2006 Student Research Conference:
19th Annual Student Research Conference

Science

Markov Processes and the Simple Harmonic Oscillator in Discrete Space
James Park* and Adam Bezinovich
Prof. Taner Edis, Faculty Mentor

Markov processes have been very well studied in applied mathematics, but generally a constant transition matrix is assumed. Many standard tools of analysis cannot be applied when the transition matrix is non-constant. Computer simulations can be a useful tool for their study. We have been studying a model of the simple harmonic oscillator in discrete space, which is such a Markov process. In an attempt to discover long term trends and behavior, simulations were carried out over an extended period of time. Since the transition matrix in this case is randomly changing, the amplitude of the oscillation does not appear to exhibit any sort of stable average over time. This is expected with a dynamic transition matrix.

Keywords: discrete space, markov, harmonic, oscillator

Topic(s):Physics

Presentation Type: Oral Paper

Session: 7-2
Location: VH 1416
Time: 8:30

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