| 11-23-2009 16:00 | Seminar | 10,000 hours of modeling, analysis, and simulation | This is a Math 507 seminar for graduate math majors. | |
| 11-20-2009 12:00 | Applied Mathematics and Computation Seminar | Karhunen-Loeve expansion and Monte Carlo Simulation for flow in porous media | It is well known that flow in porous media is strongly affected by
spatial variability in the medium and is additionally subject to
uncertainties.
Using stochastic models to incorporate uncertainty and variability in
the equations that govern flow and transport in heterogeneous media
yields stochastic partial differential equations. The Monte Carlo method can be used to
find approximate solutions to these equations. We present some
Monte Carlo simulations based on Karhunen-Loeve decompositions of
stochastic processes.
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| 11-18-2009 12:00 | Number Theory Seminar | John H. Conway's book, Chapter 2, Part I | | |
| 11-16-2009 16:00 | Colloquium | Problems for the clairvoyant demon | Coin tosses are the very essence of probability theory. Yet, there are a number of simply stated problems that have resisted solution. These may involve Peter Winkler's clairvoyant demon, and they may sometimes be cast in the domain of so-called dependent percolation. Three such problems and their extensions are discussed in this talk. The only prerequisite expected of the audience is an affinity for tossing a fair coin. | |
| 11-13-2009 12:00 | Applied Mathematics and Computation Seminar | ABCO2 | Storage and sequestration of CO2 in subsurface has become a popular research topic in many fields of science and engineering. This is mostly due to anticipated environmental benefits but also thanks to a rich collection of associated models and problems that this idea provides. The talk will be expository and will give an overview of technologies and of mathematical and computational challenges that arise. The mathematical models relevant to CO2 sequestration include standard multiphase multicomponent flow and reactive transport, phase transitions, multiscale data, capillary and adsorption/desorption hysteresis, and coupling with poro-elasticity. | |
| 11-11-2009 12:00 | Number Theory Seminar | John H. Conway on Quadratic Reciprocity, Part 2 | | |
| 11-09-2009 16:00 | Seminar | Getting Math Off the Ground: Applied Mathematics at Boeing (sponsored by SIAM) | Steve Keeler is manager of the Geometry and Optimization group in Boeing's Applied Mathematics organization. The group specializes in geometric modeling, computer-aided geometric design, numerical optimization, multidisciplinary design optimization, data fitting and optimal control. They work with engineers on the design and manufacture of commercial aircraft, military and space systems. They also conduct research and development and do consulting and software development for non-Boeing customers. In the course of a year they may work on 100 different applications of mathematics. Steve joined Boeing after completing his doctorate in math at the University of Washington.
Boeing's Applied Mathematics group works with engineers on the design and manufacture of Boeing products, conducts applied research and development, and does consulting and software development for non-Boeing customers. This talk is about the types of problems and applications we deal with and the mathematical disciplines and other skills which are important. It's also about why it's fun to do industrial applied math, how the personal rewards are different from those in academic research, and how we handle the occasional exasperations of corporate life. There are some suggestions for a mathematician contemplating an industrial career.
