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

Wednesday

Thursday

Friday

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

Wednesday

Thursday

Friday

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