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IMA Workshop
Nonlinear Continuum Mechanics, Rheology and the Dynamo
March 18-22, 2002


Mathematics in Geosciences, September 2001 - June 2002

Organizers:

Gerald Schubert
Department of Geophysics and Planetary Physics
University of California, Los Angeles
schubert@ucla.edu

Shun-Ichiro Karato
Department of Geology and Geophysics
University of Minnesota
karato@umn.edu

Peter Olson
Department of Earth and Planetary Sciences
Johns Hopkins University
olson@jhu.edu

e="Verdana, Arial, Helvetica, sans-serif" size="2">Donald L. Turcotte
Department of Geological Sciences
Cornell University
turcotte@geology.cornell.edu

During the past decade, geoscientists have come to appreciate the often-dominant role played by complex and nonlinear rheologies in the deformation of geologic materials. This is nowhere more evident than in the earth's crust and mantle where effective viscosities can vary over many orders of magnitude and different modes of deformation occur. On the largest scale, plate tectonics occurs because of the poorly understood multi-rheological behavior of crustal and mantle rocks. On a smaller scale, complex geomorphic features, such as those in evidence in the Sierra Nevada, are the outcome of flows which are dramatically influenced by variable viscosity, phase transitions, and other physical and chemical properties. Nonlinear rheology, through a number of microscopic processes and macroscopic interactions such as thermal feedback, results in a rich variety of flow behavior including strain localization and instability leading to faulting. Such behaviors are ultimately responsible for such diverse geologic phenomena as plate tectonics and earthquakes. Pyroclastic flows, associated with volcanic events, occur when these environments contribute to a punctuated or even explosive discharge of molten materials, particularly in the presence of water which not only catalytically alters the rheology but, when superheated, produces steam under very great pressure and very abruptly changes the dynamic equilibrium. Water, in its interaction with other earth materials, also has a profound effect on the landscape. Alone, its erosive effects modify topography on a long geologic time scale. However, if a flow transports granular material, those grains impact and erode irregularities in underlying materials, an effect that is demonstrably unstable. This mechanism, associated with catastrophic flooding, can have an overnight effect on the landscape. The clays that are produced are an important agent in the formation of topography and have an especially complex rheology. Wind and ice can operate in a similar way, completing the triad of aeolian influences. Another invasive process, known as "undercutting," results from the hydrostatic injection of water or steam into cracks in rock; its cooling and freezing, and subsequent expansion, cause existing cracks to grow as well as new cracks to be initiated. Water, even in microscopic quantities, has a dramatic influence on the strength of rocks and could contribute to the migration of seismicity and the triggering of seismic events at great distances from an earthquake. Sea ice is another excellent example of a material with a nonlinear rheology.

Nonlinear rheology, taken in the broadest sense, may be the single most important aspect of the behavior of earth materials. While rheology is not an issue for flows in the earth's liquid outer core, understanding the mechanisms and nonlinear interactions involved in the generation and reversal of the earth's magnetic field by dynamo action in the core remains a great challenge in geophysics. Though progress has been made toward the solution of the coupled nonlinear equations of motion and electrodynamics for the extreme parameter values appropriate to the rapidly rotating and relatively inviscid core of the earth, novel approaches are required to proceed substantially further.

Keywords: mantle, lithosphere, seismic creep, pyroclastic flows, aeolian flows, drainage networks, rheology, plate tectonics, dynamo, earthquakes, erosion, core.

WORKSHOP SCHEDULE

Monday Tuesday
MONDAY, MARCH 18
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
8:00 am Coffee and Registration

Reception Room EE/CS 3-176

8:55 am Douglas N. Arnold, Robert Gulliver, and Gerald Schubert Welcome and Introduction
Today's chair: Shun-ichiro Karato (Yale University)
9:10 am Yves Gueguen
Ecole Normale Superieure, Paris
A Crackling Crust (une croute craquante)
10:10 am Coffee Break Reception Room EE/CS 3-176
10:30 am Slava Solomatov
New Mexico State University
Mantle dynamics: Grain size does matter
11:30 am Vladimir Lyakhovsky
Geological Survey of Israel, Jerusalem

