|COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring.|
Quadratic invariants for clusters of resonant wave triads
If you have a question about this talk, please contact Kathryn de Ridder.
Topological Dynamics in the Physical and Biological Sciences
We consider clusters of interconnected resonant triads arising from the Hamiltonian three-wave equation. A cluster consists of N modes forming a total of M connected triads. We investigate the problem of constructing a linearly independent set of quadratic constants of motion. We show that this problem is equivalent to an underlying basic linear problem, consisting of finding the null space of a rectangular M × N matrix A with entries 1, -1 and 0. In particular, we prove that the number of independent quadratic invariants is equal to J = N – M >= N – M, where M is the number of linearly independent rows in A. We formulate an algorithm for decomposing large clusters of complicated topology into smaller ones and show how various invariants are related to certain parts and linking types of a cluster, including the basic structures leading to M* < M. We illustrate our findings by examples taken from the Charney-Hasegawa-Mima wave model.
This talk is part of the Isaac Newton Institute Seminar Series series.
This talk is included in these lists:
Note that ex-directory lists are not shown.
Other listsMillennium Maths Project public lectures Beer Talks Cambridge University Mountaineering Club
Other talksQuantum Trajectories in the Laboratory TBC Title: TBA (Prof. Thomas F. Krauss FRSE, University of York) Question writing Open Problems in Noisy Quantum Metrology Inferno XXVI, Purgatorio XXVI, Paradiso XXVI