Mathematics, Computer Science, & Physics, 2011
  • Mathematics, Computer Science, & Physics, 2011

     

     

    Fibonacci and Joplin: The String from Sequence to Syncopation
    Jeff Morckel
    Faculty Mentor: Keith Wilkinson

    The mathematical sequence known as the Fibonacci Sequence is thought to have an aesthetic appeal; often, the sequence is used to describe properties of music. The music of many famous composers reflects the Fibonacci Sequence, and this study shows that American composer Scott Joplin is part of that list. My analysis is based on an article written by Kevin Jones, a music professor in England. In this analysis, the notes of Joplin’s ragtime music are characterized as being unaccented syllables or accented syllables. Multiple pieces by Joplin were analyzed. Joplin’s music was selected because of the highly syncopated nature of the music. The syncopation causes stress to be placed on weak rhythmic pulses, providing for an uneven pattern that has a particularly high degree of aesthetic appeal. It was shown that the syllable patterns of Joplin’s ragtime music occasionally produced a Fibonacci sequence based on the interaction of syllables patterns in the right and left hands. These examples put Joplin in a class with composers such as Mozart, Haydn, and Beethoven, whose music is shown to have properties similar to the Fibonacci sequence. Joplin’s Fibonacci connections are based on rhythmic structure, unlike the other composers on the list.

     

     

    Impedance Spectroscopy: Research toward the Development of Standard Protocols and Implementation of Lithium Ion Conductivity
    Rachel Yoho
    Faculty Mentor: Patrick Shields

    The development of alternative energy technologies necessitates the evaluation of charge transport properties of diverse materials. In order to meet this growing demand, impedance spectroscopy (IS) has become an increasingly desirable method of materials analysis. Impedance spectroscopy is typically performed to find only the resistivity of the material and the rest of the spectrum is ignored. The goal of this research was two-fold: first, to develop standard procedures for electrode preparation to generate reliable data, and second, to investigate the low-frequency ranges in order to gain more information from the data already being collected. Electrode materials tested included: brass, titanium, stainless steel 316, gold sputtered titanium, and gold electroplated stainless steel 316. A standard method for electrode preparation was developed involving electropolishing stainless steel 316, nickel electroplating, and gold electroplating. A noise-blocking box was also constructed to shield the cell from environmental electromagnetic noise during data collection. The standard procedures developed produce reliable gold surfaces that have the potential to become industry standards with further materials analysis.