Liu Bie Ju Centre for Mathematical Sciences
City University of Hong Kong
Mathematical Analysis and its Applications
Colloquium

Organized by Prof. Philippe G. Ciarlet and Prof. Roderick Wong

Making Sense of Non-Hermitian Hamiltonians

by
Professor Masato Nagata
Department of Aeronautics and Astronautics
Graduate School of Engineering
and
Advanced Research Institute of Fluid Science and Engineering
Kyoto University

Date: February 28, 2007 (Wednesday)
Time: 4:30 pm to 5:30 pm
Venue: Room B6605 (Faculty Conference Room)
Blue Zone, Level 6
Academic Building
City University of Hong Kong

Abstract: We consider the bifurcation sequence of plane Couette flow with and without a system rotation. Plane Couette flow is known to be linearly stable at any finite values of the Reynolds number, thus indicating no bifurcation directly from the basic flow with a linear velocity profile. Nagata (1990) analysed the nonlinear stability of the flow when the system rotation was added and successfully continued a tertiary solution branch to the zero-rotation rate, finding 3D nonlinear solutions of plane Couette flow for the first time. Later, he showed the existence of Hopf bifurcation points on the tertiary solution branch at some rotation rate (Nagata 1998). We present periodic solutions bifurcating from the Hopf bifurcation points and show that they collide with a 2D streamwise independent solution forming a heteroclinic connection when the rotation rate is varied. We also present a branch of the periodic solution which intersects the axis of the zero-rotation rate.

             

** All interested are welcome **

For enquiry: 2788-9816

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