I am currently a NSF Mathematical Sciences Postdoctoral Fellow at the Courant Institute of Mathematical Sciences. Broadly speaking, I am a theorist interested in fluid mechanics and nonlinear dynamics, with applications to soft matter physics and biology. My research utilizes a combination of analytical techniques and numerical simulations, and I enjoy collaborating with experimentalists.
In June 2014, I graduated with my PhD in applied mathematics from MIT. My co-advisors were John Bush and Ruben Rosales. I was supported by a combination of NSF and Hertz Foundation graduate research fellowships.
My undergraduate degree is from Princeton University. I then obtained a Master's degree from the Department of Applied Mathematics and Theoretical Physics (DAMTP) at the University of Cambridge, while supported by the Churchill scholarship.
S. Ramananarivo, F. Fang*, A. U. Oza*, J. Zhang & L. Ristroph. Flow interactions lead to orderly formations of flapping wings in forward flight. Submitted, 2016.
A. U. Oza & J. Dunkel. Antipolar ordering of topological defects in active liquid crystals. New Journal of Physics (in press), 2016.
L. D. Tambasco, D. M. Harris, A. U. Oza, R. R. Rosales & J. W. M. Bush. The onset of chaos in orbital pilot-wave dynamics. Submitted, 2016.
pdf M. Labousse, A. U. Oza, S. Perrard & J. W. M. Bush. Pilot-wave dynamics in a harmonic potential: quantization and stability of circular orbits. Phys. Rev. E, 93: 033122, 2016.
pdf J. W. M. Bush, A. U. Oza & J. Moláček. The wave-induced added mass of walking droplets. Journal of Fluid Mechanics (Rapids), 755: R7, 2014.
pdf A. U. Oza, Ø. Wind-Willassen, D. M. Harris, R. R. Rosales & J. W. M. Bush. Pilot-wave hydrodynamics in a rotating frame: Exotic orbits. Physics of Fluids, 26: 082101, 2014.
pdf cover image A. U. Oza, D. M. Harris, R. R. Rosales & J. W. M. Bush. Pilot-wave dynamics in a rotating frame: on the emergence of orbital quantization. Journal of Fluid Mechanics, 744: 404-429, 2014.
pdf cover image A. U. Oza, R. R. Rosales & J. W. M. Bush. A trajectory equation for walking droplets: hydrodynamic pilot-wave theory. Journal of Fluid Mechanics, 737: 552-570, 2013.
Slides from a talk given by Peter Shor on some joint work: "Structure of unital maps and the asymptotic Birkhoff conjecture." Steklov Mathematical Institute, 2010.
pdf A. U. Oza, A. Pechen, V. Beltrani, K. Moore & H. Rabitz. Optimization search effort over the control landscapes for open quantum systems with Kraus-map evolution. Journal of Physics A 42: 205305, 2009.
Yves Couder and coworkers have discovered that millimetric droplets bouncing on a vertically vibrating fluid bath exhibit behavior analogous to single-slit diffraction, double-slit interference, tunneling, orbital quantization, and orbital level-splitting. This rich, highly nonlinear dynamical system represents the first macroscopic realization of a pilot-wave dynamics. On the theoretical side, our goal is to analyze and develop a pilot-wave theory for the walking droplets with a view to rationalizing the quantum-like phenomena.
During my PhD, I developed an integro-differential trajectory equation to model the horizontal motion of the walking droplet in the absence of boundaries. The model allowed us to rationalize the observed orbital quantization, and predicted several phenomena since observed in laboratory experiments (conducted by Dan Harris, another graduate student).
Here is a nice video by Dan Harris that summarizes some of our research.
During the 2013-2014 academic year, I supervised undergraduate student Kirin Sinha as part of the MIT Undergraduate Research opportunities Program (UROP). She continued our investigation on the orbital stability of walking drops in a rotating frame, and studied how the stability characteristics depend on the fluid parameters (e.g. density, viscosity, surface tension, etc.) She is currently a Marshall Scholar at the University of Cambridge, UK.
During Summer 2013, I supervised undergraduate student Kristin Dettmers as part of the MIT Summer Research Program (MSRP). She conducted a numerical investigation of walking droplets in a Coulomb potential, with a view to obtaining a hydrodynamic analog of a hydrogen atom. She is currently a graduate student in the Department of Mathematics, MIT.
In Spring 2016, I was the course instructor at NYU for MAT 122.003: Calculus II, an undergraduate course in calculus.
In Fall 2015, I was the course instructor at NYU for MAT 122.007: Calculus II, an undergraduate course in calculus.
In Summer 2014, I was a course instructor at MIT for 18.085: Computational science and engineering I, a graduate course in computational science.
In Spring 2013, I was the recitation instructor at MIT for 18.04: Complex variables with applications, an undergraduate course in complex analysis.
In Summer 2007, I was a tutor for single-variable calculus at the Freshman Scholars' Institute (FSI) at Princeton.