We introduce fluctuating hydrodynamics approaches on surfaces for capturing the drift-diffusion dynamics of particles and microstructures immersed within curved fluid interfaces of spherical shape. We take into account the interfacial hydrodynamic coupling, traction coupling with the surrounding bulk fluid, and thermal fluctuations. We study how the drift-diffusion dynamics of microstructures compare with and without hydrodynamic coupling within the curved fluid interface.

We use a novel machine learning method, Gaussian Process Regression, to solve a classic problem, the heat equation. We aim to find the relationship between temperature at a position on a rod and the location of a heat source under the rod. This equation-free method greatly simplifies solving the partial differential equation and proves to be accurate even with small data samples.

The Golestanian Swimmer is a three bead simple swimmer that leverages non-reciprocal motion to move through viscous media. Our three bead swimmer is propelled by the two oscillating harmonic springs that hold it together. Using computational simulation of these swimmers, we are able to investigate the role of fluid viscosity on the speed of the swimmers when moving through a spherical fluid interface.

We implement spectral clustering and semi-supervised labeling techniques on a voting network created from the UCI Congressional Voting Records data set, with the goal of understanding the voting stance of Congressional Representatives. We find interestingly that many politicians vote more akin to their opposing party.

Motivated by recent experimental systems where particles are immersed within curved two-dimensional fluid interfaces, such as colloids in a GUVâ€™s or proteins in a lipid vesicle membrane, we investigate how active kinetics can modulate the size of particle clusters that self-assemble within spherical fluid interfaces.

As a ubiquitous equation in physical theory, Poisson's equation serves as the perfect testing ground for Multi-Grid Iterative PDE solvers. Multigrid is a state-of-the-art method for increasing the convergence rates of Iterative methods for solving linear systems. These methods are particularly effective when dealing with systems with sparse matrix representations, like the Poisson equation.

While found in a variety of environments, the protein Spectrin is commonly found forming a scaffolding over the exterior of red blood cells. This scaffolding is called a Spectrin Network as the Spectrin proteins are connected by bonds forming a triangulated mesh. Motivated by the Spectrin Networks, we investigate the fluid interactions generated from generalized harmonic polymeric networks embedded in spherical fluid interfaces. We use CFD techniques to measure the significance effects of hydrodynamics.