Hari Rajesh

My primary interests lie in theoretical and computational science at the interface of chemistry, condensed matter physics, and materials science. I am particularly interested in analyzing problems using the tools of quantum and statistical mechanics. I love using computer simulations to develop theoretical models which give experimentally verifiable predictions.

At Rutgers, I have been working with Professor Rick Remsing in theoretical and computational chemical physics. As part of the Remsing Lab, I have worked on two projects. First, I analyzed the effect of long-range electrostatics on solvation dynamics. My second project focuses on analyzing the properties of nanoconfined electrolytes using lattice models and statistical mechanics. Specifically, I have been really interested in studying frustrated and topological phases in these models in order to understand the interesting electrochemical properties of nanoconfined electrolytes. You can check out my work on these projects here or by clicking the image.

(Pictured: Topological vortices in the XY model)

I also have a secondary interest in pure mathematics. Since high school, I have been investigated various interesting topics in calculus, geometry, and number theory. You can check out my extensive collection of research notes here or by clicking the image.

I have also worked on formal publications for my more interesting results. In particular, I have recently finished a project where I analyzed Pascal's triangle diagonals modulo n. I found and proved various results on the periodicity of these diagonals before analyzing so-called gaps in these diagonals. I proved various results concerning the properties of these gaps and compiled some numerical results as well. I have also contributed to the On-Line Encyclopedia of Integer Sequences (OEIS). Specifically, I have contributed to sequences A133900, A133910, and A386279. You can check out my paper on this project here.

(Pictured: Domain coloring of the function o(z)=(-1)^(2/z))