Nonlinear Elasticity, Distributed Damage, and Fracture of Rocks

Slides:  html    pdf    powerpoint

Video:  conus.avi
evolution.avi

rotation_step2.avi
rotation_step3.avi
rotation_step4.avi
rotation_step5.avi
rotation_step6.avi
rotation_step7.avi  
side.avi
top.avi

12:00 pm
Lunch Break
1:30 pm Yanick Ricard
Ecole Normale Supérieure de Lyon

A two-phase theory for compaction and damage

Slides:   pdf    postscript

2:30 pm David A. Yuen
University of Minnesota

The Dynamical Consequences in Mantle Convection from a Nonlinear Constitutive Relation in the Temperature Equation due to variable Thermal Conductivity

Slides

3:30 pm Second Chances and Discussion Shun-ichiro Karato (Moderator)
Yale University
4:00 pm IMA Tea/Reception
A variety of appetizers and beverages will be served.
IMA East, 400 Lind Hall
TUESDAY, MARCH 19
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
8:40am Coffee Reception Room EE/CS 3-176
Today's chair: Paul Tackley (UCLA)
9:10 am Stephen Morris
University of California, Berkeley

On the olivine-spinel transformation as a rheometer

Slides

10:10 am Coffee Break Reception Room EE/CS 3-176
10:30 am Paul J. Tackley
University of California, Los Angeles

Modeling The Thermochemical Evolution of Planets with Plate Tectonics or Rigid Lids

Slides:   html    pdf    powerpoint

Movies: Ra1e6_2e4c_i2.mov
Ra1e6_6e4c_i2.mov
tAR16_2e5_7.mpg
coolrc2om_t.mov

hom_c.mov
hom_t.mov
lyr_c.mov
lyr_t.mov

meanTdiff_c.mov
meanTdiff_t.mov
meanTiso_t.mov

Images:
Deformation2x.jpg
m6_varyYS_for_PR.jpg

11:30 am Thomas J. Pence
Michigan State University
A Multi-field Model for Solid-Solid Phase Transformation
12:00 pm
Lunch Break
1:30 pm Anne Davaille
Institut Physique du Globe, Paris
Thermal convection in a mantle heterogeneous in viscosity and in density
2:30 pm Andrew C. Fowler
Oxford University
Lithospheric failure on Venus
3:30 pm Second Chances and Discussion Paul Tackley, Moderator
WEDNESDAY, MARCH 20
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
8:40 am Coffee Reception Room EE/CS 3-176
Today's chair: David J. Stevenson (California Institute of Technology)
9:10 am David J. Stevenson
Caltech

Conditions for the Excitation and Maintenance of Planetary Dynamos

Slides

10:10 am Coffee Break Reception Room EE/CS 3-176
10:30 am David Gubbins
University of Leeds
Pacific Secular Variation: A result of hot lower mantle
11:30 am Dominique Jault
CNRS Grenoble
Experimental evidence of nonlinear resonance effects between retrograde precession and the tilt-over mode within a spheroid
12:00 pm
Lunch Break
1:30 pm Paul H. Roberts
University of California, Los Angeles

How can the energy requirements of the Earth's dynamo be met?

Slides

2:30 pm Chris Jones
University of Exeter

The dynamical regime in the Earth's core

Slides

3:30 pm Weijia Kuang
University of Maryland, Baltimore County

Multidisciplinary studies of deep Earth, from geodynamo to geodesy

Slides:  html    pdf    powerpoint

4:00 pm Second Chances and Discussion David J. Stevenson, Moderator
THURSDAY, MARCH 21
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
8:40 am Coffee Reception Room EE/CS 3-176
Today's chair: David Gubbins (University of California, Santa Cruz)
9:10 am W.R. Peltier
University of Toronto
The viscosity of Earth's mantle: Newtonian or non-Newtonian
10:10 am Coffee Break Reception Room EE/CS 3-176
10:30 am Gary A. Glatzmaier
University of California, Santa Cruz
Current Challenges in Dynamo Modeling
11:30 am Charles R. Carrigan
Lawrence Livermore National Lab
Viscous Encapsulation: A Potentially Important Mechanism to Explain the Occurrence of Effusive Volcanism
12:00 pm
Lunch Break
1:30 pm Friedrich H. Busse
Universitaet Bayreuth
Convection Driven Dynamos in Rotating Spherical Shells
2:30 pm Dazhi Jiang
University of Maryland

