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This month's talks available at http://www.ima.umn.edu/newsletters

IMA Newsletter #338

December 2004

2004-2005 Program

Mathematics of Materials and Macromolecules

See http://www.ima.umn.edu/matter for a full description of the 2004-2005 program on
Mathematics of Materials and Macromolecules: Multiple Scales, Disorder, and Singularities.

News and Notes

The IMA newsletter has a new look

Starting this month, the IMA newsletters and schedule announcements have a new format. The new versions are HTML files, with dynamic links to talk abstracts (click on talk titles in blue) and associated workshops and seminar series (click on the blue text in the Event Legend).

Let us know what you think of the new formats by sending email to newsfeedback@ima.umn.edu.

Schedule

Wednesday, December 1

11:15a-12:15pDiffused interface motion with surface tension and transport effectYoshihiro Tonegawa
Hokkaido University
Lind Hall 409 MS

Thursday, December 2

12:20p-1:20pClassification of Signature Curves Using Latent Semantic AnalysisCheri Shakiban
University of St. Thomas
Lind Hall 409 iPAWS

Friday, December 3

10:10a-11:10aMathematical and Computational Models for Dislocation DynamicsNasr M. Ghoniem
University of California - Los Angeles
Lind Hall 409
11:15a-12:15pOn a Multidimensional Model for the Dynamic Combustion of Compressible Reacting FluidsKonstantina Trivisa
University of Maryland
Lind Hall 409 MS
1:25p-2:25pAdventures in Industrial Mathematics: Making Better Lenses for Making Computer Chips Douglas Allan
Corning Inc.
Vincent Hall 570 IPS

Monday, December 6

11:15a-12:15pLong Time Simulation of Stochastic Differential EquationsJonathan C. Mattingly
Duke University
Lind Hall 409 MS

Tuesday, December 7

11:15a-12:15pRectangular mixed finite elements for elasticityGerard Awanou
University of Minnesota
Lind Hall 409 PS

Wednesday, December 8

11:15a-12:15pSchrodinger Vortices IDaniel Spirn
University of Minnesota
Lind Hall 409 MS

Thursday, December 9

12:20p-1:20pCortical Surface Extraction and Conformal Flattening with Minimal Metric DistortionDavid Rottenberg
University of Minnesota
Lind Hall 409 iPAWS

Friday, December 10

1:25p-2:25pImage Analysis as an Inverse Problem: Overview and ExamplesKevin Vixie
Los Alamos National Laboratory
Vincent Hall 570 IPS
2:30p-3:30pErgodicity of the 2D Navier-Stokes equations under very degenerate forcing Jonathan C. Mattingly
Duke University
Vincent Hall 311 Probability

Wednesday, December 15

11:15a-12:15pSingularities focus group: TBALind Hall 409 MS

Friday, December 24

All DayChristmas Eve. IMA closed.

Monday, December 27

All Day"Floating holiday". IMA closed.

Friday, December 31

All DayNew Year's Eve. IMA closed. Happy New Year!

Event Legend:

