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)

Jake Cherry, Alan E. Lindsay, Bryan Quaife.
Boundary Integral Methods for Particle Diffusion in Complex Geometries: Shielding, Confinement, and Escape.
To appear, Journal of Computational Physics.
[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]