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IMA Workshop 2
Complexity in Geophysical Systems
October 8-12, 2001


Mathematics in the Geosciences, September 2001 - June 2002

Organizers:

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

Vladimir Keilis-Borok
Institute of Geophysics and Planetary Physics
University of California, Los Angeles
vkb@ess.ucla.edu

Jean Carlson
Department of Physics
University of California-Santa Barbara
carlson@physics.usb.edu

The solid earth, oceans and atmospheres are profoundly nonlinear. While the oceans and atmosphere are well-described by first principles equations, many nonlinear processes in the solid earth lack such a description. Many geophysical problems possess an underlying discrete character, in contrast with a continuous one, or alternatively do not offer a well-posed PDE description but appear to be easy to characterize in a discrete fashion. Fracture of Earth materials provides a good example. Grains in a rock, approximately 1 mm in size, constitute the basic unit in this otherwise heterogeneous medium. These scenarios lend themselves in a natural way to a cellular automaton or a lattice gas formulation depending on whether the time dependence is intrinsically discrete or continuous, respectively. In an important subcategory of cellular automaton problems, the accessible states in the problems are discrete, and especially subject to delayed influences. Equations governing this class of problems are often called Boolean Delay Equations. Illustrative examples include percolation problems, with the attendant possibility of critical point behavior; earthquake and avalanche problems, including the possibility of self organized criticality and scaling; and the modeling of complex transport processes, which blend fluids with granular materials, and provide important insights in to complicated problems in the establishing of landforms and fluvial drainage patterns.

Keywords: earthquakes and avalanches, percolation, cellular automata, Boolean difference equations, sandpiles

WORKSHOP SCHEDULE

Monday Tuesday
MONDAY, OCTOBER 8
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 Vladimir Keilis-Borok
Welcome and Introduction
9:30 am Leon Knopoff
University of California, Los Angeles
Are simple models adequate for the simulation of recurrent seismicity?
10:30 am Coffee Break Reception Room EE/CS 3-176
11:00 am Leo Kadanoff
University of Chicago
Making a Splash, Breaking a Neck: The Development of Complexity in Physical Systems
12:00 pm
Lunch Break
2:00 pm Sergey Cherkis
University of California, Los Angeles

Solitons in Hierarchical Systems (an example)

Slides

3:30 pm IMA Tea/Reception
A variety of appetizers and beverages will be served.
IMA East, 400 Lind Hall
TUESDAY, OCTOBER 9
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 Raymond Hide

Analysis and interpretation of the main geomagnetic field: The magnetic field at the core-mantle boundary: some topological speculations

Slides

10:30 am Coffee Break Reception Room EE/CS 3-176
11:00 am Mikhail Vishik
University of Texas

Incompressible flows of an ideal fluid with unbounded vorticity

Slides

12:00 pm
Lunch Break
2:00 pm Susan Friedlander
University of Illinois, Chicago

A GOY model for the Navier Stokes equations with nonlinear viscosity

Slides

3:00 pm Coffee Break Reception Room EE/CS 3-176
3:30 pm
Discussion
WEDNESDAY, OCTOBER 10
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 William I. Newman
University of California-Los Angeles

Complexity and Spatio-Temporal Chaos in Material Failure: Analysis and Computation of Fiber Bundle Models

Slides

10:30 am Coffee Break Reception Room EE/CS 3-176
11:00 am David A. Yuen
University of Minnesota

Controlling Thermal Chaos in the Mantle by Feedback due to Radiative Thermal Conductivity

Slides

12:00 pm
Lunch Break
2:00 pm Clement Narteau
California Institute of Technology

Strike-slip fault network evolution in the Scaling Organization of Fracture Tectonic model

Slides:   pdf (13MB)

3:00 pm Coffee Break Reception Room EE/CS 3-176
3:30 pm
Discussion
THURSDAY, OCTOBER 11
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 Donald L. Turcotte
Cornell University
Micro and macroscopic models for material failure
10:30 am Coffee Break Reception Room EE/CS 3-176
11:00 am Vladimir G. Kossobokov
Russian Academy of Sciences

Complexity of inverse and direct cascading of earthquakes

Slides:   html    pdf

12:00 pm
Lunch Break
2:00 pm Andrei Gabrielov
Purdue University

Modeling of seismicity: a mathematician's perspective

Slides

3:00 pm Coffee Break Reception Room EE/CS 3-176
3:30 pm
Discussion
FRIDAY, OCTOBER 12
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 A. Yorke
University of Maryland, College Park
Weather Prediction
10:30 am Coffee Break Reception Room EE/CS 3-176
11:00 am Agnes Helmstetter
University of Grenoble

Sub-critical and Super-critical Regimes in Epidemic Models of Earthquake Aftershocks

Slides

12:00 pm
Discussion
12:30 pm
Lunch Break
Monday Tuesday

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

As of 10/8/2001
Name Department Affiliation
Sergey Cherkis
Physics & Astronomy University of California, Los Angeles
Fabio D'Andrea
Earth, Atmospheric & Planetary Sci. Massachusetts Insitute of Technology
Susan Friedlander
Mathematics, Statistics & CSci. University of Illinois, Chicago
Andrei Gabrielov
Earth & Atmostpheric Sciences Purdue University
Agnes Helmstetter
Geosciences University of Grenoble
Raymond Hide
   
Leo Kadanoff
Physics & Mathematics University of Chicago
Vladimir Keilis-Borok
Institute of Geophysics and Planetary Physics University of California, Los Angeles
Leon Knopoff
Physics and Astronomy University of California, Los Angeles
Vladimir Kossobokov
Int'l Inst. of Earthquake Pred. Theory & Math Geo. Russian Academy of Sciences
Anatoli Levshin
Physics University of Colorado at Boulder
George Molchan
Int'l Inst. of Earthquake Pred. Theory & Math Geo. Russian Academy of Sciences
Clement Narteau
Seismological Laboratory California Institute of Technology
William Newman
Earth & Space Sciences University of California, Los Angeles
Alexandr Shapoval
Int'l Inst. of Earthquake Pred. Theory & Math Geo. Russian Academy of Science
Donald Turcotte
Geological Sciences Cornell University
Mikhail Vishik
Mathematics University of Texas
James Yorke
Institute for Physical Sciences & Technology University of Maryland, College Park
David Yuen
Geology & Geophysics University of Minnesota
Illia Zaliapin
Institute of Geophysics and Planetary Physics UCLA

Abstracts      Material from Talks

Mathematics in the Geosciences, September 2001 - June 2002

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