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Talk Abstract

IMA Career Workshop in Computational Science and Enginerring

IMA Career Workshop in Computational Science and Enginerring

**Isaiah M. Blankson**
(Senior
Scientist/Technologist NASA Glenn Research Center, Cleveland,
OH)

**Passive Millimeter-Wave Imaging with Superresolution: Application
to Aviation Safety in Extremely Poor Visibility**

Research efforts, aimed at designing a prototype passive millimeter
wave imaging system composed of a phased antenna array and the
use of super-resolution for image reconstruction, are outlined.
Millimeter waves are much more effective than infrared in poor
weather conditions such as thick fog, clouds, snow, dust-storms
and rain. Also, images produced by passive millimeter waves
have natural appearances. The ultimate goal is to develop a
Millimeter Wave (MMW) Radiometer operating at 95 GHz, capable
of High Resolution Imaging (Super-Resolution) with application
to **aviation safety**. This research is being conducted
jointly between NASA and the Physics Faculty at Moscow State
University. The Radiometer development effort has two major
aspects, both strongly interdependent. One involves the development
and code implementation of real-time **Image Recovery**,
including Radiative Transfer formulation, simulation of Electromagnetic
Interactions with media, and Regularization and Reduction Techniques
(Theoretical). The other involves **Radiometer Design**,
including Antenna Simulations, Manufacturing, Testing and Radiometer
Field Testing (Engineering).

The application of scanning phased arrays for passive millimeter-wave imaging (PMMW) is examined within the framework of Inverse Problem Solutions and Super-resolution. Optimum mathematical processing is used to exceed the physical limit of resolution. Details of the ill-posed inverse problem and the need for regularization techniques (e.g. Tikhonov) will be presented. The contributing sources of noise in measurements are examined and the correlation to passive imaging systems is considered. Also the conditions for super-resolution and the corresponding augmented regularization technique (e.g. Tikhonov- Pytiev Reduction) will be addressed.

**James
Curry**
(University of Colorado)

**My
Education at SUN Microsystems**

Three fundamental differences between being a faculty member at a public higher education institution and a private corporation are that at a higher education institution you are, in a strong sense, a public figure; faculty members who forget that they hold the public trust when dealing with students, other faculty and staff often go astray.

A second difference is that in corporations there is a clear chain of authority that allows companies to move with agility. When I contrast that with some of the processes in place at universities it is clear that there are many different time dependent controls, sometimes positive and sometimes negative, that differ by several orders of magnitude that are at play at universities.

A third difference is that folks at corporations are seemingly rewarded for their efforts when those efforts are consistent with the over-all strategic interest of the company. The reward system at universities is both faculty dependent and faculty driven and can be internally consistent but not responsive in needed ways.

A consequence of my stay at Sun is that I now have new language and thoughts to bring to back to my department and my University more generally.

**Friendlier Flying: Stochastically Modeling Airport Arrival
Capacities During Inclement Weather**

Inclement weather reduces an airport's arrival capacity, which results in the institution of a ground delay program (GDP). The stochastic nature of weather precludes determining arrival capacities deterministically. In this talk, I will present statistical models that I developed using a seasonal clustering technique. These models are used to estimate capacity scenario distributions based on historical data from a given airport and are required inputs into a class of stochastic ground holding models that determine optimal ground delay to assign to incoming flights.

**High-Order Computation of Selected Aeromechanic and Propulsion
Problems**

The use of high-order schemes in the analysis of three model problems in aeronautics is presented. In the first problem, a combination of the flamelet method and the large eddy simulation (LES) technique is used to analyze a model of the aircraft turbine engine combustor. The LES part of the computation uses the sixth-order compact schemes for differencing and a tenth-order method for filtering. The ultimate goal of this project is to produce an appropriate procedure for predicting combustion instability, which is a phenomenon that could compromise the structural integrity of aircraft engines. In the second problem, a similar combination of numerical schemes as mentioned above, is used to compute the delicate pressure fields associated with acoustic scattering and radiation from the X24C re-entry vehicle. This project has both civilian and military applications. For the third problem, the high-order, essentially non-oscillatory (ENO) procedure is used to analyze the effect of upstream turbulence intensity on the aerodynamic performance of aircraft engine turbine blade. The various computations above use a multi-stage Runge-Kutta procedure for time integration and are carried out on the SGI 2100 machine, to take advantage of its parallelization capability. The aeromechanic and combustion studies were sponsored by the Air Force, whereas the turbomachinery project was funded by the National Science Foundation.

**The
Role of Computational Mathematics in Industrial Problems**

Modeling and simulation has taken on an increasingly important role in solving today's industrial problems. As the computational power available has increased, engineers and scientists can now model problems on PC's to a level of detail only capable with supercomputers 10 years ago. With these increasingly sophisticated models, scientists are now capable of solving problems in optimal design and control and are starting to understand issues in quantifying the uncertainty in simulation results. In this talk, I will give an overview of several problems of interest in real-world applications and discuss several approaches for solving them.

**Computing Boundary Fitted Grids for Effective 3D Visualizations
in a Digital Library**

High level mathematical functions are important for solving many problems in the mathematical and physical sciences. The Airy functions Ai and Bi provide closed form solutions to field equations that arise in quantum mechanics, optics and electromagnetism. The gamma and beta functions provide the starting point for the computation of more complex functions such as the Riemann zeta function and others that occur in number theory, probability theory and mathematical physics. Although visualization can help one gain a deeper understanding of these ``special functions'', the singularities, poles and other complexities which make their computational domains irregular, discontinuous, or multi-connected can make the creation of effective visualizations quite difficult. The author will examine the use of numerical grid generation techniques to tackle this problem and show how this research is being used to create dynamic interactive 3D visualizations for a massive project at the National Institute of Standards and Technology (NIST) called the NIST Digital Library of Mathematical Functions.

**An
IMA Computational Science Tutorial with Applications to the
Czochralski Crystal Growth Process**

Computational Science is an emerging multi-disciplinary area of research that encompasses applications, applied mathematics, numerical analysis, and computer science. Using tools and techniques from computational science, one can develop powerful numerical simulations of real world phenomenon. However, going from application to computational results, via computational science, requires: knowledge of the application area; mathematical modeling; numerical analysis; algorithm development; software implementation; program execution; visualization of results; analysis of results; and code validation. This tutorial will demonstrate how each of these requirements are met in the case of simulating crystal growth processes.

**How to get a smoother ride on BART**

Although transit districts such as San Francisco's Bay Area Rapid Transit (BART) have controlled their trains automatically for decades, the control systems have limited capability in terms of train position location and speed control. The advent of modern radio-based train control systems provide a new domain for applying optimization techniques. While heuristic control algorithms improve performance for limited situations, optimization techniques will more broadly address the need for control enhancement. We consider the problem of smoothing train operations in two situations, when two trains are traveling close together and during delays. In addition, we present and evaluate several objective function formulations. Initial results indicate the applicability of using interior-point methods to enhance train control systems.

Material from Talks

Minorities and Applied Mathematics - Connections to Industry and Government Laboratories