Research

I study the existence and stability of traveling waves in a reaction-diffusion system modeling the interplay between protest level and social tension under different intervention strategies. The parameters chosen in the system determine whether the protest level, social tension, and authority presence enhance or inhibit one another, and thereby qualitatively determine the solution behavior.

Poster

ArXiv  Paper 

Second preprint coming soon!

Designing stable mRNA sequences is crucial for chemical synthesis, metabolic engineering, and vaccine design. A single protein can be encoded by many different RNA sequences (see the codon wheel chart below), each folding into a distinct secondary structure with different stability. I developed an algorithm using dynamic programming and statistical mechanics to select the "good" sequences. The algorithm evaluates millions of codon combinations with possible secondary structures, and then uses Boltzmann sampling to generate candidates with optimal stability. A Python package is currently in development.

arXiv preprint coming soon!

(Python package in development)

In deep water, colliding solitary waves can create remarkably stable, multi-wave structures. I investigated one such phenomenon in the 2D Benjamin-Ono equation, a model for internal fluids with great depth. Using numerical simulations and modulation theory, I analyzed a unique four-wave structure emerging from oblique soliton collisions (the Mach reflection problem) is a traveling wave solution. This work provides an analytical approach to study 2D solitary wave interactions and the resulting quasi-resonant multi-wave structures in non-integrable systems.

arXiv preprint coming soon!