Academic year 2006 - 2007

A Note on Stephan's Conjecture 77 by Chris Burns ('05) and Ben Purcell ('07) This paper proves a conjecture made by Ralf Stephan based on an exhaustive analysis of the On-Line Encyclopedia of Integer Sequences. The conjecture concerns the reduction of binary strings in a one dimensional version of the Same Game.


P.B. Kruskal ('05), J.J. Stanis, B.L. McNaughton, and P.J. Thomas
A binless correlation measure reduces the variability of memory reactivation estimates.

Academic year 2007 - 2008

Dan Hemberger ('07), Department of Astronomy,
Cornell University
James A. Walsh, Department of Mathematics,
Oberlin College

Symplectic integrators have proven far superior to Runge-Kutta type methods in approximating the long-term, qualitative behavior of solutions to Hamiltonian systems of ODEs. In this paper we discuss what a symplectic map is and why these maps serve as the basis for a very effective numerical integration scheme for Hamiltonian systems. In particular, we use a fourth-order symplectic integration algorithm to unearth fractal structure in phase space for the trilinear 3-body problem. We also provide a comparison with a fourth-order Runge-Kutta scheme. The surprisingly simple code for the symplectic integrator was written and executed in Matlab by the first author.





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Updated: November 29, 2007