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| 11-09-2009 10:30 - 12:30 | External | College of Science Meeting with President and Provost | | |
| 11-06-2009 12:00 | Applied Mathematics and Computation Seminar | Non-uniform Particle Size Explains Reduction in Filtration Rates with Transport Distance in Porous Media | Recent experimental studies of downward migration of polydisperse,
micron-sized particles in porous media revealed that the classical
colloid filtration theory fails to adequately predict irreversibly
attached particle concentrations. This failure stems from an observed
non-linear decrease
in the irreversible particle attachment with transport distance. Here we
present
a theoretical analysis based on particle size distribution that captures
the
key features of these experimental results. We find that irreversible
attachment
rates are influenced by the surface area of particles rather than mass
or volume, as expressed by a strong correlation between the irreversible
attachment
rate and the radius of the particles squared. Our analysis reveals
that a small fraction (less than four percent) of the poly-disperse
particle population
is responsible for a decrease in the average irreversible attachment
with transport distance. These particles have a larger average diameter
than
the rest of the population and, consequently, a higher than average
irreversible
attachment rate. Hence, the dependence of irreversible particle
attachment
on transport distance is a consequence of the non-uniformity of the
particle
sizes. | |
| 11-04-2009 12:00 | Number Theory Seminar | John H. Conway's view of Quadratic Reciprocity | | |
| 11-03-2009 16:00 | Probability Seminar | Random matrix theory | I will present a (very) brief introduction of quantities of interest in random matrix theory and why probabilists should care. I will then go on to explain a couple of ensembles I have worked on, and how I came to study random matrix theory via number theory. | |
| 11-02-2009 16:00 - 17:00 | Colloquium | Demonstrating Numerical Methods in the Classroom, and the Open Source Project FEMhub | In my experience, students of numerical methods enjoy the course
much more if they have a chance to see live demonstrations of the
algorithms in classroom (and they do their programming assignments
with less grumble). This may not necessarily mean additional workload
for the instructor. There are excellent free tools that can be run
from any web browser and they just work. One such example is the JODE
applet for ordinary differetial equations that I will show. The
only shortcoming of this applet is that it does not show how things
are actually done, which is essential for a numerical methods course.
Therefore, we have developed a web notebook based on Python, where
the students can see how the methods are implemented, they can check
them out, and they can implement their own algorithms and make them
easily available to everyone. We will demonstrate this using a few
elementary numerical methods such as the Taylor polynomial, rootfinding,
and polynomial interpolation.
The second part of the talk is specifically about finite element
methods (FEM). Nowadays, many students, researchers, and teams
develop their own FEM codes and make them freely available
via internet. However, it is virtually impossible to compare
their performance and results, or to collaborate on their
development, because of lack of a common platform and design
standards. The open source project FEMhub is aimed at changing
that. Its goals are to:
* Make it very easy to download and install many open source
FEM codes at once.
* Provide easy access to open source tools for geometrical
modeling, mesh generation, and visualization.
* Allow the user to define the problem only once and have it
solved by means of various codes for comparison purposes.
* Provide a browser tool so that all codes in FEMhub are
accessible through the internet, for people who cannot
or do not want to install the package, or do not have the
necessary CPU power.
* Make it possible to run realistic FEM computations from any
classroom equipped with internet access.
* Create a quality assessment procedure and legal certification
mechanism for open source FEM codes. This effort is a joint
project with NIST.
Currently, FEMhub contains the packages SfePy, LibMesh, Phaml,
FiPy and Hermes as FEM engines, lots of tools to ease visualisation
(matplotlib, mayavi, pyglet), and a web notebook which is based on
the Sage notebook. The development is very active and increasingly
more people are contributing on a voluntary basis. | |
| 11-02-2009 12:00 - 13:00 | Applied Mathematics and Computation Seminar | Computing with adaptive higher-order finite elements | In this talk I will briefly introduce our group, its motivation
and goals, some results that we obtained so far, and what we hope
to accomplish in the future.
In particular, I will explain why we believe that it makes sense
to design numerical methods that are independent of the partial
differential equations (PDE) solved. The current standard in my
field is to develop sophisticated error estimates and techniques
that only work (or work efficiently) for a narrow class of PDE.
In contrast to that, our methods work in the same way for any
PDE or multiphysics PDE system, and they can even be used in
other fields such as computer graphics or robotics. Examples
will be shown.
Main ideas of adaptive higher-order finite element methods
(hp-FEM) will be explained and their extremely fast, exponential
convergence will be demonstrated via live computations and
compared to the slow, algebraic convergence of traditional
low-order FEM.
