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Wolfram Summer School

June 24–July 14, 2018
Bentley University, Waltham, MA

Alumni

Nicholas Lucas

Class of 2013

Bio

In 2011, Nicholas Lucas began his college academic career as a part of the Miami Dade College Honors College Program, majoring in the field of Physics. In the Fall, he will be transferring to Georgia Institute of Technology to pursue a double degree in Applied Physics and Applied Mathematics. Nicholas is highly interested in mathematics, physics, astronomy, and computer science. During his tenure at Miami Dade College, Nicholas founded the Physics Club on his campus and led the organization as its president for the past two years. He has also worked with a team at Miami Dade College in scientific research on the topic of Magnetohydrodynamic Shock Heating of the Solar Corona. Nicholas' primary research interests are particle physics and deep space cosmology.

Project: Classes of Generalized Newtonian Three-Body Orbits

The three-body problem describes the motion of three bodies, given initial conditions for the mass, position, and velocity of the three at a given time. In the case of classical mechanics, this problem deals with the motion of three celestial bodies in accordance with one another. In 1887, Henri Poincare showed that there is no analytical solution to the three-body problem in terms of elementary functions.

Stephen Wolfram shows a case of this on page 314 of A New Kind of Science, where two bodies of identical mass follow an elliptical orbit and one idealized planet moves up and down through the plane of the orbit. This system is highly sensitive to initial conditions and a minuscule change in position of the idealized planet leads to very different trajectories.

My project is to study this problem and create a classification system for the trajectories, starting with low dimensional reduction to keep parameters low, beginning with one dimension, and then extrapolating to more general systems. Once the classification system is created, I will alter the force laws between the bodies to see how the classification scheme is altered.

Favorite Four-Color, Four State Turing Machine

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