Lefschetz Center for Dynamical Systems Seminar
*#*#*# PLEASE NOTE NEW ROOM FOR THIS YEAR! |
Abstract: I will explain some recent work with Thierry Gallay on the construction of finite dimensional invariant manifolds in the phase space of the Navier-Stokes equation on ${\bf R}^n$. These manifolds control the long-term behavior of small solutions, give geometric insight into the host of existing results on the asymptotics of such solutions, and allow one to extend those results in a number of ways. Our results also allow us to prove the stability of certain vortex solutions of the Navier-Stokes equation, even at very large Reynold's number.
Solid Mechanics/Materials Science Seminar Series
Some Dynamic Failure Events in Solids | |
Abstract: A high-speed infrared (IR) imaging system has been designed and built to image two dimensional transient temperature fields. The system features and 8 X 8 array of HgCdTe IR detectors that can acquire temporally frozen images at rates up to one million frames per second. The system was used to image the evolving temperature fields in some dynamic failure events in solids such as a dynamically loaded stationary crack and a propagating shearband. For mode I cracks in ductile materials, a procedure to estimate J integral from the thermal images is proposed. In case of shearbands, the thermal images revealed a non-uniform temperature structure with a spatial periodicity along the length of the band. Such a structure is interpreted as evidence for unstable shear deformation within the band, analogous to certain hydrodynamic instabilities.
Center for Fluid Mechanics Seminar
PDE Seminar
<--- 2001 Index