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IMA Workshop
Dynamical Systems in Celestial Mechanics and Climate Dynamics
October 29-November 2, 2001


Mathematics in the Geosciences, September 2001 - June 2002

Organizers:

Michael Ghil
Department of Atmospheric Sciences and IGPP
University of California-Los Angeles
ghil@atmos.ucla.edu
http://webster.atmos.ucla.edu/~ghil/

William I. Newman
Departments of Earth and Space Sciences, Physics and Astronomy, and Mathematics
University of California-Los Angeles
win@ucla.edu

Ferenc Varadi
Institute of Geophysics and Planetary Physics
University of California-Los Angeles
varadi@ucla.edu

Dynamical systems theory provides fundamental ideas and tools for the modeling, analysis, and prediction of the climate system. The successive bifurcation approach, in particular, has provided a systematic way to help understand increasingly complex climate behavior, in space and time. The ideas and tools of nonlinear dynamics are most easily grasped and applied in the context of low-dimensional models, but have been applied more recently to large and detailed models, such as the general circulation models used in atmospheric, oceanic, and climate-system dynamics. The workshop will be dedicated to the systematic application of this approach to the full hierarchy of climate models. For didactic and methodological purposes, we shall emphasize relatively simple models with a clear mathematical description, such as paleoclimate models and their astronomical forcing.

Conservative Hamiltonian systems will be illustrated by models of planetary motion, while forced-dissipative systems will be illustrated primarily by models of the Quaternary ice ages and other paleoclimate models. The study of the Solar System's stability has motivated many advances in dynamical systems theory. The workshop will emphasize the applications of these advances to the largely unsolved problems of the actual system's evolution on various time scales. Paleoclimate models will be formulated, based on physico-chemical principles and the available empirical evidence, as closed mathematical systems. These systems will be analyzed and the results compared with the most recent information on past climate change.

Keywords: bifurcations, celestial mechanics, climate dynamics, transitions

WORKSHOP SCHEDULE

Monday Tuesday
MONDAY, OCTOBER 29
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
8:30 am Coffee and Registration

Reception Room EE/CS 3-176

9:15 am Douglas N. Arnold, Robert Gulliver, and Ferenc Varadi Welcome and Introduction
9:30 am Joseph A. Burns
Cornell University

The Renaissance in Solar System Dynamics

Slides

10:30 am Coffee Break Reception Room EE/CS 3-176
11:00 am William I. Newman
UCLA

Numerical Integration, Lyapunov Exponents, and the Outer Solar System

Slides:   pdf (5MB)

12:00 pm
Lunch Break
2:00 pm Richard Rand
Cornell University

A Nonlinear Quasiperiodic Mathieu Equation

pdf (568KB)

3:00 pm Coffee Break Reception Room EE/CS 3-176
3:30 pm Wang Sang Koon
California Institute of Technology

Invariant Manifolds, the Three-Body Problem and a Petit Grand Tour of Jovian Moons

slides.pdf     paper.pdf

4:40 pm IMA Tea/Reception
A variety of appetizers and beverages will be served.
IMA East, 400 Lind Hall
TUESDAY, OCTOBER 30
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
8:30 am Coffee Reception Room EE/CS 3-176
9:30 am James F. Kasting
Pennsylvania State University

Climate Stability (and Instability) on Long Time Scales

Slides:   html    pdf

10:30 am Coffee Break Reception Room EE/CS 3-176
11:00 am Michael Ghil
University of California-Los Angeles

Quaternary glaciations and celestial mechanics

Slides

12:00 pm
Lunch Break
2:00 pm Glen R. Stewart
University of Colorado

Resonant Planet-Disk Interactions in the Solar System

Slides

3:00 pm Coffee Break Reception Room EE/CS 3-176
3:30 pm Ferenc Varadi
University of California-Los Angeles

