My primary research interests are fluid mechanics and physical applied mathematics, with applications to soft matter physics and biological systems. I collaborate with experimentalists and enjoy the dynamic interplay between mathematical modeling and experimental validation, the goal being to develop a consistent theoretical framework capable of making testable predictions. To this end, I utilize a combination of modeling, analysis and numerical simulation tools to develop of a physical picture that informs novel laboratory experiments and scientific applications.

My research has recently been directed towards understanding hydrodynamic interactions in “active systems,” in which collections of objects both generate and interact with fluid flows. In particular, I have developed and analyzed mathematical models for the dynamics of droplets bouncing on a vibrating fluid bath, freely-translating flapping swimmers, and liquid crystal-like assemblies comprised of microscale biological components.

Prior to joining NJIT, I was a NSF Mathematical Sciences Postdoctoral Fellow at the Courant Institute of Mathematical Sciences, New York University.

- PhD, Mathematics, Massachusetts Institute of Technology, 2014
- MASt, Applied Mathematics & Theoretical Physics, University of Cambridge, 2009
- AB, Chemistry (minor in Applied & Computational Mathematics), Princeton University, 2008

- fluid-structure interaction
- pattern formation
- hydrodynamics of active matter
- collective behavior in biological systems

A goal of my research program is to understand the role of hydrodynamic interactions in mediating collective behavior in active matter systems, which are driven out of equilibrium by internal or external energy input. While there has been significant progress in understanding dry active systems, such as shaken granular materials, much less is known about active particles that are coupled through waves in a fluid.

For example, I have developed an integro-differential trajectory equation for droplets that bounce while walking on a vibrating fluid bath. These “walkers” have recently attracted considerable scientific interest, as they offer an intriguing visualization of wave-particle coupling on a macroscopic scale. I am also developing discrete-time delay equations for flapping swimmers that interact through their self-generated fluid flows, with a view to understanding how hydrodynamics can mediate schooling and flocking behavior in animal collectives. For both problems, I use a combination of mathematical analysis and numerical simulations to explain experimental observations and predict new phenomena that can be tested experimentally.

- J. Arbelaiz, A. U. Oza & J. W. M. Bush. Promenading pairs of walking droplets: Dynamics and stability.
*Physical Review Fluids*, 3: 013604, 2018. - A. U. Oza, E. Siéfert, D. M. Harris, J. Moláček & J. W. M. Bush. Orbiting pairs of walking droplets: Dynamics and stability.
*Physical Review Fluids*, 2: 053601, 2017. - S. Ramananarivo, F. Fang, A. U. Oza, J. Zhang & L. Ristroph. Flow interactions lead to orderly formations of flapping wings in forward flight.
*Physical Review Fluids (Rapid Communications)*, 1: 071201(R), 2016. - A. U. Oza & J. Dunkel. Antipolar ordering of topological defects in active liquid crystals.
*New Journal of Physics*, 18: 093006, 2016. - 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. - 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.