Lindsay research group.

Alan E. Lindsay, Ph.D.

Associate Professor of Applied Math.
Dept. of Applied and Computational Mathematics and Statistics (ACMS)
Director, Notre Dame Biophysics.
University of Notre Dame.

Office: Crowley Hall 201G
Ph: +1 (574) 631 3511
Email: a.lindsay@nd.edu

Research: Using mathematics to understand the role of randomness in biological function.

Partial Differential Equations: Linear and nonlinear PDEs. Singular perturbations, asymptotic analysis, homogenization theory, finite time blow-up.
Stochastic processes: Diffusion processes, first passage time theory, master equations, extreme and rare events processes.
Computational: Monte Carlo methods, rare event simulation stochastic simulation methods. Adaptive meshing for singularly perturbed PDEs. Finite difference, finite element, boundary integral methods.
Data driven mathematical Modeling: Data driven modeling, data assimilation, agent based modeling, reaction diffusion equations and free boundary value problems. Applications to immune signaling, chemoreception and development.

Research curently supported by NSF DMS-2052636. Latest CV (June. 2024)

Free boundary PDE model of nuclear growth.

Biological stochastic processes, Monte Carlo Methods.

Singular perturations and adaptive numerics.

Publications and preprints

Jake Cherry, Alan E. Lindsay, Bryan Quaife.
Boundary Integral Methods for Particle Diffusion in Complex Geometries: Shielding, Confinement, and Escape.
[arXiv] [PDF]
Andrew J. Bernoff, Alan E. Lindsay.
Kinetic Monte Carlo methods for three-dimensional diffusive capture problems in exterior domains.
Royal Society Open Science, 12(2): 241033, (2025).
[Journal] [arXiv] [PDF]
Thomas Hillen, Maria R. D'Orsogna, Jacob C. Mantooth, Alan E. Lindsay
Mean first passage times for transport equations.
SIAM Journal on Applied Mathematics, 85(1), (2025).
[Journal] [arXiv] [PDF]
Charles Naudet, Alan E. Lindsay
Numerical bifurcation analysis of post-contact states in mathematical models of Micro-Electromechanical Systems.
Mathematics and Computers in Simulation, Vol. 220, (2024), pp. 296–308.
[Journal] [arXiv] [PDF]
Andrew J. Bernoff, Alexandra Jilkine, Adrián Navarro Hernández, Alan E. Lindsay.
Single cell directional sensing from just a few receptor binding events.
Biophysical Journal, Vol.122, Issue 15 (2023), pp. 3108--3116.
[Journal] [PDF]
Jonathan Morgan, Alan E. Lindsay.
Modulation of antigen discrimination by duration of immune contacts in a kinetic proofreading model of T cell activation with extreme statistics.
PLoS Computational Biology, 9(8):e1011216 (2023).
[Journal] [bioRxiv] [PDF]
Alan E. Lindsay, Andrew J. Bernoff, Adrián Navarro Hernández.
Short-time diffusive fluxes over membrane receptors yields the direction of a signaling source.
Royal Society Open Science, 10(4): 221619 (2023).
[Journal] [bioRxiv] [PDF]
Jake Cherry, Alan E. Lindsay, Adrián Navarro Hernández, Bryan Quaife.
Trapping of planar Brownian motion: Full first passage time distributions by Kinetic Monte-Carlo, asymptotic and boundary integral methods.
SIAM Multiscale Modeling and Simulation, Vol. 20, Iss. 4 (2022).
[Journal] [arXiv] [PDF]
Jonathan Morgan, Johannes Pettmann, Omer Dushek, Alan E. Lindsay.
T-cell microvilli simulations show operation near packing limit and modulation of antigen recognition.
Biophysical Journal, Volume. 121, Issue 21, (2022), pp. 4128–4136.
[Journal] [bioRxiv] [PDF]
V. Leech, J.W. Hazel, J.C. Gatlin, A. E. Lindsay, A. Manhart.
Mathematical modeling accurately predicts the dynamics and scaling of nuclear growth in discrete cytoplasmic volumes.
Journal of Theoretical Biology, Vol. 533, (2022), 110936.
[Journal] [PDF]