IPSIndustrial Problems Seminar
MSMaterials Seminar
PSIMA Postdoc Seminar
iPAWS Image Processing and Analysis Working Seminar
ProbabilityUMN Probability Seminar
Abstracts
Douglas Allan (Corning Inc.) Adventures in Industrial Mathematics: Making Better Lenses for Making Computer Chips
Abstract: This talk presents some real-life examples of mathematics and numerical simulation used in a manufacturing industry. Examples include one story with a mathematical moral. The exponential improvement over time in computer speed and memory relative to cost and size makes ever-increasing demands on the many technologies that are part of computer chip manufacture. One strategy for shrinking the size of computer chip features is to do photolithography with light sources of smaller wavelength. At smaller (now ultraviolet) wavelengths, each photon carries more energy. These energies are now high enough to slowly cause damage in the glass lenses used in photolithography optics, destroying the optics over time. This talk presents some aspects of the mathematical analysis of laser-induced damage in glass and emphasizes how mathematical analysis and computer simulation play a role in modern materials research and manufacturing.
Gerard Awanou (University of Minnesota) Rectangular mixed finite elements for elasticity
Abstract: We present a family of stable rectangular mixed finite elements for plane elasticity. Each member of the family consists of a space of piecewise polynomials discretizing the space of symmetric tensors in which the stress field is sought, and another to discretize the space of vector fields in which the displacement is sought. These may be viewed as analogues in the case of rectangular meshes of mixed finite elements recently proposed for triangular meshes. As for the triangular case the elements are closely related to a discrete version of the elasticity differential complex.
Jonathan C. Mattingly (Duke University) Long Time Simulation of Stochastic Differential Equations
Abstract: I will discuss some methods for the long time simulation of stochastic ordinary differential equations. I will show the shortcomings of the forward Euler method and give some remedies. In particular, I will discuss some simple adaptive ideas.
Jonathan C. Mattingly (Duke University) Ergodicity of the 2D Navier-Stokes equations under very degenerate forcing UMN Probability Seminar
Abstract: The stochastically forced Navier-Stokes equation (SNS) is both an important model of physical interest and an important testing ground to develop methods to analyze stochastic partial differential equations. Consider the two dimensional Navier-Stokes equation subject to random excitation. I will give essentially optimal conditions on the structure of the sochastic forcing under which the dynamics possesses a unique statistical steady state. The conditions use information on the geometry of the forcing and are independent of the viscosity (or Reynolds number). Hence the results hold for a fixed forcing as the viscosity is made smaller. These very recent results are the culmination of a long project undertaken by the speaker, his collaborators and others in the community to understand the ergodic theory for dissipative SPDEs and Hormander's "sum of squares" theorem for hypo-elliptic operators in an infinite dimensional setting. The talk will also touch on the tools from Malliavin calculus and anticipative stochastic processes used to prove the result. This is joint work with Etienne Pardoux and Martin Hairer building on earlier joint works with Ya Sinai and Weinan E when only a few degrees of freedom are stochastically excited. The result amounts to a version of Hormander's "sum of squares" theorem for hypo-elliptic operators in an infinite dimensional setting. The result gives some analytic control of how randomness moves from one scale to another. There will be connections to ideas from Inertial Manifolds and Determining Modes as one of the main ideas is that the small scale motion is enslaved to the large scale motion.
Cheri Shakiban (University of St. Thomas) Classification of Signature Curves Using Latent Semantic Analysis
Abstract: In this talk we discuss the Euclidean signature curves for two and three dimensional closed curves and will give a formulated and discrete method for finding such a curve. Then we will discuss an analog of Latent Semantic Analysis (LSA) and show how an optimal combination of normalizing transformations is utilized to categorize signature curves. Further we will present some data reduction techniques and noise-reduction methods and will introduce a system for determining the correct category of a new object from a pre-existing database of information on objects. We will then give two examples, one in sorting leaves in the Euclidean plane and the other in sorting DNA supercoils as space curves.
Daniel Spirn (University of Minnesota) Schrodinger Vortices I
Abstract: Under the limit of large Ginzburg-Landau parameter, Schrodinger vortices condense down to point particles and satisfy a simple Kirchhoff's Law - just like Euler point vortices. Given some technical variational results (to be discussed in the next seminar) I will describe the proof of vortex dynamics for the Schrodinger-Ginzburg-Landau equations.
Yoshihiro Tonegawa (Hokkaido University) Diffused interface motion with surface tension and transport effect
Abstract: We discuss a problem of phase boundary motion with hydrodynamic effect via a diffused interface model. The energy law leads us to study the problem where the velocity of the phase boundary is determined by the sum of mean curvature and fluid velocity. Via the Allen-Cahn type equation coupled with a viscous flow equation, we aim to establish the existence of a global weak solution in the setting of geometric measure theory. An analogue of Serrin's condition for the Navier-Stokes turns up for the existence. This is a joint work with Chun Liu.
