Application of Partial Differential Equations to Drum Head Vibration, Signal Transmission and Chemical Communication in Insects
American Journal of Applied Mathematics
Volume 4, Issue 4, August 2016, Pages: 169-174
Received: May 10, 2016; Accepted: May 28, 2016; Published: Jun. 17, 2016
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Constance Atieno Ojwando, Department of Industrial and Engineering Mathematics, Technical University of Kenya, Nairobi, Kenya
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The application of partial differential equations to drumhead vibration, signal transmission and chemical communication in insects has been investigated. This study looked at three cases in communication namely: a single drumbeat on an idealized circular drumhead being struck at the centre of the circular membrane; signal transmission in a Coaxial cable and finally concentration of pheromone in still air within a tunnel. The governing equation of Case I was solved using separation of variables method whereas Laplace transform was used to solve Cases II and III. MATLAB software was then used to obtain simulations on the solutions obtained from the three cases. It was concluded that vibrations of a circular drumhead as a result of a single drumbeat mainly concentrates around the centre of the membrane and tends to flatten out further away from the centre. Signal propagation decreases with increasing distance and so the shorter the cable the less signal strength is lost. Finally, concentration of pheromone can only last for a given time and distance.
Cable, Vibration, Signal, Idealized Circular Drumhead, Pheromone Evaporation
To cite this article
Constance Atieno Ojwando, Application of Partial Differential Equations to Drum Head Vibration, Signal Transmission and Chemical Communication in Insects, American Journal of Applied Mathematics. Vol. 4, No. 4, 2016, pp. 169-174. doi: 10.11648/j.ajam.20160404.11
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