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Thomas P. Witelski

Professor in the Department of Mathematics
Mathematics
295 Physics Building, Box 90320, Durham, NC 27708-0320
120 Science Drive, Durham, NC 27708-0320
Office hours Please email me to request a meeting time  

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


IMEX 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 Cite

COARSENING 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 Cite

A Three-Dimensional Tumor Growth Model and Its Boundary Instability

Journal Article Communications on Applied Mathematics and Computation · January 1, 2024 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 Cite
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