Overview
My primary area of expertise is the solution of nonlinear ordinary and partial differential equations for models of physical systems. Using asymptotics along with a mixture of other applied mathematical techniques in analysis and scientific computing I study a broad range of applications in engineering and applied science. Focuses of my work include problems in viscous fluid flow, dynamical systems, and industrial applications. Approaches for mathematical modelling to formulate reduced systems of mathematical equations corresponding to the physical problems is another significant component of my work.
Current Appointments & Affiliations
Professor in the Department of Mathematics
·
2011 - Present
Mathematics,
Trinity College of Arts & Sciences
Professor in the Department of Mechanical Engineering and Materials Science
·
2016 - Present
Pratt School of Engineering
Professor in the Thomas Lord Department of Mechanical Engineering and Materials Science
·
2021 - Present
Thomas Lord Department of Mechanical Engineering and Materials Science,
Pratt School of Engineering
Recent Publications
A Three-Dimensional Tumor Growth Model and Its Boundary Instability
Journal Article Communications on Applied Mathematics and Computation · June 1, 2025 In this paper, we investigate the instability of growing tumors by employing both analytical and numerical techniques to validate previous results and extend the analytical findings presented in a prior study by Feng et al. (Z Angew Math Phys 74:107, 2023) ... Full text CiteIMEX methods for thin-film equations and Cahn–Hilliard equations with variable mobility
Journal Article Computational Materials Science · July 1, 2024 We explore a class of splitting schemes employing implicit-explicit (IMEX) time-stepping to achieve accurate and energy-stable solutions for thin-film equations and Cahn–Hilliard models with variable mobility. These splitting methods incorporate a linear, ... Full text CiteCOARSENING OF THIN FILMS WITH WEAK CONDENSATION
Journal Article SIAM Journal on Applied Mathematics · January 1, 2024 A lubrication model can be used to describe the dynamics of a weakly volatile viscous fluid layer on a hydrophobic substrate. Thin layers of the fluid are unstable to perturbations and break up into slowly evolving interacting droplets. A reduced-order dyn ... Full text CiteEducation, Training & Certifications
California Institute of Technology ·
1995
Ph.D.
The Cooper Union ·
1991
B.S.E.