# My Research

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### Work I've Done

My Trident Paper: Stability of Nonlinear Swarms on Flat and Curved Surfaces

My Honors Paper: Limit Behavior of Swarms of Coupled Agents

My collaboration with the Naval Research Lab: The Dynamics of Interacting Swarms

My Google Scholar profile

You can watch my Trident presentation below:

### Trident Project

In 2017, I received the Trident Scholarship from the Naval Academy. The Trident Scholarship allowed me to devote 24 credit-hours (total) towards research. My advisor, Prof Kostya Medynets, and I chose to look at mathematical swarm models. In particular, we were interested in the parabolic potential model, a model for swarms based on spring-like attraction. In a system of \(N\) agents, each of which has position vector \(r_i\), the parabolic potential model has the following equation of motion:\[\ddot{r}_i=(1-\lvert\dot{r}_i\rvert^2)\dot{r}_i-(r_i-R)\] where \(R\) is the center of mass of the system, given by\[R=\sum_{i=1}^Nr_i\] Expected limit behavior is pictured below:

Over the course of a year, we proved several new results about the stability of this system. We were fortunate to observe some behavior that has never been seen before.

Prof Medynets has his own website, which you can see here.

### Work at NRL

In the summer of 2017, I worked at Naval Research Laboratory in Washington, DC with Dr. Ira Schwartz. Primarily, I researched swarm collisions in systems subject to delay. We summarized our findings in a report, titled "The Dynamics of Interacting Swarms". It is available on the ArXiv.

### Mathematica, ROS, and Gazebo Integration

In the course of my work on swarming, I have looked at applications to UAVs. I spent some time getting differential equation models (simulated in Wolfram Mathematica) to drive virtual drones (simulated in Gazebo) using ROS, the Robot Operating System to interface between the two. A video of my work is available on Youtube:

### Awards

In 2018, I received the Julian Clancy Frazier Award for excellence in Mathematics.