Modeling Nonlinear Dynamics from Equations and Data with Applications to Solids, Fluids, and Controls (Computational Science and Engineering) - Hardcover

Haller, George

 
9781611978346: Modeling Nonlinear Dynamics from Equations and Data with Applications to Solids, Fluids, and Controls (Computational Science and Engineering)
Hardcover
ISBN 10: 1611978343 ISBN 13: 9781611978346
Publisher: Society for Industrial & Applied Mathematics,U.S., 2025

Synopsis

This concise text presents an introduction to the emerging area of reducing complex nonlinear differential equations or time-resolved data sets to spectral submanifolds (SSMs). SSMs are ubiquitous low-dimensional attracting invariant manifolds that can be constructed systematically, building on the spectral properties of the linear part of a nonlinear system. The internal dynamics within SSMs then serve as exact, low-dimensional models with which the full system evolution synchronizes exponentially fast.

SSM-based model reduction has a solid mathematical foundation and hence is guaranteed to deliver accurate and predictive reduced-order models under a precise set of assumptions. This book illustrates the power of SSM reduction on a large collection of equation- and data-driven applications in fluid mechanics, solid mechanics, and control.

Audience
This book is intended for graduate students, postdocs, faculty, and industrial researchers working in model reduction for nonlinear physical systems arising in solid mechanics, fluid dynamics, and control theory. It is appropriate for courses on differential equations, modeling, dynamical systems, and data-driven modeling.

"synopsis" may belong to another edition of this title.

About the Author

George Haller is a professor of mechanical engineering at ETH Zurich, where he holds the Chair in Nonlinear Dynamics and heads the Institute for Mechanical Systems. His prior appointments include tenured faculty positions at Brown, McGill, and MIT. He also served as the inaugural director of Morgan Stanley's fixed-income modeling center. Professor Haller is the recipient of a Sloan Fellowship in mathematics, an ASME Thomas Hughes Young Investigator Award, a School of Engineering Distinguished Professorship (McGill), the Stanley Corrsin Award of the APS, and the Lyapunov Award of the ASME. He is an external member of the Hungarian Academy of Science and a fellow of SIAM, APS, and ASME.

"About this title" may belong to another edition of this title.

Publisher
Society for Industrial & Applied Mathematics,U.S.
Publication date
2025
Language
English
ISBN 10 
1611978343
ISBN 13 
9781611978346
Binding
Hardcover
Number of pages
151