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.
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.
An account of how complex patterns form in sustained nonequilibrium systems; for graduate students in biology, chemistry, engineering, mathematics, and physics.
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.
'This book gives an excellent didactic introduction to pattern
formation in spatially extended systems. It can serve both as the
basis for an advanced undergraduate or graduate course as well as a
reference. It is one of those books that will never outlive its
usefulness. It is a must for anyone interested in non-linear,
non-equilibrium physics.' Eberhard Bodenschatz, MPI for Dynamics
and Self-Organization, University of Goettingen, Cornell
University
'This book fills a long-standing need, and is certain to be an
instant classic. The physics of pattern forming systems is diverse
but the theoretical core of the subject, along with many of the
most important applications, can be learned from this splendid
book. It is bound to be a key text for courses, as well as a much
cited reference.' Stephen Morris, University of Toronto
'This book by Cross and Greenside presents a comprehensive
introduction to an important area of natural science and assembles
in one volume the essential conceptual, theoretical and
experimental tools a serious student will need to obtain a modern
understanding of pattern formation outside of equilibrium. The
masterful 50-page introduction lays out the essential questions and
provides motivation to the reader to explore the subsequent
chapters, beginning with simple ideas and growing progressively in
mathematical sophistication and physical depth. Careful attention
is paid to the relationship between the theoretical methods and
controlled laboratory experiments or numerical simulations. I can
highly recommend this book to any student or researcher interested
in a deepened understanding of nonequilibrium spatiotemporal
patterns.' Pierre Hohenberg, New York University
'… clearly written and follows a logical structure, making and
excellent introduction to the field at the graduate student level.'
UK Nonlinear News
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