Picture: Mean First Passage Time of a Diffusive Particle in a Circular Domain with Disk Exits

Advisors: Dr. Alan Lindsay

My Role: Graduate Researcher

This project aimed to develop an algorithm to calculate MFPTs of particles with different geometric exits to benchmark derivations and analytical calculations using asymptotic analysis.

Paper 1 Preprint: https://arxiv.org/abs/2506.17173

Picture: 3 Inclusion Propagation of Director Field on a Sphere with 3 +1 Inclusions

Advisors: Dr. Hossein Firouznia and Dr. Scott Weady

My Role: Graduate Researcher

This project aimed to develop an algorithm based on surfacefun to model lamin fibre networks under the nuclear envelope.

Picture: Configuration Space of a Needle Swimmer

Advisors: Dr. Jean-Luc Thiffeault

My Role: Graduate Researcher

This project aimed to develop an algorithm for visualizing the configuration space of microswimmers in lattice-confined environments, alongside creating a passive Brownian particle model for various swimmer geometries. Analytical calculations alongside numerical validation, were computed to determine turn times and mean exit times for the swimmers. The study revealed that turn times follow a Poisson process, with wider swimmers exhibiting longer turn and exit times as anticipated. Trajectories of elliptical and needle swimmers were analyzed, to show the covariance for a needle swimmer in the xy-direction is non-zero as compared to an elliptical swimmer.

Advisor: Dr. Yukun Yue

My Role: Co-Advisor and Investigator

We developed a scheme for the Cahn-Hilliard-Navier-Stokes system by using both the Scalar Auxilliary Variable method along with a projection method to obtain numerical results. We then compared our results to previous works to get a sense of how the system is behaving. 

Advisor: Dr. Skylar Grey

My Role: Co-Advisor and Investigator

Prescription stimulants such as Adderall are sometimes used as study aids because of their reputation for improving focus in people with ADHD. Current research suggests that prescription stimulants are not effective study aids for those without ADHD, however the medications are highly addictive. We built a mathematical model of the SEIR type to study the spread of stimulant use among college students. Due to the lack of data available on this topic, we collected our own data using an IRB exempted survey methodology. We used the next-generation matrix method to compute the equation for R_0, which we will calculate once we have finished parameter estimation. We performed a sensitivity analysis of our model to determine which parameters were significantly correlated with the ratio of Susceptibles to Susceptibles with prescription. 

Advisors: Dr. Zhiquiang Cai and Brooke Hejnal

My Role: Undergraduate Researcher

In this project, under the direction of Dr. Zhiquiang Cai and Brooke Hejnal, I was able to learn how to use Neural Networks to model PDEs, and how to adapt and develop a neural network for PDEs, as well as how to use research clusters.