Seminars and Colloquia by Series

An introduction for PDE constrained optimization

Series
PDE Seminar
Time
Tuesday, August 26, 2008 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Eldad Haber – Mathematics & Computer Science, Emory University
Optimization problems with PDE constraints are commonly solved in different areas of science and engineering. In this talk we give an introduction to this field. In particular we discuss discretization techniques and effective linear and nonlinear solvers. Examples are given from inverse problems in electromagnetics.

Zonal jets as transport barriers in planetary atmospheres - An application of KAM theory for Hamiltonians with degeneracy

Series
CDSNS Colloquium
Time
Monday, August 25, 2008 - 16:30 for 2 hours
Location
Skiles 269
Speaker
Francisco J. Beron-Vera – Marine & Atmospheric Science, University of Miami
The connection between transport barriers and potential vorticity (PV) barriers in PV-conserving flows is investigated with a focus on zonal jets in planetary atmospheres. A perturbed PV-staircase model is used to illustrate important concepts. This flow consists of a sequence of narrow eastward and broad westward zonal jets with a staircase PV structure; the PV-steps are at the latitudes of the cores of the eastward jets. Numerically simulated solutions to the quasigeostrophic PV conservation equation in a perturbed PV-staircase flow are presented. These simulations reveal that both eastward and westward zonal jets serve as robust meridional transport barriers. The surprise is that westward jets, across which the background PV gradient vanishes, serve as robust transport barriers. A theoretical explanation of the underlying barrier mechanism is provided, which relies on recent results relating to the stability of degenerate Hamiltonians under perturbation. It is argued that transport barriers near the cores of westward zonal jets, across which the background PV gradient is small, are found in Jupiter's midlatitude weather layer and in the Earth's summer hemisphere subtropical stratosphere.

The ubiquitous Lagrangian

Series
Analysis Seminar
Time
Monday, August 25, 2008 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Maria Clara Nucci – Dept. of Mathematics and Informatics, University of Perugia
In any standard course of Analytical Mechanics students are indoctrinated that a Lagrangian have a profound physical meaning (kinetic energy minus potential energy) and that Lagrangians do not exist in the case of nonconservative system.  We present an old and regretfully forgotten method by Jacobi which allows to find many nonphysical Lagrangians of simple physical models (e.g., the harmonic oscillator) and also of nonconservative systems (e.g., the damped oscillator).  The same method can be applied to any equation of second-order, and extended to fourth-order equations as well as systems of second and first order. Examples from Physics, Number Theory and Biology will be provided.

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