Bio-Mimetic Swimmers in Incompressible Fluids

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.

Inhalt
Introduction.- Part I: Modeling of bio-mimetic swimmers in 2D and 3D incompressible fluids.- Bio-mimetic fish-like swimmers in a 2D incompressible fluid: Empiric modeling.- Bio-mimetic aquatic frog- and clam-like swimmers in a 2D fluid: Empiric modeling.- Bio-mimetic swimmers in a 3D incompressible fluid: Empiric modeling.- Part II: Well-posedness of models for bio-mimetic swimmers in 2D and 3D incompressible fluids.- Well-posedness of 2D or 3D bio-mimetic swimmers: the case of Navier-Stokes equations.- Part III: Micromotions and local controllability for bio-mimetic swimmers in 2D and 3D incompressible fluids.- Local controllability of 2D and 3D swimmers: the case of non-stationary Stokes equations.- Local controllability of 2D and 3D swimmers: the case of Navier-Stokes equations.- Part IV: Transformations of swimmers' internal forces acting in 2D and 3D incompressible fluids.- Transformation of swimmers' forces acting in a 2D incompressible fluid.- Transformation of swimmers' forces acting in a 3D incompressible fluid.- Part V: Global steering for bio-mimetic swimmers in 2D and 3D incompressible fluids.- Swimming capabilities of swimmers in 2D and 3D incompressible fluids: Force controllability.