Problems in solar system dynamics

Slides

4:45 pm Illustrations: Ferenc Varadi
University of California-Los Angeles
Simulation and time series analysis (software demonstration)
WEDNESDAY, OCTOBER 31
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
8:30 am Coffee Reception Room EE/CS 3-176
9:30 am Roger Temam
Indiana University
Some recent developments on the Primitive Equations
10:30 am Coffee Break Reception Room EE/CS 3-176
11:00 am Andrew Majda
New York University
Mathematical Strategies for Stochastic Climate Modelling
12:00 pm
Lunch Break
2:00 pm Special Seminar:
James A. Sethian
University of California, Berkeley
Ordered Upwind Methods: Computing Viscosity Solutions to Optimal Control and Non-Viscosity Solutions to Wave Propagation
3:30 pm Richard Kleeman
Courant Institute of Mathematical Sciences
Predictability in dynamical systems relevant to climate and weather
4:30 pm Discussion (chaired by Michael Ghil) Ask not what climate can do for you, but what you can do for understanding & predicting climate
THURSDAY, NOVEMBER 1
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
8:30 am Coffee Reception Room EE/CS 3-176
9:30 am Edriss S. Titi
University of California, Irvine

Mathematical Study of Certain Geophysical Models

Slides

10:30 am Coffee Break Reception Room EE/CS 3-176
11:00 am Jinqiao Duan
Illinois Institute of Technology

Stochastic dynamics of coupled ocean-atmosphere models

Slides

12:00 pm
Lunch Break
2:00 pm Steve Shkoller
University of California, Davis
A Variational Level-Set Approach for Two-Phase Incompressible Fluids
3:00 pm Coffee Break Reception Room EE/CS 3-176
3:30 pm Shouhong Wang
Indiana University
Topology of 2D Incompressible Flows
6:00 pm Workshop Dinner Gardens of Salonica
19 Fifth Street N.E., Minneapolis
FRIDAY, NOVEMBER 2
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
8:30am Coffee Reception Room EE/CS 3-176
9:30 am James E. Howard
University of Colorado, Boulder

Asteroidal Satellites

Slides

10:30 am Coffee Break Reception Room EE/CS 3-176
11:00 am Daniel Schertzer
University of Paris VI

Chaos, ergodic theory and multifractal singularities of stochastic differential equations

Slides:   html    pdf    powerpoint

12:00 pm
Conclusion and Lunch
Monday Tuesday

LIST OF CONFIRMED PARTICIPANTS
(in addition to postdocs and long-term participants)

As of 10/30/2001
Name
Department Affiliation
Doug Arnold   Institute for Mathematics & its Applications
Joseph Burns Theoretical & Applied Mechanics Cornell University
Colin Cotter Mathematics Imperial College, University of London
Dacian Daescu Mathematics University of Iowa
Doug Dokken Mathematics University of St. Thomas
Jinqiao Duan Applied Mathematics Illinois Institute of Technology
Gregory S. Duane   Institute for Mathematics & its Applications
Fabien DuBuffet Geology and Geophysics University of Minnesota
Michael Efroimsky Physics Harvard University
Jason Frank   CWI
Hongjun Gao Mathematics Nanjing Normal University
Michael Ghil Atmospheric Sciences University of California, Los Angeles
Robert Gulliver   Institute for Mathematics & its Applications
James E. Howard Laboratory for Atmospheric and Space Physics University of Colorado
James Kasting Geosciences Pennsylvania State University
Daniel Kern    
Seongjai Kim Mathematics University of Kentucky
Richard Kleeman Center for Atmospheric Ocean Science Courant Institute of Mathematical Sciences
Wang Sang Koon   California Institute of Technology
Hyeona Lim Mathematics Michigan State University
Andrew Majda Courant Institute of Mathematical Sciences New York University
William Newman Earth & Space Sciences University of California, Los Angeles
Richard Rand Theoretical & Applied Mechanics Cornell University
Fadil Santosa   Institute for Mathematics & its Applications
Arnd Scheel Mathematics University of Minnesota
Daniel Schertzer Centre de Calcul Recherche Reseau Jussieu
George Sell Mathematics University of Minnesota
Robert Shcherbakov Earth & Atmospheric Sciences Cornell University
Jianhong Shen Mathematics University of Minnesota
Steve Shkoller Mathematics University of California, Davis
Glen R. Stewart Lab Atmos/Space Physics University of Colorado, Boulder
Roger Temam Institute for Scientific Computing & Appl. Math. Indiana University
Edriss Titi Mathematics University of California, Irvine
Donald Turcotte Geological Sciences Cornell University
Ferenc Varadi Insitute of Geophysics and Planetary Physics University of California, Los Angeles
Shouhong Wang Mathematics Indiana University
Xiaoming Wang Courant Institute of Mathematical Science New York Universtiy
Toshio Yoshikawa   Institute for Mathematics & its Applications
David A. Yuen Geology & Geophysics University of Minnesota

Mathematics in the Geosciences, September 2001 - June 2002

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