The Full Story
Research
In my PhD, I want to develop predictive mathematical models that will improve the development of medical devices and the treatment of disease. In terms of mathematical tools, I am particularly interested in partial differential equations. My research interest was born through my interest in biological systems and their ability to be quantified using mathematics.
Current Research
University of Arizona
Currently, I am interested in fluid dynamics and the immersed boundary method with applications in mathematical biology. Specifically, I research nematocysts, the stinging cells of cnidarians, as a natural system that can inform the design of microinjectors for targeted drug delivery.
Past Research
Brown University REU
Advisor: Bjorn Sandstede, Alexandria Volkening
Fellow through the National Science Foundation at Brown University.
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Extended an agent-based model of pigment cells on Zebrafish, allowing pigment cells to form into well-known stripe pattern in a different domain with different initial conditions.
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Refactored code for improved runtime efficiency, wrote new functions for the extension, and created handles for separate parameter testing in MATLAB.
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Applied Euler method using matrix setup to numerically simulate stretching of pigment cells.
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Explored different parameter regimes to evaluate for stability of the model.
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Ran a parameter sweep to assess ideal initial conditions and coefficients for differential equations that simulated interaction of pigment cells.
Wake Forest University
Honors Thesis
Advisor: John Gemmer
I did an expository thesis broadly studying reaction diffusion equations.
• I am studied a modified version of the planar Belousov-Zhabotinsky reaction.
• I developed a finite difference code that can simulate the evolution of this system.
• Beyond numerical simulations, I analytically explored different parameter regimes in which not only spots but spiral waves, stripes and other patterns emerge. Specifically, by explicitly calculating the parameter values for which a Turing bifurcation occurs I found the parameter regimes when specific patterns emerge.
Wake Forest University
URECA Fellow
Advisor: John Gemmer
Fellow through the Undergraduate Research Experience and Creative Activity (URECA) grant at Wake Forest University.
• Developed a non-linear differential equation model of the vestibular system and used qualitative methods to analyze the behavior.
• Applied techniques from linear algebra, multivariable calculus, projective geometry, and differential equations to study this problem.
• Conducted qualitative analysis of the model in a Mathematica script.
• Verified results by solving the model numerically using ODE45 in MATLAB.
