experiments, simulation, and analytics. It contains numerous worked examples and over 150 exercises. This book will also interest scientists who want to learn about the experiments, simulations, and theory that explain how complex patterns form in sustained nonequilibrium systems.

Preface; 1. Introduction; 2. Linear instability: basics; 3. Linear instability: application to reacting and diffusing chemicals; 4. Nonlinear states; 5. Models; 6. One-dimensional amplitude equation; 7. Amplitude equations for two-dimensional patterns; 8. Defects and fronts; 9. Patterns far from threshold; 10. Oscillatory patterns; 11. Excitable media; 12. Numerical methods; Appendixes; References; Index.

Designed for graduate students in biology, chemistry, engineering, mathematics, and physics, this introductory textbook provides a systematic account of the experiments, simulations, and theory that explain how complex patterns form in sustained nonequilibrium systems. It contains numerous illustrative worked examples, and over 150 exercises.

Michael Cross is a Professor of Theoretical Physics at the California Institute of Technology, USA. His research interests are in nonequilibrium and nonlinear physics including pattern formation, chaos theory, nanomechanical systems, and condensed matter physics, particularly the theory of liquid and solid helium.
Henry Greenside is a Professor in the Department of Physics at Duke University, USA. He has carried out research in condensed matter physics, plasma physics, nonequilibrium pattern formation, and theoretical neurobiology. He is also involved with outreach programs to stimulate interest in science and physics at junior high school and high school levels.