Tracy L. Stepien, Cole Zmurchok, James B. Hengenius, Rocio Marilyn Caja Rivera, Maria R. D’Orsogna, Alan E. Lindsay.
Moth mating: Modeling female pheromone calling and male navigational strategies to optimize reproductive success.
Appl. Sci. (2020), 10(18), 6543.
[Journal] [PDF]
Sean D. Lawley, Alan E. Lindsay, Christopher E. Miles
Receptor organization determines the limits of single-cell source location detection.
Phys. Rev. Lett. (2020), 125, 018102.
[Journal] [PDF]
Frederic Paquin-Lefebvre, Bin Xu, Kelsey L. DiPietro, Alan E. Lindsay, Alexandra Jilkine
Pattern formation in a coupled membrane-bulk reaction-diffusion model for intracellular polarization and oscillations.
Journal of Theoretical Biology, (2020), Vol. 497, 21, 110242.
[Journal] [PDF]
Paul Rumbach, Alan E. Lindsay, David B. Go
Turing patterns on a plasma-liquid interface.
Plasma Sources Sci. Technol. (2019) 28 105014.
[Journal] [PDF]
R. A. Fernandes, K. A Ganzinger, J. C. Tzou, P. Jonsson, S. F. Lee, M. Palayret, V. T. Chang, M. Da Cunha Santos, C. Macleod, A.E. Lindsay, O. Dushek, A. Tilevik, S. J. Davis, D. Klenerman.
A cell-topography based mechanism for ligand discrimination by the T-cell receptor.
PNAS, (2019) 116 (28) 14002-14010
[Journal] [bioRxiv]
K.L. DiPietro, A.E. Lindsay
Adaptive solution to two dimensional partial differential equations in curved domains using the Monge-Ampere simulation equation.
SIAM Journal on Scientific Computing, (2019) 44(2), pp. 1331--1356.
[Journal] [PDF]
K.L. DiPietro, R. D. Haynes, A.E. Lindsay, W. Huang, Y. Yu.
Moving mesh simulation of contact sets in two dimensional models of elastic-electrostatic deflection problems.
Journal of Computational Physics (2018), 375, pp. 763--782.
[Journal] [PDF]
A.J. Bernoff, A.E. Lindsay, D.D. Schmidt.
Boundary homogenization and capture time distributions of semi-permeable membranes with periodic patterns of reactive sites.
Multiscale Modeling and Simulation (2018) 16(3), pp. 1411--1447.
[Journal] [PDF]
A.E. Lindsay, B. Quaife, L. Wendelberger.
A boundary element method for computing the vibrational modes of elastic plates with localized punctures.
Advances in Computational Mathematics (2018), 44(4), pp. 1249--1273.
[Journal] [PDF]
A.E. Lindsay, A.J. Bernoff.
Numerical approximation of diffusive capture rates by planar and spherical surfaces with absorbing pores.
SIAM Journal on Applied Math. (2018), 78(1), pp. 266--290.
[Journal] [PDF]
K.L. DiPietro, A.E. Lindsay.
Monge-Ampere simulation of fourth order PDEs in two dimensions with application to elastic-electrostatic contact problems.
Journal of Computational Physics, 349, (2017), pp. 328-350.
[Journal] [PDF]
A.E. Lindsay, J.C. Tzou, T. Kolokolnikov.
Optimization of first passage times by multiple cooperating mobile traps.
SIAM Multiscale Modeling and Simulation (2017), Vol. 15, No. 2, pp. 920-947.
[Journal] [PDF]
A.E. Lindsay, A.J. Bernoff, M.J. Ward.
First Passage Statistics for the Capture of a Brownian Particle by a Structured Spherical Target with Multiple Surface Traps.
SIAM Multiscale Modeling and Simulation, (2017), Vol. 15, No. 1 : pp. 74--109.
[Journal] [PDF]
A.E. Lindsay, R.T. Spoonmore, J.C. Tzou.
Hybrid asymptotic-numerical approach for estimating first passage time densities of the two-dimensional narrow capture problem.
Physical Review E. (2016) 94, 042418.
[Journal] [PDF]
A.E. Lindsay.
Regularized Model of Post-Touchdown Configurations in Electrostatic MEMS: Bistability Analysis.
Journal of Engineering Math. (2016) Vol. 99, No. 1, pp. 65--77.
[Journal] [PDF]
A.E. Lindsay, W. Hao, A.J. Sommese
Vibrations of thin plates with small clamped patches.
Proceedings of the Royal Society A. (2015), Vol. 471, No. 2184.
[Journal] [PDF]
