Dealing with stiffness in low-Mach number flows Video
(flv)
Abstract: Numerical simulation of
low-Mach number flows presents challenges
because of the stiffness introduced by the disparity of time
scales
between acoustic and convective motions. In particular, the
acoustic,
high-speed modes often contain little energy but determine
the time step
for explicit schemes through the CFL condition. A natural
idea is
therefore to separate the acoustic modes from the rest of the
solution
and to treat them implicitly, while the advective motions are
treated
explicitly or semi-implicitly.
In this talk, we present a numerical allspeed algorithm that
respects
low-Mach number asymptotics but is suitable for any Mach
number. We use
a splitting method based on a Hodge/Helmholtz decomposition
of the
velocities to separate the fast acoustic dynamics from the
slower
anelastic dynamics. The acoustic waves are treated
implicitly, while the
advection is treated semi-implicitly. The splitting mechanism
is
demonstrated on two applications. The first application is a
combustive
flow, where Euler equations are completed by an enthalpy
evolution
equation. Then, we present a stratified atmospheric flow
where the
presence of gravity waves adds one more degree of complexity.
Benchmark
results are presented that compare well with the literature.
October 17, 2008, 1:25pm, 570 Vincent Hall Thomas H. Burns (Director, Applied
Technology & Research, Starkey Labs, Inc.)
Virtual prototyping of hearing aids using numerical
modeling and supercomputing Video (flv)
Abstract:
In an effort to efficiently manufacture quality products,
numerical models and empirical measurements are used to predict
(virtually) the performance of a hearing aid. Finite element
analysis is used to study multi-physics processes such as
thermo-mechanically induced stress due to heat flow from
soldering, acoustic and structural interactions due to
transducer vibration, and mechanical shock failure due to drop
testing. Following a synopsis of hearing-aid anatomy, the
presentation will show numerous animations depicting results
from the virtual prototypes.
Dr. Burns received a Ph.D. in engineering acoustics from Penn
State, specializing in signal processing of acoustical
holography measurements. He joined Starkey Labs in November of
1999, following periods as a consultant in concert hall
acoustics at Kirkegaard Associates, and a senior design
engineer of condenser microphones at Shure. Currently, he is
the Director of Starkey’s Applied Technology and Research
Group, and serves on the Hearing Aid Measurement Standards
committee for ANSI Bioacoustics (S3/WG48). By day, he directs
an advanced development team of engineers at Starkey. By
night, he changes diapers and lulls his kids to sleep by
playing Chopin Nocturnes on his concert grand.
Image registration with applications in medical imaging
towards drug
discovery and development
Abstract: Imaging can be used to
develop effective biomarkers to provide
information on diseases and assessing therapeutic effects. In
the past
decade, several imaging modalities have been used for early
detection of
drug response. Although many imaging techniques are available
to the
medical community, no single method provides all the necessary
information. For instance structural MR and CT imaging
modalities
provide anatomical information whereas PET and optical imaging
can
provide functional information. Often, it is useful to combine
complementary information from different modalities, through a
technique
known as image registration. In addition, statistical
characterization
of morphological differences within and between groups or
automated
identification and labeling of specific anatomical structures
with an
atlas requires image registration. Therefore it is essential to
understand image registration techniques to enable their
effective use
in imaging applications. In this talk, I will describe recent
advances
in image registration and provide examples of how it is being
used in
medical imaging towards drug discovery and development.
January 23, 2009, 1:30pm, Lind Hall 305 [note room change] The DE Shaw group
The DE Shaw group recruiting event. Contact Person:
Elie Yuan
.
February 6, 2009, 1:25pm, 570 Vincent Hall Richard B. Lehoucq (Computational
Mathematics and Algorithms Department, Sandia
National Laboratories) http://www.cs.sandia.gov/~rlehoucq
Peridynamics: a case study for the role of an applied
mathematician at a national lab
Abstract:
The purpose of my talk is to introduce peridynamics as a proxy
for discussing the role of an applied mathematician at a
national lab. The peridynamic balance of linear momentum
replaces the local source term of the classical continuum
balance law with a nonlocal term. The source term represents
internal force interaction, and in peridynamics is represented
by an integral operator that sums internal forces separated by
a finite distance. This integral operator is not a function of
the deformation gradient, allowing for a more general notion of
deformation than in the classical theory that is well aligned
with the kinematic assumptions of molecular dynamics. I review
some of the mathematical results achieved during the last two
years.