I will mention the main ideas of our novel adaptive multimesh
hp-FEM that makes it possible to discretize a PDE system monolithically
(i.e., as if it was a single equation) while using individual
(optimal) meshes for all physical fields in the system. Numerical
comparisons to standard (single-mesh) hp-FEM will be presented.
We will show that even fluid flows can be handled as multiphysics
problems with velocity components and pressure approximated using
different meshes.
We will show that the multimesh hp-FEM makes it possible to design
simple and efficient adaptive algorithms for time-dependent PDE
problems based on dynamically-changing meshes. (Automatic adaptivity
for time-dependent problems is much more difficult than adaptivity
for statonary ones because of the necessity of mesh unrefinement).
I will explain the main idea and show several computational videos
related to various problems (flame propagation, thermally-conductive
flow, microwave heating, thermoelasticity, single and two-phase flow,
heat and moisture transfer in concrete, Gross-Pitaevski equation
of quantum physics, etc).
If some time is left, I will say a few words about our open source
project FEMhub whose objective is to create an open source distribution
of finite element codes with unified Python interface.
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| 10-30-2009 12:00 - 13:00 | Applied Mathematics and Computation Seminar | From Quantum Mechanics to Computational Materials Design | Computational materials design can be defined broadly as finding new
materials or even just candidate materials with the potential for desired
properties or property combinations using only computer simulations (in
silico).
Computational materials design is an attractive goal and is featured
prominently in all Department of Energy white papers on clean energy and
energy storage. However, until now there are only few examples of successful
applications of computational materials design. I will give a broad
overview, intended for non specialists, of the tools available in condensed
matter theory and materials science for use in computational materials
design, with a focus on mathematical and computational issues. Examples of
completed and ongoing computational materials design projects illustrate the
difficulties.
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| 10-28-2009 12:00 | Number Theory Seminar | John Conway's book, Chapter 1, Part 4 | | |
| 10-26-2009 16:00 | Colloquium | An algebraic operator approach to risk theory | We introduce an algebraic operator framework for solving high-order
integro-differential equations relevant in risk theory. The method relies on
transforming integro-differential equations into boundary value problems,
which are solved by symbolic techniques. Namely, the factorization of the
differential operator can be lifted to the level of boundary value problems,
amounting to iteratively solving first-order boundary problems. We illustrate
the method by analyzing functions of interest in risk theory. | |
| 10-23-2009 12:00 - 13:00 | Applied Mathematics and Computation Seminar | Spatial Discretization Issues in Ocean Circulation Models | Computational models of ocean circulation have applications ranging from global climate modeling to limited-area modeling of near-shore regions. This process requires the numerical solution of a system of partial differential equations describing fluid flow, as adapted to this situation. Solving such a system numerically requires discretizations both in space and in time. In the case of the horizontal spatial discretization, there are known deficiencies in some traditional approaches that are widely used in operational ocean circulation models. One such deficiency is that nonphysical grid-scale numerical noise can arise in certain situations. Another is a potentially inaccurate propagation of gravity waves and/or Rossby waves, depending on the discretization chosen and the relation between the grid resolution and a length scale known as the Rossby radius. A relatively new discretization method for partial differential equations, the discontinuous Galerkin method, has a potential of overcoming the above deficiencies.
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| 10-21-2009 12:00 | Number Theory Seminar | Can you see the values of 3x^2+6xy-5y^2 ? | | |
| 10-20-2009 16:00 | Probability Seminar | Intro to quantum probability and quantum computing III | In this third (and last in the series) talk we will cover quantum Fourier transform, the phase estimation procedure and quantum walks. | |
| 10-19-2009 16:00 | Seminar | The GTA Experience | Did you have a particularly successful teaching episode? Or do you have questions or concerns about your recitation sections? In this meeting you will have a chance to share your teaching experiences of the past few weeks. This will be an opportunity to share things that worked and solicit advice about difficulties or questions you may have. Join us in a guided discussion to address your issues and ideas related to teaching.
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