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.

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.

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 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.

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.

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.