Department of Mathematics

The Florida State University

This Week in Mathematics

1 - 5 February 1999

Monday: 1 February 1999

No Graduate Student Seminar, 1:30 p.m., 204B Love Building

Special Colloquium Coffee, 3:00 p.m., 499 SCL
Special Colloquium, 3:30 p.m., 499 SCL

Mark Sussman, University of California at Davis

Computing Droplet Break-Up Using An Adaptive Coupled Level Set/Volume Of Fluid Method For Incompressible Two Phase Flow
We investigate the break-up of liquid droplets using an adaptive method for incompressible two-phase flow. These flows are characterized by steep density, and viscosity gradients, along with stiff surface tension effects at the free surface between the liquid and gas. Our method is designed to handle complex interfacial topology such as the break-up of liquid jets into droplets. We compare our method to experiments for the model problem of a drop hanging from a faucet. We apply our method to micro-scale jetting applications where it is important not only to model the motion of the free-surface, but also to accurately take into account the geometry of the jetting device. We present 2d axisymmetric and fully 3d results.

Tuesday: 2 February 1999

Algebraic Geometry Seminar, 2:00 p.m., 102 Love Building

Angela Vierling and Chia Stockwell, Florida State University

More Basics, and Local Properties of Curves

Applied Topology Seminar, 3:35 p.m., 104 Love Building

Mariel Vazquez, Florida State University

The Topology of Xer Site-Specific Recombination

Wednesday: 3 February 1999

(Real) Analysis Seminar, 2:30 p.m., 201 Love Building

Reading through "Oscillatory Integrals with Polynomial Phases" by Phong and Stein

Complex/Symbolic Seminar, 3:35 p.m., 102 Love Building

Theo Mora, Florida State University

Should I, Should I Not Use Groebner Bases in Cryptography?

Thursday: 4 February 1999

Algebra Seminar, 2:00 p.m., 104 Love Building

Eriko Hironaka, Florida State University

Lie Algebras and Representation Theory

Joint Mathematics and Statistics Colloquium, 3:30 p.m., 001 OSB

Monica Hurdal, Florida State University

Mathematical and Computer Modeling of the Human Brain
The visual cortex is often studied in investigations of the human brain because it constitutes a relatively large part of the cerebral cortex and conclusions regarding the visual cortex can be extended to other regions of the brain. Much of the information from the visual system is recognized as first being processed by the primary visual cortex and is then passed to other regions of the brain involved in more complex processing. If the head is modeled as three concentric spherical shells and neural sources of brain activity are modeled as dipoles, then a mathematical model which incorporates biophysical properties can be used to estimate the location of sources which generate a set of electrical potentials measured on the surface of the scalp. This model is known as dipole source localisation. Monte Carlo simulations and mathematical analysis verify the benefits of proposed improvements to the localisation model.
      The primary visual cortex has a retinotopic mapping in that one spot in the retinal visual field maps directly to a spot on the primary visual cortex. However, there is disagreement as to the amount of cortex that is allocated to the representation of central vision or other portions of the visual field. A mathematical formulation of this mapping will be presented. Then, a model which uses dipole source localisation and various brain research technologies, including magnetic resonance imaging and visual evoked potentials, will demonstrate how this mapping can be investigated non-invasively in humans. Finally, it will be shown how conformal flat maps of the brain can be created which offer several advantages over existing flat mapping approaches and will assist in comparing functional and anatomical information within and between subjects.

Topology Tea Time, 3:00 p.m., 204 Love Building
Topology Seminar, 3:35 p.m., 104 Love Building

Penelope Kirby, Florida State University

Splitting Manifold Approximate Fibrations

Friday: 5 February 1999

Colloquium Coffee, 3:00 p.m., 499 SCL
Colloquium, 3:30 p.m., 499 SCL

Chingwei M. Shieh, Pennsylvania State University

Parallel Numerical Methods for Unsteady Computational Fluid Dynamics and Computational Aeroacoustics
The direct numerical simulation of unsteady compressible turbulent flows at high Reynolds numbers remains beyond the capability of today's computers. This is because of the wide range of spatial and temporal scales present in the turbulent flow. If the radiated noise associated with the flow is also to be captured, the difficulties are increased. It is clear that additional progress will be based on harnessing the power of parallel computers. This involves continued improvements in hardware and operating systems as well as the development of more efficient algorithms designed for particular problems.
      In this colloquium, various issues that arise from the development of an efficient parallel algorithm in distributed memory architectures, such as the IBM SP-2, will be discussed. Parallel implementations of various common algorithms in CFD, with their merits and limitations, are presented. This leads to a review of the development of a parallel, high-order accurate, multiblock, and multigrid flow solver for cavity noise prediction. This solver uses a high-order accurate dual time-stepping algorithm that has shown promise in viscous aeroacoustic simulations. The accuracy of the solution obtained with this method is comparable to typical explicit CAA algorithms, but eliminates the stringent time step requirement set by the numerical stability of such schemes. Inner fictitious subiterations are performed with a four-stage Runge-Kutta method, with the implementation of multigrid to accelerate convergence. Unsteady flow field and sound generation from a two-dimensional cavity has been simulated in the subsonic flow regime. To account for the turbulent nature of the flow, the one-equation turbulence model by Spalart-Allmaras has been used in the analysis. The mechanisms for cavity noise generation are discussed.

Scientific Computing Seminar, 4:30 p.m., 200 Love Building

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