Research Overview

At the intersection of Scientific Computing, Mathematical Modeling, and Mathematical Biology.

Focus Areas

My work involves developing and implementing advanced numerical methods, finite difference schemes, Matched Interface and Boundary (MIB) methods, and Finite Element Methods (FEM), to solve multidimensional partial differential equations on high-performance computing platforms. Applications span drug design, protein engineering, and mathematical modeling of social systems.

Mathematical Biology Implicit solvation models, biomolecular solvation analysis, ensemble averaged electrostatics, PDE modeling of molecular surfaces.
Scientific Computing Electrostatic analysis, material interface problems, biomolecular simulations on HPC platforms.
Numerical Methods for PDEs Matched Interface and Boundary (MIB) method, Alternating Direction Implicit (ADI) methods.
Mathematical Modeling Social dynamics modeling, gang dynamics, crime curtailment, intervention strategy analysis.

Current Projects

Biomolecular Solvation

Developing a Variational Implicit Solvation Model incorporating Size-Modified Poisson-Boltzmann (SMPB) theory, diffuse interface approaches, and ensemble averaged electrostatics for accurate free energy calculations in drug design and protein engineering.

Poisson-Boltzmann Free Energy Protein Engineering

High-Order Numerical Schemes

Developing robust solvers for interface problems and stiff systems, with focus on three-dimensional p-Laplace equations using finite difference methods, efficient ADI time-stepping for parabolic equations, and MIB methods for complex geometry in solvation models.

p-Laplace ADI Methods MIB Method

Social Dynamics Modeling

Beyond physics-based modeling, I apply ODE systems to understand social phenomena. Recent work assesses the impact of intervention programs on gang dynamics using mathematical modeling approaches adapted from epidemiological compartmental models.

ODE Systems Gang Dynamics Compartmental Models Stability Analysis

Computational Tools

FORTRAN MATLAB Python R VMD HPC / Slurm Finite Difference Methods Variational Implicit Solvent Models Matched Interface and Boundary

Selected Visualizations

Electrostatic potential of protein 451c
Electrostatic Analysis Electrostatic surface potential of protein 451c (PDB ID) mapped onto surface generated after solving the p-Laplace equation (p = 1.2). Visualized in VMD.
Comparison of numerical schemes for p-Laplace equation
Numerical Scheme Efficiency Comparison of ADI, Crank-Nicolson, and Picard's Iteration for solving the p-Laplace equation across 23 proteins. ADI proves computationally most efficient.
Schematic diagram of crime dynamics
Social Dynamics Compartmental model depicting how crime and criminal activity propagate through a community under various intervention strategies.