|
|
|
I have always had a strong inclination toward applied physics
research. Because of this, I was drawn to plasma physics and
controlled fusion research, which was the field of my doctoral thesis at
the University of Wisconsin, and subsequent research at the University
of Maryland, Florida Atlantic University, and James Madison University
up through the early 1980s. After that I became interested in
electronics applications and education, especially microprocessor
applications, and applied computational physics. Computation in
one form or another had been a major part of my physics efforts since my
college days in the early 1960s.
The year 1987 was a
watershed year in paleontology. That year, nuclear physicist Luis
Alvarez, and his geologist son, Walter, overthrew the paradigm of the
evolution of life on earth with their discovery of anomolously high
iridium levels in the layer of clay separating the Cretaceous rocks from
the Tertiary rocks, everywhere on the earth's surface--a layer known as
the K-T boundary. (Physics Today, July 1987). They theorized
that the iridium came from a huge asteroid which struck the earth 58
million years ago, killing off most of the species on earth, including
the dinosaurs, and all animals larger that 25 kg. The theory was
at first highly controversial, but was dramatically confirmed by the
discovery of the crater in Yucatan in 1991. (Science 252,
p377). In 1984 and '86, Raup & Sepkoski published
papers (Science 231, p833) suggesting that mass extinctions occurred
every 26 M years. Since several of these were caused by
asteroid impacts, it was natural to seek astronomical reasons for these
periodicities, and this was widely done. It seemed to me that one
reasonable avenue to explore was periodicities within the solar system
itself. With a view to this, I began looking for a better way to
perform long-term precise computations of the orbits of the bodies in
the solar system. I approached
this problem on several fronts. I new that Jack Wisdom, and
others, at MIT had developed a parallel processing system based on the
8086 and 8087. With the advent of very inexpensive tiny
microprocessors (the Philips 87C751) it seemed possible to creat a
massively parallel computer which would reside on a card in an IBM
PC. I wrote a grant proposal to Philips for 50 of these
processors, with a programmer, and began designing such a circuit, but
before the harware was finished, it was made obselete by the development
of the Pentium family. A second
approach was the development of better computation algorithms. I
developed a high-order approximation polynomial, which could generate a
polynomial which would exactly match known values of position, velocity,
and acceleration for a large number of points, (say 10), and could then
be used to extrapolate the orbit forward in time as much as one full
planet-year. As a test, we applied the system to a two-particle
system, for which the orbit was an ellipse, and the extrapolation worked
beautifully. However when we tried it with any larger number of
particles, it failed catastrophically. It turned out that the
problem was that the polynomial was not unique, and gave wildly
incorrect values BETWEEN the data points. The only polynomial
which converges to the right solution is the MacLaurin series. About this
time, two JMU mathematics faculty, Jim Sochacki and Ed Parker, were
studying chaotic behavior in population dynamics. As part of this
work, they discovered a modification of the Picard Iteration which they
were able to show efficiently generates the MacClaurin Series.
Their method is shockingly powerful and shockingly simple. With
their help, I applied it to the problem of celestial mechanics, and it
succeeded beautifully. Jim and Ed have applied their method to
over a hundred systems of differential equations, and it has yet to fail
to solve any of them. The method does have limitations. It
cannot integrate a trajectory through a non--integrable infinity (say a
black hole), and if the MacLaurin Series converges slowly, so will the
Parker-Sochacki method. I think they may have re-discovered
Dirichlet's Lost Method. In my opinion, for solving systems of
differential equations, the Parker Sochacki Method
is the most significant advance in the history
of mathematics. It has formed the core of my research ever
since. During the
summer of 1994, as holder of the La Rose Fellowship, I supervised
student Geoffrey Williams in a project to implement the use of a
Charge-Coupled Device at the Stokesville Observatory. In this
project we installed the CCD and a Macintosh computer on the telescope,
acquired images, successfully transferred the images to IBM PC's, and
wrote computer programs for both image processing and celestial
mechanics (orbit) calculations. The ultimate goal of this project
was asteroid tracking, so it also involved using the internet to acquire
asteroid orbital data from JPL and the Minor Planet Institute in St.
Petersburg, Russia. During
the spring of 1998, I was able to take a leave of absence and spent the
semester collaborating on celestial mechanics work with Samuel J.
Goldstein (now deceased) of the UVA Astronomy Department. In the meantime
I have also been carrying out some studies of analytic applications of
the Parker Sochacki method to calculating magnetic fields, which has
application in plasma physics and in magnetic resonance imaging.
This work is ongoing, but has resulted in several presenations at
American Physical Society meetings. I occasionally
also study and present work related to electronics, which arises from my
work as a teacher of the subject. This has included studies of
how the resistance of transformer windings affects the design of linear
power supplies. People
interested in my research can contact me via email or telephone at the
JMU Physics Dept. |