10 citations · 19 across the 10 of their papers we have counts for
14 papers
Amortized Generative Modeling of Invariant Measures across A Family of Kuramoto-Sivashinsky PDEs
Arnab Roy, Tobin A. Driscoll
The long-run statistics of chaotic dissipative partial differential equations are described by invariant measures, and when the equation carries a parameter these measures form a f…
Parameter estimation for evaporation-driven tear film model in two space dimensions
Qinying Chen, Tobin Driscoll
The tear film (TF) plays a critical role in maintaining ocular surface health, and its disruption through tear breakup (TBU) is closely associated with dry eye disease. Evaporation…
Stable evaluation of derivatives for barycentric and continued fraction representations of rational functions
Tobin A. Driscoll, Yuxing Zhou
Fast algorithms for approximation by rational functions exist for both barycentric and Thiele continued fraction (TCF) representations. We present the first numerically stable meth…
Operator learning for models of tear film breakup
Qinying Chen, Arnab Roy, Tobin A. Driscoll
Tear film (TF) breakup is a key driver of understanding dry eye disease, yet estimating TF thickness and osmolarity from fluorescence (FL) imaging typically requires solving comput…
RationalFunctionApproximation.jl: Rational Approximation On Discrete and Continuous Domains
Tobin A. Driscoll
Unlike polynomials, rational functions can represent functions having poles or branch cuts with root-exponential convergence and no Runge phenomenon. Recent developments of the AAA…
Greedy Thiele continued-fraction approximation on continuum domains in the complex plane
Tobin A. Driscoll, Yuxing Zhou
We describe an adaptive greedy algorithm for Thiele continued-fraction (TCF) approximation of a function defined on a continuum domain in the complex plane. The algorithm iterative…
Evaporation-driven tear film thinning and breakup in two space dimensions
Qinying Chen, Tobin A. Driscoll, Richard J. Braun
Evaporation profiles have a strong effect on tear film thinning and breakup (TBU), a key factor in dry eye disease (DED). In experiments, TBU is typically seen to occur in patterns…
Extensional Flow of a Free Film of Nematic Liquid Crystal with Moderate Elasticity
M. J. Taranchuk, L. J. Cummings, T. A. Driscoll +1
Motivated by problems arising in tear film dynamics, we present a model for the extensional flow of thin sheets of nematic liquid crystal. The rod-like molecules of these substance…
Fitting ODE models of tear film breakup
Tobin A. Driscoll, Richard J. Braun, Rayanne A. Luke +5
The contribution of different physical effects to tear breakup (TBU) in subjects with no self-reported history of dry eye are quantified. An automated system using a convolutional…
Parameter Estimation for Mixed-Mechanism Tear Film Thinning
Rayanne A. Luke, Richard J. Braun, Tobin A. Driscoll +2
Etiologies of tear breakup include evaporation-driven, divergent flow-driven, and a combination of these two. A mathematical model incorporating evaporation and lipid-driven tangen…
Preconditioned nonlinear iterations for overlapping Chebyshev discretizations with independent grids
Kevin W. Aiton, Tobin A. Driscoll
The additive Schwarz method is usually presented as a preconditioner for a PDE linearization based on overlapping subsets of nodes from a global discretization. It has previously b…
An adaptive partition of unity method for multivariate Chebyshev polynomial approximations
Kevin W. Aiton, Tobin A. Driscoll
Spectral polynomial approximation of smooth functions allows real-time manipulation of and computation with them, as in the Chebfun system. Extension of the technique to two-dimens…
An adaptive partition of unity method for Chebyshev polynomial interpolation
Kevin W. Aiton, Tobin A. Driscoll
For a function that is analytic on and around an interval, Chebyshev polynomial interpolation provides spectral convergence. However, if the function has a singularity close to the…
Simulation of Parabolic Flow on an Eye-Shaped Domain with Moving Boundary
Tobin A. Driscoll, Richard J. Braun, Joseph K. Brosch
During the upstroke of a normal eye blink, the upper lid moves and paints a thin tear film over the exposed corneal and conjunctival surfaces. This thin tear film may be modeled by…