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Complexity in Geophysical Systems
Mathematics in the Geosciences, September 2001 - June 2002
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
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
| Monday | Tuesday |
| MONDAY,
OCTOBER 8
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted. |
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|---|---|---|---|
| 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 |
||
| 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. |
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| 8:30 am | Coffee | Reception Room EE/CS 3-176 | |
| 9:30 am | Raymond
Hide |
||
| 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 |
|
| 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 |
|
| 3:00 pm | Coffee Break | Reception Room EE/CS 3-176 | |
| 3:30 pm |
Discussion
|
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| 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 |
||
| 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 |
|
| 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
|
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| 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 |
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| 12:00 pm |
Lunch
Break
|
||
| 2:00 pm | Andrei
Gabrielov Purdue University |
||
| 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 |
|
| 12:00 pm |
Discussion
|
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| 12:30 pm |
Lunch
Break
|
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| Monday | Tuesday |
LIST
OF CONFIRMED PARTICIPANTS
(in addition to postdocs and long-term participants)
| 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 |
|
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