Publications

(2021). Automatic detection of the cornea location in video captures of fluorescence. Modeling and Artificial Intelligence in Ophthalmology.

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(2020). Parameter Estimation for Evaporation-Driven Tear Film Thinning. Bulletin of Mathematical Biology.

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(2019). ComplexRegions.jl: A Julia package for regions in the complex plane. Journal of Open Source Software.

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(2019). Mathematical Models of the Tear Film. Chapter in Ocular Fluid Dynamics: Anatomy, Physiology, Imaging Techniques, and Mathematical Modeling, from Springer-Birkhäuser.

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(2019). A Model for Tear Film Dynamics during a Realistic Blink. Journal for Modeling in Ophthalmology.

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(2019). An Adaptive Partition of Unity Method for Multivariate Chebyshev Polynomial Approximations. SIAM Journal on Scientific Computation.

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(2018). Models for Tear Break Up Dynamics and Imaging. 7th European Conference on Computational Fluid Dynamics.

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(2018). Simulation of parabolic flow on an eye-shaped domain with moving boundary. Journal of Engineering Mathematics.

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(2018). An adaptive partition of unity method for Chebyshev polynomial interpolation. SIAM Journal on Scientific Computing.

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(2017). On Tear Film Breakup (TBU): Dynamics and Imaging. Mathematical Medicine and Biology.

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(2017). Fundamentals of Numerical Computation.

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(2017). Exploring ODEs.

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(2017). Blink Characterization Using Curve Fitting and Clustering Algorithms. Journal for Modeling in Ophthalmology.

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(2016). Simulation of Thin Film Equations on an Eye-Shaped Domain with Moving Boundary. APS March Meeting Abstracts.

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(2016). New Directions in Numerical Computation. Notices of the American Mathematical Society.

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(2016). Mathematical Modeling of Glob-Driven Tear Film Breakup. Investigative Ophthalmology & Visual Science.

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(2015). Tear Film Dynamics Around a Rigid Model Blob. APS Meeting Abstracts.

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(2015). Solute Dynamics and Imaging in the Tear Film on an Eye-Shaped Domain. APS Meeting Abstracts.

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(2015). Rectangular spectral collocation. IMA Journal of Numerical Analysis.

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(2015). Modeling Tear Film Evaporation and Breakup with Duplex Films. APS Meeting Abstracts.

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(2015). Computed Tear Film and Osmolarity Dynamics on an Eye-Shaped Domain. Mathematical Medicine and Biology.

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(2015). A Model Problem for Blob-Driven Tear Film Breakup (TBU). APS Meeting Abstracts.

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(2014). Optimal domain splitting for interpolation by Chebyshev polynomials. SIAM Journal on Numerical Analysis.

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(2014). Heat Transfer and Tear Film Dynamics over Multiple Blink Cycles. Physics of Fluids.

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(2014). DATA DRIVEN MATHEMATICAL MODELING OF THE SINGLE VENTRICLE ANATOMY AND PHYSIOLOGY. Critical Care Medicine.

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(2014). Chebfun Guide.

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(2013). Coupling Osmolarity Dynamics within Human Tear Film on an Eye-Shaped Domain. APS Meeting Abstracts.

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(2013). Automatic Linearity Detection.

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(2013). A Model for the Tear Film and Ocular Surface Temperature for Partial Blinks. Interfacial Phenomena and Heat Transfer.

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(2012). Thin Film Dynamics on a Prolate Spheroid with Application to the Cornea. Journal of Engineering Mathematics.

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(2012). Forming Delocalized Intermediate States with Realistic Quantum Dots. Journal of Applied Physics.

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(2012). Chebfun for PDEs.

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(2012). Automatic Fréchet Differentiation for the Numerical Solution of Boundary-Value Problems. ACM Transactions on Mathematical Software (TOMS).

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(2012). A Model Problem for Tear Film Distribution on a Moving Rectangular Domain. APS Meeting Abstracts.

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(2012). A Fast Treecode for Multiquadric Interpolation with Varying Shape Parameters. SIAM Journal on Scientific Computing.

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(2011). Adaptive Methods for Analysis of Composite Plates with Radial Basis Functions. Mechanics of Advanced Materials and Structures.

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(2010). Radial Basis Function Interpolation on Irregular Domain through Conformal Transplantation. Journal of Scientific Computing.

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(2010). A Transformative Model for Undergraduate Quantitative Biology Education. CBE—Life Sciences Education.

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(2009). Learning MAtlAB.

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(2009). Chebfun Version 2.

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(2008). The Chebop System for Automatic Solution of Differential Equations. BIT Numerical Mathematics.

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(2008). Recent Progress on Modeling the Human Tear Film. APS Division of Fluid Dynamics Meeting Abstracts.

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(2008). Radial and Circular Slit Maps of Unbounded Multiply Connected Circle Domains. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

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(2008). An Overset Grid Method for the Study of Reflex Tearing. Mathematical Medicine and Biology.

