Swimming Phenomenon from the Viewpoint of Controllability Theory for Partial Differential Equations

Washington State University, Pullman WA

Investigators

Abstract

This project develops new methodology to study controllability properties of swimming locomotion. Unlike other approaches available in this area, which reduce the analytical study of swimming phenomena to finite dimensional models, in this study, the problem is attacked in its original intrinsic realm of highly nonlinear infinite dimensional distributed parameter systems. A particular feature of the approach is that it links the swimmer?s motion to an explicit analysis of its internal forces and shape-changing strategy. The former is determined by the choice of respective scalar multiplicative controls, while the latter is regarded as a geometric control. These types of controls are novel in the context of mathematical controllability theory for partial differential equations. This field is of great interest in biological and engineering applications, especially when dealing with propulsion systems in fluids. Of particular importance are three-dimensional models of bio-mimetic devices, which employ the change of their geometry, inflicted by internal forces, as the means for self-propulsion in a fluid. A specific focus of this project is the development of methodology as to how one can recalculate the swimmer?s internal forces into the forces that act upon the surrounding fluid as determined by the swimmer?s shape. This is a key issue for understanding the nature of swimming phenomena and these models are critical for better understanding of the mechanics of swimming and flying motions of biological organisms.