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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.
Foluso Ladeinde (SUNY Stony Brook)
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.
Minorities
and Applied Mathematics - Connections to Industry and Government
Laboratories
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