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(2007). Single-Equation Models for the Tear Film in a Blink Cycle: Realistic Lid Motion. Mathematical Medicine and Biology.

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(2007). Pade-Based Interpretation and Correction of the Gibbs Phenomenon. Advances in the Gibbs Phenomenon, Ed. by A. Jerri.

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(2007). Adaptive Residual Subsampling Methods for Radial Basis Function Interpolation and Collocation Problems. Computers & Mathematics with Applications.

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(2007). A Overset Grid Method for Fourth Order Evolution Equations of Human Tear Film. APS Division of Fluid Dynamics Meeting Abstracts.

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(2006). Eigenvalue Stability of Radial Basis Function Discretizations for Time-Dependent Problems. Computers & Mathematics with Applications.

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(2006). Computation of Multiply Connected Schwarz-Christoffel Maps for Exterior Domains. Computational Methods and Function Theory.

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(2005). The Effect of the Small-Aspect-Ratio Approximation on Canonical Electrostatic MEMS Models. Journal of Engineering Mathematics.

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(2005). Polynomials and Potential Theory for Gaussian Radial Basis Function Interpolation. SIAM Journal on Numerical Analysis.

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(2005). Algorithm 843: Improvements to the Schwarz-Christoffel Toolbox for MATLAB. ACM Transactions on Mathematical Software (TOMS).

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(2004). Curvature Flow in Conformal Mapping. Computational Methods and Function Theory.

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(2004). Computing Eigenmodes of Elliptic Operators Using Radial Basis Functions. Computers & Mathematics with Applications.

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(2004). Approximations in Canonical Electrostatic MEMS Models.

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(2003). Numerical Examination of a Model of Thermo-Acoustic Instabilites in Lean, Pre-Mixed Combustors.. APS Division of Fluid Dynamics Meeting Abstracts.

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(2003). Isospectral Shapes with Neumann and Alternating Boundary Conditions. Physical Review E.

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(2003). A Crash Course in Matlab.

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(2002). Schwarz–Christoffel Mapping.

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(2002). Observations on the Behavior of Radial Basis Function Approximations near Boundaries. Computers & Mathematics with Applications.

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(2002). Interpolation in the Limit of Increasingly Flat Radial Basis Functions. Computers & Mathematics with Applications.

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(2001). A Padé-Based Algorithm for Overcoming the Gibbs Phenomenon. Numerical Algorithms.

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(2001). A General Conformal-Mapping Approach to the Optimum Electrode Design of Coplanar Waveguides with Arbitrary Cross Section. IEEE Transactions on Microwave Theory and Techniques.

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(2000). Staggered Time Integrators for Wave Equations. SIAM Journal on Numerical Analysis.

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(2000). Note on Nonsymmetric Finite Differences for Maxwell's Equations. Journal of Computational Physics.

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(1999). Computational Conformal Mapping (Book Review). SIAM Review.

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(1999). A Fast Spectral Algorithm for Nonlinear Wave Equations with Linear Dispersion. Journal of Computational Physics.

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(1998). Uses of the Berenger PML in Pseudospectral Methods for Maxwell's Equations. IUTAM Symposium on Computational Methods for Unbounded Domains.

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(1998). Schwarz-Christoffel Mapping in the Computer Era. Proceedings of the International Congress of Mathematicians.

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(1998). Numerical Conformal Mapping Using Cross-Ratios and Delaunay Triangulation. SIAM Journal on Scientific Computing.

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(1998). From Potential Theory to Matrix Iterations in Six Steps. SIAM Review.

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(1998). A Block Pseudospectral Method for Maxwell's Equations: I. One-Dimensional Case. Journal of Computational Physics.

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(1997). Pseudospectral Methods for Large-Scale Bioacoustic Models. 1997 IEEE Ultrasonics Symposium Proceedings. An International Symposium (Cat. No. 97CH36118).

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(1997). Eigenmodes of Isospectral Drums. SIAM Review.

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(1996). Pseudospectra for the Wave Equation with an Absorbing Boundary. Journal of Computational and Applied Mathematics.

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(1996). Matrix Iterations: The Six Gaps between Potential Theory and Convergence.

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(1996). Algorithm 756: A MATLAB Toolbox for Schwarz-Christoffel Mapping. ACM Transactions on Mathematical Software (TOMS).

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(1995). A Mostly Linear Model of Transition to Turbulence. Physics of Fluids.

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(1993). Pseudospectra of the Wave Operator with an Absorbing Boundary.

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(1993). Hydrodynamic Stability without Eigenvalues. Science.

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(1993). Error Bound on the Solution of a Linear Differential Equation in Chebyshev Series. International Journal of Systems Science.

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(1992). Computational Efficiency of a Functional Expansion Algorithm for Linear Quadratic Optimal Control. Proceedings of the 31st IEEE Conference on Decision and Control.

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(1992). A New Direction in Hydrodynamic Stability: Beyond Eigenvalues.

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