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Eddy Flow estimation Under various measurement paradigms


The aim of this project was to determine what type of measurement devices deployed in a 2D flow field was able to accurately determine the flow parameters of the eddy current. We considered moored obsevers which measure velocity and floaters only track position. Some of the parameters we have studied include the quantity of observers and the distribution of obsevers. We utilized simulations with the Kalman filter to determine which observation settings yielded accurate estimations of the current paramters modeled by a stochastic linear system.

Analyzing granular impact with computational topology


Granular media are a conglomeration of macroscopic particles, e.g. pebbles, rice, sand, or packaging materials. We were interested in their application in impact absorbation. One way of studying impact in granular media is to examine the force network that propagates throughout the system of particles. A better understanding of the force propagation can help us determine the relation between the material properties of the granular media and its ability to absorb the shock from impact. Our goal was to study the force networks using persistent homology, a computational method which reduces a snapshot into its topological features. Examining each contact between particles and for each video frame is very computationally expensive. We instead reduce the each frame to a low-dimensional summary of its topology and proceed with the analysis.

Domain decomposition methods for the Helmholtz Equation


Domain decomposition methods (DDMs) are a class of parallel iterative methods for approximating solutions to partial differential equations. In this project, the goal was to add to the class of DDMs specifically for the Helmholtz Equation.

Domain decomposition methods for the Monge-Ampere Equation


In this project, the goal was to study domain decomposition methods (DDMs) for the fully nonlinear Monge-Ampere equation.

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