Applied Mathematics

These were group research projects in my first and second summers in Bard College (at the Cognitive Science lab).

Mathematical Acoustics

mindlin-model-output2 mindlin-model-output1

Analysis of various mathematical models that describe different kind of oscillations produced in a bird song.

I wrote an RK4 differential equation solver in C to verify and analyze a mathematical model of bird songs. Using Mathematica, several other models of song production were explored and the effects of change of parameters were demonstrated. Using AUTO and XppAut, bifurcation diagrams for a few models were produced. The main thrust of the project was to understand interesting and chaotic oscilation patterns that may occur in bird songs.

Experimental Efforts

expt-setup fft-frequencies

Investigation of the onset and dependency of oscillation in a bird song upon changing several physical parameters such as the length and thickness of a bird’s vocal tract.

We built an artificial syrinx (vocal tract) using latex material and carried out our sound measurement experiments using a custom-built setup. The data from the experiment was collected using a data logger and a LabView interface I created, and analyzed using some code I wrote in Mathematica.

microscope-imaging  pressure-reading

We have also used Microscopy imaging to study the behavior of artificial vocal membranes under different amount of forces.

Resources:

Mathematica Program for Exploring the Laje-Gardner-Mindlin Model

Poster in BSRI Conference

Experiment Setup and Sample Data

Back To Projects

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