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The Symplectic Geometry of Fish
Joris Vankerschaver
UCSD
Abstract:
Fish, or in general any mechanical object moving in an inviscid fluid, can be described by means of a number of interesting differential-geometric structures, amongst other bundles and connections, groups of diffeomorphisms, and symplectic reduction. I will describe some of these structures and outline their role in fluid dynamics. Along the way, a number of parallels will appear with other dynamical systems: time permitting, we will describe a Kaluza-Klein description of fluid-structure interactions (making the link with magnetic particles), and we will see how the flux homomorphism from symplectic geometry makes an appearance through an old construction of Kelvin.
Tuesday, November 2, 2010
11:00AM AP&M 2402
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Randolph E. Bank
Philip E. Gill
Michael Holst
Administrative Contact:
[ Click to Send Email ]
Joris Vankerschaver
UCSD
Abstract:
Fish, or in general any mechanical object moving in an inviscid fluid, can be described by means of a number of interesting differential-geometric structures, amongst other bundles and connections, groups of diffeomorphisms, and symplectic reduction. I will describe some of these structures and outline their role in fluid dynamics. Along the way, a number of parallels will appear with other dynamical systems: time permitting, we will describe a Kaluza-Klein description of fluid-structure interactions (making the link with magnetic particles), and we will see how the flux homomorphism from symplectic geometry makes an appearance through an old construction of Kelvin.
Tuesday, November 2, 2010
11:00AM AP&M 2402