Nonlinear Science: Emergence and Dynamics of Coherent Structures (Oxford Applied & Engineering Mathematics S.) - Hardcover

Scott, Alwyn

Hardcover

ISBN 10: 0198501072 ISBN 13: 9780198501077

Publisher: Oxford University Press, 1999

Synopsis

The study of nonlinear systems has quietly revolutionized the realm of science. Models of physical phenomena had previously been assumed to be linear, or nearly so. This allowed the construction of equations which were relatively simple to solve. It has, however, become increasingly evident that this assumption of linearity leads the theorist to miss qualitatively significant phenomena. For nonlinear systems, it is now known, the whole is greater than the sum of its parts, leading to the emergence of new structures that have their own features, lifetimes and peculiar ways of interacting. Since these interactions are also nonlinear, new dynamics give rise to other emergent structures appearing at yet higher levels of description. Thus the molecules of chemistry emerge from nonlinear interactions between the elements of atomic physics, providing a structural basis for the proteins and ribonucleic acids of biochemistry, and so on, up through the many levels of activity in a living organism. The intricacy of this hierarchical perspective is much closer to reality, and its discovery is a watershed in the history of science. This book is intended for graduate students and researchers in physics, applied mathematics, biomathematics, biophysics and engineering. Unknown function:

About this title

Review

"... refreshingly different. ... Another impressive feature is the numerous exercises at the end of each chapter. ... the book is excellent first reading on the fascinating and important subject of coherent structures in spatially extended dynamical systems' -- SIAM News

"I will recommend this book as a reference-text for undergraduate students...as well as a basic book for an interdisciplinary Ph D. course in Natural Sciences and Engineering. The book is a basic one for all the bridge courses with Biology as the Biophysics and Biocomputing, and in particular, for the emerging area of astrobiology." -- Luis Vazquez, Zentralblatt fur Mathematik

From the Author

The whole is greater than the sum of its parts.
This book introduces a revolution that has quietly transformed the realms of science over the past quarter century. Up to the mid-1970s, models of physical phenomena were usually assumed to be linear, or nearly so, allowing advantage to be taken of the convenient but often unrealistic property that complicated causes can be resolved into more simple components, the effects of which are treated separately. Over the past two decades, however, it has become increasingly evident that the assumption of linearity leads the theorist to miss qualitatively significant phenomena.

For a nonlinear system, it is now known, "the whole is greater than the sum of its parts," leading to the emergence of new structures that are spatially or temporally coherent. Awareness of this is becoming recognized as a watershed in science, suggesting a new understanding of its organization and structure.

Such emergent structures are very much "things," having their own features and peculiar ways of interacting. Since these interactions are also nonlinear, new dynamics give rise to yet other emergent structures appearing at higher levels of description. Thus the molecules of chemistry emerge from nonlinear interactions among the elements of atomic physics, providing a structural basis for the proteins and ribonucleic acids of biochemistry, and so on, up through the many levels of activity of a living organism. The intricacy of this hierarchical perspective reflects that of reality, and it should be appreciated by all who would contribute to the biologically and socially oriented sciences of the future.

As the curtain rises on the science of the twenty-first century, the nonlinear phenomenon of emergence is destined to play a leading role. I hope this book will help those who wish to participate in the unfolding drama.

Edition details

• Publisher: Oxford University Press
• Publication date: 1999
• Language: English
• ISBN 10: 0198501072
• ISBN 13: 9780198501077
• Binding: Hardcover
• Number of pages: 492