Nambu Mechanics and its Connection to Adaptive Numerical Integration
by
Klas Modin/Gustaf Söderlind(Numerical Analysis, Centre for Mathematical Sciences, Lund University)
→
Europe/Stockholm
FB55
FB55
Description
In 1973 Professor Yoichiro Nambu, 2008 Nobel Prize Laureate in
Physics, published the influential paper "Generalized Hamiltonian Mechanics"
in which a generalization of Hamiltonian mechanics, today called Nambu
mechanics, is presented. The governing equations in Nambu's framework are obtained from several "Hamiltonian" functions, each corresponding to a conservation law.
Within numerical analysis the concept of "geometric numerical integration" has grown rapidly since 1990. The idea is to construct numerical time-integration methods that preserve various geometric structures which occur in mechanics and theoretical physics, e.g. symmetries. Such methods are superior to previous methods, since they give a qualitatively correct description of the dynamics, for example in terms of energy conservation.
Variable time-step adaptivity for geometric integrators is realised through time-transformations. Somewhat surprisingly, it turns out that such transformations naturally can be described with Nambu's mechanics. Thus, Nambu mechanics is an excellent framework for the construction and analysis of adaptive geometric numerical methods.
