Research Projects

Current Projects

Past Projects

Brown Pelicans at Half Moon Bay, taken by Garry Hayes

Collective Bird Flights

Birds are often found to fly collectively. In fact, many species of birds, such as pelicans, flamingoes and cranes, often fly in a linear formation. Focusing on the horizontal dynamics under the effect of heaving motion, we posed a math model comprising of a system of Delayed Differential Equations to describe interactions among the birds within the flock. Through simulating our model, we reproduce results which agrees qualitatively with past experimental findings from NYU Applied Math Lab. Currently, we are applying analytical and computational methods to study the flock stability of collective flights.

This work is in collaboration with Dr. Christiana Mavroyiakoumou, supervised by Professor Leif Ristroph.

Hydrodynamics of Finite-length Pipes at Intermediate Reynolds Numbers

How does water or beverage liquid flow from the lower tip to the upper tip when we are sipping through a drinking straw? A general answer is that the pressure difference generates the flow through the straw, but many different hydrodynamic laws exist to model such flow: for example, the Hagen-Poiseuille Law characterizes the laminar flow generated in a long thin pipe with flow rate scaling linearly with pressure drop; the Torricelli describes the flow generated through a short fat orifice with pressur drop scaled quadratically by the flow rate; and the full Navier-Stokes Equation can be applied to study the fully developed turbulent flow through a long fat tube. Hence, it remains to be figured out which flow regime does the flow through a straw fall into.

One may characterize the applicabilities for those laws by two dimensionless parameters: the Reynolds Numbers, which is proportional with the flow rate, and the aspect ratio of the length of a pipe over its effective radius. Yet, a survey within NYU Applied Math Lab shows that the data in terms of the parameters do not fall into any of those flow regimes, meaning that such flow has to fall into a completely new law. Hence, we carried out experiments to test the flow through steel pipes of various aspect ratios, and straws made of paper or plastic for drinking coffee, soda and bubble tea. Analyzing the data, we built a math model by breaking down the pressure drop through the development of the flow. Excitingly, this model can be applied to predict the hydrodynamic properties of a flow through a pipe in all four regimes, including the three well-studied regimes and the newly found one.

This project was in collaboration with Olivia Pomerenk, Simon Carrillo Segura and Fangning Cao, supervised by Professor Leif Ristroph.
From left to right: a plastic bubble tea straw, a plastic coffee straw, a paper coffee straw and a plastic soda straw, taken by Professor Leif Ristroph
I was testing the flow rate, taken by Professor Leif Ristroph
Left panel (from top to bottom): the Inflow-outflow Clepsydra pair, the Multi-step Clepsydra and the Sinking-bowl Clepsydra; right panel (from top to bottom): the Rotating Clepsydra and the modern water clock. (shared by Rugorim, sgss8, Maahmaah, hamptonauction and Antiquorum)

The Water Clocks

How did ancient people measure time passage? Many civilizations used various forms of fluid devices receiving or leaking water, generally called "Clepsydra," to keep time measurement: ancient Greek people used Outflow Clepsydras or Inflow-outflow Clepsydra pairs; ancient Chinese people used Multi-step Clepsydras; and ancient Persians used Sinking-bowl Clepsydras. Yet, when talking of time measurement, we are concerned about its robustness in time measurement - the pointers on a modern clock rotate at a constant angular velocity to enable linear measurement so that one can tell the time easily at any moment. Water, however, as indicated by the Navier-Stokes Equation, naturally performs nonlinear behavior, and thus we are interested in the particular geometry for those Clepsydras for which they could achieve robust measurements.