FOR RELEASE: May 24, 2000
Contact: Blaine P. Friedlander Jr.
Office: (607) 255-3290
E-Mail: [email protected]
Compuserve: Bill Steele, 72650,565
http://www.news.cornell.edu
ITHACA, N.Y. -- At first glance, H(x,y) = (x^2 + c - ay,x) looks like an unassuming algebraic expression.
But to Karl Papadantonakis, it's one step to understanding the universe. The Cornell senior -- who is from Baltimore -- is on a quest to grasp this chaotic, dynamical equation known as Henon mapping.
Henon maps, which produce multi-colored, swirling and complex images, could assist physicists in understanding such things as turbulent fluid flows, or astronomers to predict the sometimes erratic, periodic motion of celestial bodies, such as asteroids, in precise, mathematical terms. Comprehending these dynamical systems is a daunting task, and mathematicians approach the challenge by stripping away some of the complexity.
As mathematicians now regularly master dynamics in one dimension -- in geometric shapes known as fractals, closely related to the highly patterned images known as Mandelbrot sets -- the next step is to understand the two-variable Henon mappings. And that's just what this senior seeks to do.
Papadantonakis will begin graduate studies next fall at the California Institute of Technology. He was introduced to the thrill of the mathematical hunt in a freshman honors class taught by John Hubbard, Cornell professor of mathematics. The professor, he says, "Really made linear algebra and calculus interesting."
At the time, Hubbard was trying to understand the dynamics of a Henon map as its parameters change. Papadantonakis joined the professor in unraveling the challenge and in that effort, he produced many graphical images, one of which appeared on the cover of Vector Calculus, Linear Algebra and Differential Forms: A Unified Approach, a 1998 textbook by Hubbard and his wife Barbara Burke Hubbard. He says: "That was fun, the book cover is featured on Amazon.com."
Beyond participating in the math department's Henon mapping work group, Papadantonakis has brought his math skills to the computing and engineering worlds. After enrolling in a two-semester electrical engineering course on developing computer chips, he and fellow senior Travis Mclesky designed one of the three integrated circuits that came out of the class: A scalable, multiplier chip that when fully developed could have significant implications for boosting computer speed.
"Multiplication is the key to arithmetic, and the speed of all processors depends on multipliers," Papadantonakis says. "I found a unique way to reduce delays by avoiding global data signals."
While Papadantonakis understands equations, both the simple and quadratical, he is the very model of a modern writer musical. A lover of jazz harmonies -- with affinity toward the flat 9th and sharp 11th chords -- Papadantonakis is not only an accomplished pianist, he also composes.
Before entering Cornell, he spent five summers learning to compose at the Walden School of Music in Dublin, N.H., and has participated in the annual Cornell Jazz Festival.
Such compositions as "Snapple Gap" -- an eight-minute piece replete with off-beat eighth notes, a dash of bossa nova, a pinch of ragtime, and a vibraslap (rattlesnake sound) for good measure -- can be found on his Cornell web site (www.people.cornell.edu/pages/kp30) in an MP3 file format. He says: "Though I was originally attracted to jazz because of its colorful harmonies, I now have a sense of jazz rhythm, and enjoy making my improvisation and written pieces very rhythmic."
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