Research
My independent research program follows a single through-line: rigorous numerical methods applied to physical systems. The work ranges from cut-cell finite volume methods for problems with complex geometry to kinetic theory and Direct Simulation Monte Carlo for rarefied gas dynamics. I conduct it independently, with academic collaborators, and the aim is to make existing methods more honest before reaching for new ones.
Submitted
Update-Magnitude State Redistribution (UM-SRD): A Shut-off Extension of Weighted SRD for Cut-Cell Methods
CAMCOS, 2026 · Paper ID 260523-Karell
The paper presents a single cut-cell finite volume framework that handles both structured and randomly perturbed domain boundaries within the same formulation.
With acknowledgments to Marsha Berger and Andrew Giuliani.
Working Papers
Defect Subspaces and Localized Instabilities in Cut-Cell Finite-Volume Operators
Characterizes cut-cell instability in explicit finite-volume methods as a low-dimensional geometric phenomenon: m small cut cells produce an m-dimensional unstable subspace localized at the defects, and state redistribution acts asymptotically in that direction. Yields a geometry-only stability criterion for the blended scheme that requires no global eigenvalue computation.
arXiv:2508.12390 · physics.plasm-ph, 2025
I compute transport coefficients from the Chapman–Enskog expansion with BGK collision operators and argue, on structural grounds, that the resulting 1/ν divergence extends to other local collision operators — making it intrinsic to the Chapman–Enskog approach rather than a closure artifact. I propose a phenomenological effective collision frequency ν_eff = ν√(1 + Kn²), motivated by gradient-driven decorrelation, that preserves conservation laws and thermodynamic consistency while yielding finite transport coefficients across all collisionality regimes.
Deriving the Minimum Value of Donated Food to Justify Food Rescue
A closed-form viability threshold for food-rescue pickups under the PATH Act enhanced deduction, with a stochastic profit model and a disk-geometry trip-cost estimate. Simulated over 311 real donor–recipient pairs across the Upper West Side, Stamford, and Trenton, 84–85% of trips clear the threshold on tax savings alone.
Elsewhere
Full publication list on Google Scholar.