February 20, 2009, 1:25pm, 570 Vincent Hall Viktoria A. Averina (School
of Mathematics, University of Minnesota) http://www.tc.umn.edu/~aver0050/
Simple mathematics in biomedical applications
Abstract: One will rarely find a
job listing from a biomedical company
directly asking for a mathematician. Yet many biomedical
applications
ranging from research to manufacturing require a mathematical
aptitude.
The restrictions imposed by physical, clinical and human
factors call
for mathematical solutions to be as simple as possible. I
will give a
brief background introduction to the applications and
describe several
problems in no mathematical depth whatsoever.
American option pricing models and obstacle problems Video (flv)
Abstract: We first give a brief
overview of American option pricing models and numerical
methods. We treat American option models as a special class of
obstacle problems. Finite element formulation is introduced
together with error analysis of numerical solutions. Some
interesting properties about sensitivity of the option price to
the payoff function are proved. We also give a criterion for
the convergence of numerical free boundaries (optimal exercise
boundaries) under mesh refinement. Some future research plans
will be discussed.
Bio:
Yongmin Zhang is a risk management consultant at Wells Fargo.
Prior to the current position, he was a lead research analyst
in Capital Market Research Group of Washington Mutual (now part
of J. P. Morgan). His area is in fixed income and mortgage
analysis. Before he joined this group, he was an assistant
professor at State University of New York where he did research
in turbulent flow and American options with more than thirty
publications and taught numerous courses in applied mathematics
and statistics. Prior to this appointment, he was a research
scientist at SUNY Research Foundation. He was a co-principle
investigator for various grants from US Department of Energy.
He holds his Ph.D. in Applied Mathematics from University of
Chicago.
April 24, 2009, 1:25pm, 570 Vincent Hall Vanessa Lopez (IBM T.J. Watson
Research Center) Computing invariant solutions of PDEs with symmetries
Abstract: We consider the problem
of numerically computing solutions of evolutionary nonlinear
partial differential
equations (PDEs) with
a finite-dimensional group of symmetries. Specifically, we look
for solutions that are fixed by elements of
the equations' symmetry
group. The latter class includes time-periodic solutions. We
work with the complex Ginzburg-Landau equation
(CGLE)
in one space dimension, which has a 3-parameter group of
symmetries generated by space-time translations and
a rotation
of the (complex) amplitude. The spectral-Galerkin method used
to discretize the PDE will be described, along
with the approach
for solving the resulting system of nonlinear algebraic
equations which allowed us to identify multiple new
solutions in a chaotic
region of the CGLE.
Due to the relatively small number of unknowns considered
(2,000 - 3,000 after discretization), it was
possible to use a direct
method for linear systems as part of the process for solving
the nonlinear system. However, for problems
with a large
number of unknowns, iterative methods for linear systems are
required. We will conclude our talk with a
discussion on the use
of such methods for solving these types of problems.
May 1, 2009, 1:25pm, 570 Vincent Hall Paul Rejto (Directory of
Computational Biology, Oncology Research
Unit, Pfizer)
Computational challenges in cancer therapeutics Video (flv)
Abstract: Recent advances have
dramatically advanced our understanding of cancer
at the molecular level. In turn, new therapeutic agents that
target
specific molecular defects in cancer have been developed,
though cancer
remains a significant health threat. Following an introduction
to the
molecular biology of cancer, a statistical approach to
distinguish
driver mutations from passengers based on non-random clustering
will be
discussed. Next, approaches to pharmaceutical intervention will
be
reviewed and an integrated approach to link targeted
therapeutics with
specific patient populations will be shown. Throughout, open
questions
will be presented with a focus on problems of potential
mathematical
interest.
