Authors:
- Presents a concise mathematical theory for bio-mimetic swimmers in the framework of a coupled system of PDEs and ODEs
- Builds on the authoritative research pioneered by the author over the last two decades
- Consists of an original modelling approach, well-posedness results, and a controllability theory on steering potential
Part of the book series: Advances in Mathematical Fluid Mechanics (AMFM)
Part of the book sub series: Lecture Notes in Mathematical Fluid Mechanics (LNMFM)
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Table of contents (11 chapters)
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Front Matter
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Modeling of Bio-Mimetic Swimmers in 2D and 3D Incompressible Fluids
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Front Matter
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Well-Posedness of Models for Bio-Mimetic Swimmers in 2D and 3D Incompressible Fluids
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Front Matter
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Micromotions and Local Controllability for Bio-Mimetic Swimmers in 2D and 3D Incompressible Fluids
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Front Matter
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Transformations of Swimmers’ Internal Forces Acting in 2D and 3D Incompressible Fluids
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Front Matter
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Global Steering for Bio-Mimetic Swimmers in 2D and 3D Incompressible Fluids
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Front Matter
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Back Matter
About this book
This monograph presents an original, concise mathematical theory for bio-mimetic swimmers in the framework of a coupled system of PDEs and ODEs. The authoritative research pioneered by the author serves as the basis for the method adopted here. This unique methodology consists of an original modelling approach, well-posedness results for the proposed models for swimmers, and a controllability theory that studies the steering potential of the proposed swimmers. A combination of this sort does not currently exist in the literature, making this an indispensable resource.
Structured in five parts, the author establishes the main modeling approach in Part One. Part Two then presents the well-posedness results for these models. Parts Three through Five serve to develop a controllability theory for the swimmers, which are conceived of as artificial mechanical devices that imitate the swimming motion of fish, eels, frogs, and other aquatic creatures in nature. Several illustrative examples are provided in the last portion that serve as potential research topics.
Bio-Mimetic Swimmers in Incompressible Fluids will appeal to graduate students and researchers studying fluid dynamics and control theory, as well as engineers interested in these areas.Keywords
- Bio-mimetic swimmers
- Fluid dynamics
- Fluid dynamics modeling
- Fluid dynamics PDEs
- Fluid dynamics ODEs
- Incompressible fluid
- Incompressible fluid dynamics
- Navier-Stokes equations
- Well-posedness ODEs
- Well-posedness Navier-Stokes
- Incompressible fluids modelling
- Controllability fluid dynamics
- Controllability incompressible fluids
- Navier-Stokes swim
- Navier-Stokes incompressible
Authors and Affiliations
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Department of Mathematics and Statistics, Washington State University, Pullman, USA
Alexander Khapalov
Bibliographic Information
Book Title: Bio-Mimetic Swimmers in Incompressible Fluids
Book Subtitle: Modeling, Well-Posedness, and Controllability
Authors: Alexander Khapalov
Series Title: Advances in Mathematical Fluid Mechanics
DOI: https://doi.org/10.1007/978-3-030-85285-6
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
Softcover ISBN: 978-3-030-85284-9Published: 28 October 2021
eBook ISBN: 978-3-030-85285-6Published: 27 October 2021
Series ISSN: 2297-0320
Series E-ISSN: 2297-0339
Edition Number: 1
Number of Pages: XIII, 173
Number of Illustrations: 5 b/w illustrations, 44 illustrations in colour
Topics: Mathematical Modeling and Industrial Mathematics, Mathematical and Computational Biology, Materials Science, general, Control and Systems Theory