Numerical modeling of the development of kink-bands in anisotropic rocks

Slides:   html    pdf    powerpoint

Video:  p20_m10.avi
phi20_m2.avi
phi20_m8.avi

3:00 pm Michael R. Riedel
University of Potsdam
Plastic Instabilities as a Possible Physical Mechanism Causing Intermediate-Depth and Deep-Focus Earthquakes
3:30 pm Second Chances and Discussion David Gubbins, Moderator
6:00 pm Workshop Dinner Bangkok Thai Restaurant
425 13th Ave. S.E.
FRIDAY, MARCH 22
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
8:40am Coffee Reception Room EE/CS 3-176
Today's chair: Gary A. Glatzmaier (University of California, Santa Cruz)
9:10 am Bruce Buffett
University of British Columbia
Large-Eddy Simulations of Convection in the Earth's Core
10:10 am Coffee Break Reception Room EE/CS 3-176
10:30 am Gerald Schubert
University of California, Los Angeles
A Numerical Finite-Element Approach to the Solution of the Dynamo Problem
11:30 am Second Chances and Discussion Gary A. Glatzmaier, Moderator
Monday Tuesday

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

As of 3/20/2002
Name
Department Affiliation
Doug Arnold   Institute for Mathematics & its Applications
Bruce Buffet Earth & Ocean Sciences University of British Columbia
F.H. Busse Theoretische Physik IV Universitaet Bayreuth
Charles Carrigan University of California Lawrence Livermore National Laboratory
Ann Davaille Lab. de Dynamique des Systemes Geologiques Institut de Physique du Globe de Paris
Fabien Dubuffet   Minnesota Supercomputing Institute
Roger Fosdick Aerospace Engineering & Mechanics University of Minnesota
Andrew C. Fowler Mathematical Institute Oxford University
Gary Glatzmaier Earth Sciences University of California, Santa Cruz
Dave Gubbins Earth Sciences University of Leeds
Yves Gueguen Terre Atmosphere Ocean Ecole Normale Superieure
Robert Gulliver   Institute for Mathematics & its Applications
Dominique Jault Laboratoire de Geophysique Interne et Tectonophy Centre National de la Recherche Scientifique
Dazhi Jiang Geology University of Maryland
Chris Jones Mathematical Sciences University of Exeter
Shun-ichiro Karato Geology and Geophysics Yale University
Weijia Kuang National Aeronautics & Space Administration NASA Goddard Space Flight Center
John Lister Applied Mathematics and Theoretical Physics University of Cambridge
Vladimir Lyakhovsky   Geological Survey of Israel
Stephen Morris Mechanical Engineering University of California, Berkeley
William Newman Earth & Space Sciences University of California, Los Angeles
R. Peltier Physics University of Toronto
Thomas J. Pence Materials Science & Mechanics Michigan State University
Yanick Ricard   Ecole Normale Suprierure de Lyon
Guillaume C.M. Richard   Laboratoire de Dynamique Terrestre et Planetaire
Michael Riedel   GeoForschungsZentrum Potsdam
Paul Roberts Institute of Geophysics & Planetary Physics University of California, Los Angeles
Fadil Santosa   Institute for Mathematics & its Applications
Gerald Schubert Geophysics & Planetary Physics University of California, Los Angeles
Valera P. Shcherbakov   Geophysical Observatory Borok""
Slava Solomatov Physics New Mexico State University
David J. Stevenson Geological and Planetary Sciences California Institute of Technology
Paul Tackley Earth and Space Sciences University of California, Los Angeles
Tomohiko Yanagawa Earth and Planetary Sciences Kyushu University
David A. Yuen Geology & Geophysics University of Minnesota
K. Zhang Mathematical Sciences University of Exeter

2001-2002 IMA Thematic Year on Mathematics in the Geosciences

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