A.E. Lindsay, J. Lega, K.B. Glasner.
Regularized Model of Post-Touchdown Configurations in Electrostatic MEMS: Interface Dynamics.
IMA Journal of Applied Mathematics, (2015) 80(6), pp. 1635--1663.
[Journal] [PDF]
A.E. Lindsay, M.J. Ward, T. Kolokolnikov.
The Transition to Point Constraint in a Mixed Biharmonic Eigenvalue Problem.
SIAM Journal on Applied Mathematics, (2015) 75(3), pp. 1193--1224.
[Journal] [PDF]
A.E. Lindsay, J.C. Tzou, T. Kolokolnikov.
Narrow escape problem with a mixed trap and the effect of orientation.
Physical Review E (2015) Vol.91, No.3.
[Journal] [PDF]
T. Kolokolnikov, A.E. Lindsay.
Recovering multiple small inclusions in a three dimensional domain using a single measurement.
Inverse Problems in Science and Engineering, (2015) Vol. 23, No. 5, pp. 377--388.
[Journal] [PDF]
F. Tonolini, S. Chan, M. Agnew, A.E. Lindsay, J. Leach.
Reconstructing high-dimensional two-photon entangled states via compressive sensing.
Scientific Reports (2014), Vol. 4, No. 6542.
[Journal] [PDF]
A.E. Lindsay, J. Lega, K.B. Glasner.
Regularized model of post-touchdown configurations in electrostatic MEMS: Equilibrium Analysis.
Physica D: Nonlinear Phenomena, (2014) Vol. 280-281, pp. 95--108.
[Journal] [PDF]
A.E. Lindsay.
An asymptotic study of blow up multiplicity in fourth order parabolic partial differential equations.
DCDS-B, (2014), 19(1) pp. 189--215.
[Journal] [PDF]
A.E. Lindsay, J. Lega, F.J. Sayas.
The quenching set of a MEMS capacitor in two-dimensional geometries.
Journal of Nonlinear Science, (2013), 23(5), pp. 807--834.
[Journal] [PDF]
A.E. Lindsay, K.B. Glasner.
The stability and evolution of curved domains arising from one dimensional localized patterns.
SIAM Journal on Applied Dynamical Systems, (2013), 12(2), pp. 650--673.
[Journal] [PDF]
N.D. Brubaker, A.E. Lindsay.
The onset of multi-valued solutions of a prescribed mean curvature equation with singular nonlinearity.
European Journal of Applied Mathematics, (2013), 25(5), pp. 631--656.
[Journal] [PDF]
A.E. Lindsay, J. Lega.
Quenching solutions of a fourth order PDE with a singular nonlinearity modelling a MEMS capacitor.
SIAM Journal on Applied Mathematics, (2012), 72(3), pp. 935--958.
[Journal] [PDF]
A.E. Lindsay, D.R. Brecher.
Simulation of the CEV process and the local martingale property.
Mathematics and Computers in Simulation, (2012), 82(5), pp. 868--878.
[Journal] [PDF]
M.C. Kropinski, A.E. Lindsay, M.J. Ward.
Asymptotic Analysis of Localized Solutions to Some Linear and Nonlinear Biharmonic Eigenvalue Problems.
Studies in Applied Mathematics, (2011), 126(4), pp. 347--408.
[Journal] [PDF]
A.E. Lindsay , M.J. Ward.
Asymptotics of some nonlinear eigenvalue problems modelling a MEMS Capacitor. Part II: multiple solutions and singular asymptotics.
European Journal of Applied Mathematics, (2011), 22(2), pp. 83--123.
[Journal] [PDF]
A.E. Lindsay, M.J. Ward.
An Asymptotic Analysis of the Persistence Threshold for the Diffusive Logistic Model in Spatial Environments with Localized Patches.
DCDS-B, (2010), 14(3), pp. 1139--1179.
[Journal] [PDF]
A.E. Lindsay, M.J. Ward.
Asymptotics of some nonlinear eigenvalue problems for a MEMS capacitor: Part I: Fold point asymptotics.
Methods and Applications of Analysis, (2008), 15(3), pp. 297--326.
[Journal] [PDF]
A.E. Lindsay, K.A. Lindsay and J.R. Rosenberg.
New concepts in compartmental modelling.
Computing and Visualization in Science, (2007) 10(2), pp. 79--98.
[Journal]
A.E. Lindsay, K.A. Lindsay and J.R. Rosenberg.
Increased computational accuracy in multi-compartmental cable models by a novel approach for precise point process localization.
Journal of Computational Neuroscience, (2005), 19, pp. 21--37.
[Journal]