• Newton-Krylov continuation of amplitude-modulated rotating waves in sheared annular electroconvection Gregory M. Lewis, Jamil Jabbour, M. C. Pugh, and Stephen W. Morris Physical Review E 110, 014212, published July 24, 2024.
  • A study of the numerical stability of an ImEx scheme with application to the Poisson-Nernst-Planck equations M.C. Pugh, David Yan, and F.P. Dawson Applied Numerical Mathematics 2021 163:239-253. Matlab code is available on github. Note: an earlier version, arXiv:1905.01368v1, also contained: a linear stability analysis of the SBDF2 scheme, a study of the effect of Richardson Extrapolation on numerical stability, and a study of the stability domain of the logistic equation.
  • Adaptive time-stepping schemes for the solution of the Poisson-Nernst-Planck equations David Yan, M.C. Pugh, and F.P. Dawson Applied Numerical Mathematics 2021 163:254-269
  • Modelling and optimizing a system for testing electronic circuit boards Stephen Y. Chen, Odile Marcotte, Mario Leonardo Morfin Ramirez and Mary Pugh, Mathematics-in-Industry Case Studies 2017 8:4
  • Theory of linear sweep voltammetry with diffuse charge: Unsupported electrolytes, thin films, and leaky membranes David Yan, Martin Z. Bazant, P. M. Biesheuvel, Mary C. Pugh, and Francis P. Dawson Phys. Rev. E 95, 033303 (2017) Note: Equations (49) and (51) should both have exp(-v/SC) not exp(v/SC). Equation (52) should all have exp(-v/2SC) not exp(v/2SC).
  • A Finite Volume Method and Experimental Study of a Stator of a Piezoelectric Traveling Wave Rotary Ultrasonic Motor with V. Bolborici and F.P. Dawson, Ultrasonics, 54(2014)809-820.
  • Time Dependent Finite Volume Model of Thermoelectric Devices with F.P. Dawson, A. El-Dieb and D. Yan, IEEE Transactions on Industry Applications, 50(2014)1:600-608.
  • Modeling of Composite Piezoelectric Structures with the Finite Volume Method
    with V. Bolborici and F.P. Dawson, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 59(2012)1:156-162. The Technical Report: Modeling of Composite Piezoelectric Structures with the Finite Volume Method has some extra explanations, formulae, and results.
  • A Dynamic Model of a High Temperature Arc Lamp
    with F.P. Dawson and B. Halliop, IEEE Transactions on Industry Applications, 46(2010)6:2233-2242.
  • Modeling of Piezoelectric Devices with the Finite Volume Method
    with V. Bolborici and F.P. Dawson, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control 57(2010)7:1673-1691.
  • Nonnegative solutions for a long-wave unstable thin film equation with convection
    with M. Chugunova and R.M. Taranets, SIAM Journal on Mathematical Analysis, 42(2010)4:1826-1853. The Tecnical report on a long-wave unstable thin film equation with convection has some extra results and proofs with extra details.
  • A Dynamic Model of a High Temperature Arc Lamp
    with F.P. Dawson and B. Halliop, IEEE Industry Applications Society Annual Meeting, 2008:1519-- 1526,
  • Mathematical Models of Mother/Child Attachment
    appeared in Fields Proceedings of "Fields-MITACS Industrial Problems Workshop 2006"
  • Notes on Blowup and Long Wave Unstable Thin Film Equations
    appeared in Proceedings of MSRI workshop "Women in Mathematics: The Legacy of Ladyzhenskaya and Oleinik"
  • A finite locus effect diffusion model for the evolution of a quantitative trait
    with J. R. Miller and M. B. Hamilton, J. Math. Bio. 52(2006)6:761-787
  • Selfsimilar Blowup of Unstable Thin-film Equations
    with D. Slepcev, Indiana Univ. Math. J. 54(2005)6:1697-1738
  • Global effects in Figure/Ground segregation by a model with only local interactions
    with N. Rubin, preprint, 2001.
  • Heteroclinic orbits, mobility parameters and stability for thin film type equations
    with R. S. Laugesen, Elect. J. Diff. Eq. 2002(2002)95:1-29
  • Energy levels of steady states for thin film type equations
    with R. S. Laugesen, J. Diff. Eq., 182(2002)2:377-415
  • Advances in Random Matrix Theory, Zeta Functions, and Sphere Packing
    with T.C. Hales and P. Sarnak, Proc. Natl. Acad. Sci. USA 97(2000)24:12963-12964.
  • Finite-time Blow-up of Solutions of Some Long-wave Unstable Thin Film Equations
    with A. Bertozzi, Indiana Univ. Math. J. 49(2000)4:1323-1366
  • Linear Stability of Steady States for Thin Film and Cahn-Hilliard Type Equations
    with R. Laugesen, Arch. Ration. Mech. Anal. 154(2000)1:3-51
  • Computational Modeling of Orientation Tuning Dynamics in Monkey Primary Visual Cortex
    with D. L. Ringach, R. Shapley, and M. J. Shelley, J. of Computational Neuroscience vol. 8 no. 2, March 2000, pp 143-159.
  • Properties of Steady States for Thin Film Equations
    with R. Laugesen, EJAM 11(2000)3:293-351.
  • Singularity Formation in Thin Jets with Surface Tension
    with M. Shelley, CPAM 51(1998)733-795.
  • Long-wave instabilities and saturation in thin film equations
    with A. Bertozzi, CPAM 51(1998)625-661.
  • The Lubrication Approximation for Thin Viscous Films: Regularity and Long Time Behavior of Weak Solutions
    with A. Bertozzi, CPAM 49(1996)2:85-123.
  • The Lubrication Approximation for Thin Viscous Films: the Moving Contact Line with a `Porous Media' Cut Off of Van der Waals Interactions
    with A. Bertozzi, Nonlinearity, 7(1994)1535-1564.
  • Global Solutions for Small Data to the Hele-Shaw Problem
    with P. Constantin, Nonlinearity, 6(1993)393-416.