Dealing with stiffness in low-Mach number flows Caroline Gatti-Bono (Lawrence Livermore National Laboratory)
October 3, 2008, 1:25pm, 570 Vincent Hall Video
(flv)
more...
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.
Virtual prototyping of hearing aids using numerical modeling and supercomputing Thomas H. Burns (Lawrence Livermore National Laboratory)
October 17, 2008, 1:25pm, 1:25pm, 570 Vincent Hall
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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 Starkeyâ€™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 Belma Dogdas (Merck Research Labs)
November 14, 2008, 1:25pm, 570 Vincent Hall
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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.
The DE Shaw group recruiting event. Contact Person: Elie Yuan
January 23, 2009, 1:25pm, 1:25pm, 570 Vincent Hall
Peridynamics: a case study for the role of an applied
mathematician at a national lab Richard B. Lehoucq (Computational
Mathematics and Algorithms Department, Sandia
National Laboratories)
February 6, 2009, 1:25pm, 570 Vincent Hall
more...
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.
Simple mathematics in biomedical applications Viktoria A. Averina (School of Mathematics, University of Minnesota)
February 20, 2009, 1:25pm, 570 Vincent Hall
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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 Yongmin Zhang (Capital Market Finance/Wells Fargo)
February 27, 2009, 1:25pm, 570 Vincent Hall
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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.
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.