Konstantina Trivisa (University of Maryland) On a Multidimensional Model for the Dynamic Combustion of Compressible Reacting Fluids
Abstract: In this work we present a multidimensional model for the dynamic combustion of compressible reacting fluids formulated by the Navier Stokes equations in Euler coordinates. For the chemical model we consider a one way irreversible chemical reaction governed by the Arrhenius kinetics. The existence of globally defined weak solutions of the Navier-Stokes equations for compressible reacting fluids is established by using weak convergence methods, compactness and interpolation arguments in the spirit of Feireisl and P.L. Lions.
Kevin Vixie (Los Alamos National Laboratory) Image Analysis as an Inverse Problem: Overview and Examples
Abstract: In this talk I present a viewpoint that makes many of the image analysis and processing tasks look very similar to one another. This view -- that we are solving an inverse problem in which the tasks are the choice of regularization and the modeling of the measurement operator -- carefully highlights where effort and insight need to be focused. Since specification of regularization is nothing more or less than the specification of the prior assumptions on what ideal images are like, this task can be seen to take on great importance, especially when -- as is often the case -- the data is sparse. The mathematical issues and their practical impact will be discussed and illustrated with examples.
Visitors in Residence
Douglas Allan Corning Inc. 12/2/2004 - 12/3/2004
Douglas N. Arnold University of Minnesota 7/15/2001 - 8/31/2006
Donald G. Aronson University of Minnesota 9/1/2002 - 8/31/2005
Gerard Awanou University of Minnesota 9/2/2003 - 8/31/2005
Maria-Carme Calderer University of Minnesota 9/1/2004 - 6/30/2005
Qianyong Chen University of Minnesota 9/1/2004 - 8/31/2006
L. Pamela Cook University of Delaware 9/7/2004 - 12/31/2004
Brian DiDonna University of Minnesota 9/1/2004 - 8/31/2006
Masao Doi University of Tokyo 9/18/2004 - 12/1/2004
Tim Garoni University of Minnesota 8/25/2003 - 8/31/2005
Nasr M. Ghoniem University of California - Los Angeles 12/3/2004 - 12/3/2004
Matthias Gobbert University of Maryland - Baltimore County 8/25/2004 - 12/24/2004
Robert Gulliver University of Minnesota 9/1/2004 - 6/30/2005
Chuan-Hsiang Han University of Minnesota 9/1/2004 - 8/31/2005
Richard D. James University of Minnesota 9/1/2004 - 6/30/2005
Sookyung Joo University of Minnesota 9/1/2004 - 8/31/2006
Chiu Yen Kao University of Minnesota 9/1/2004 - 8/31/2006
Richard Kollar University of Minnesota 9/1/2004 - 8/31/2005
Matthias Kurzke University of Minnesota 9/1/2004 - 8/31/2006
Frederic Legoll University of Minnesota 9/3/2004 - 8/31/2006
Debra Lewis University of Minnesota 7/15/2004 - 8/31/2006
Xiantao Li University of Minnesota 8/3/2004 - 8/31/2006
Fanghua Lin New York University 9/1/2004 - 12/31/2004
Chun Liu Pennsylvania State University 9/1/2004 - 6/30/2005
Zuhan Liu Xuzhou Normal University 9/14/2004 - 12/5/2004
Mitchell Luskin University of Minnesota 9/1/2004 - 6/30/2005
Jonathan C. Mattingly Duke University 11/22/2004 - 12/14/2004
Peter Philip University of Minnesota 8/22/2004 - 8/31/2006
Petr Plechac University of Warwick 9/1/2004 - 12/31/2004
Lea Popovic University of Minnesota 9/2/2003 - 8/31/2005
David Rottenberg University of Minnesota 12/9/2004 - 12/9/2004
Rolf Ryham Pennsylvania State University 9/1/2004 - 6/30/2005
Arnd Scheel University of Minnesota 7/15/2004 - 8/31/2006
George R Sell University of Minnesota 9/1/2004 - 6/30/2005
Cheri Shakiban University of St. Thomas 12/2/2004 - 12/2/2004
Tien-Tsan Shieh Indiana University 9/1/2004 - 6/30/2005
Peter J. Sternberg Indiana University 8/15/2004 - 6/30/2005
Vladimir Sverak University of Minnesota 9/1/2004 - 6/30/2005
Peter Takac Universitaet Rostock 10/15/2004 - 12/15/2004
Yoshihiro Tonegawa Hokkaido University 11/27/2004 - 12/4/2004
Konstantina Trivisa University of Maryland 12/3/2004 - 12/3/2004
Kevin Vixie Los Alamos National Laboratory 12/8/2004 - 12/10/2004
Zhi-Qiang Wang Utah State University 9/1/2004 - 12/31/2004
Stephen J. Watson Northwestern University 9/1/2004 - 6/30/2005
Olaf Weckner Massachusetts Institute of Technology 11/16/2004 - 12/14/2004
Baisheng Yan Michigan State University 9/1/2004 - 6/30/2005
Emmanuel Yomba University of Ngaoundéré 10/6/2004 - 3/30/2005
Legend: Postdoc or Industrial Postdoc Long-term Visitor

Participating Institutions: Consiglio Nazionale delle Ricerche, Georgia Institute of Technology, Indiana University, Iowa State University, Kent State University, Lawrence Livermore National Laboratory, Los Alamos National Laboratory, Michigan State University, Mississippi State University, Northern Illinois University, Ohio State University, Pennsylvania State University, Purdue University, Rice University, Sandia National Laboratories, Seoul National University (BK21), Seoul National University (SRCCS), Texas A & M University, University of Chicago, University of Cincinnati, University of Delaware, University of Houston, University of Illinois - Urbana-Champaign, University of Iowa, University of Kentucky, University of Maryland, University of Michigan, University of Minnesota, University of Notre Dame, University of Pittsburgh, University of Texas at Austin, University of Wisconsin, University of Wyoming, Wayne State University
Participating Corporations: 3M, Boeing, Corning Inc., ExxonMobil, Ford Motor Company, General Electric, General Motors, Honeywell, IBM Corporation, Johnson & Johnson, Lockheed Martin, Lucent Technologies, Motorola, Schlumberger-Doll Research, Siemens, Telcordia Technologies