Peer-reviewed Publications

My research activity focuses on the modeling and analysis of nonlinear phenomena (understanding how nonlinearities manifest themselves; qualitative and quantitative analysis of the behaviors or structures resulting from nonlinear effects). I approach these questions with a range of methods such as mathematical modeling, numerical simulations, and analysis of differential or difference equations, which all work in concert to reveal and explain new nonlinear behaviors. Such an exploration often leads to novel, applications-inspired, mathematical results. Many of my publications are concerned with physical (fluids, thin plates or membranes, nonlinear optics) or biological (bacterial colonies, infectious diseases, mosquito abundance) systems. I am also interested in machine learning, in using data assimilation methods to forecast the dynamics of nonlinear systems, and in how discrete or continuous nonlinear dynamical systems connect to other areas of mathematics, such as graphical enumeration.

Reviews

  1. A. C. Newell, T. Passot and J. Lega, Order parameter equations for patterns, Ann. Rev. Fluid Mech. 25, 399-453 (1993).
  2. Joceline Lega, Traveling hole solutions of the complex Ginzburg-Landau equation: a review, Physica D 152-153, 269-287 (2001).
  3. J. Lega and T. Passot, Hydrodynamics of bacterial colonies, Nonlinearity 20, C1-C16 (2007). (Cover illustration).

Defects in Systems far from Equilibrium

  1. P. Coullet, C. Elphick, L. Gil, and J. Lega, Topological defects of wave patterns, Phys. Rev. Lett. 59, 884-887 (1987).
  2. J. Lega, Forme spirale de la dislocation des ondes stationnaires, C. R. Acad. Sci. Paris, 309 II, 1401 (1989).
  3. S. Ciliberto, P. Coullet, J. Lega, E. Pampaloni and C. Perez-Garcia, Defects in roll-hexagon competition, Phys. Rev. Lett. 65, 2370-2373 (1990).
  4. Nicholas M. Ercolani, Nikola Kamburov, Joceline Lega, The phase structure of grain boundaries, Phil. Trans. R. Soc. A 376, 20170193 (2018).

Defect-mediated Turbulence

  1. P. Coullet and J. Lega, Defect-mediated turbulence in wave patterns, Europhys. Lett. 7, 511-516 (1988).
  2. P. Coullet, L. Gil, and J. Lega, Une forme de turbulence associée aux défauts topologiques, Bulletin de la Société Française de Physique, 67, 12 (1988); Mathematical Modeling and Numerical Analysis 23, 385-394 (1989).
  3. P. Coullet, L. Gil, and J. Lega, Defect-mediated turbulence, Phys. Rev. Lett. 62, 1619-1622 (1989).
  4. P. Coullet, L. Gil, and J. Lega, A form of turbulence associated with defects, Physica 37 D, 91-103 (1989).
  5. L. Gil, J. Lega and J.L. Meunier, Statistical properties of defect-mediated turbulence, Phys. Rev. A 41, 1138-1141 (1990).
  6. J. Lega, Defect-mediated turbulence, Computer Methods in Applied Mechanics and Engineering 89, 419-424 (1991).

Phenomenological Properties of Systems far from Equilibrium

  1. P. Coullet, J. Lega, B. Houchmanzadeh and J. Lajzerowicz, Breaking chirality in nonequilibrium systems, Phys. Rev. Lett. 65, 1352-1355 (1990).
  2. P. Coullet, J. Lega and Y. Pomeau, Dynamics of Bloch walls in a rotating magnetic field: a model, Europhys. Lett. 15, 221-226 (1991).
  3. J. Lega, Secondary Hopf bifurcation of a one-dimensional periodic pattern, Eur. J. Mech. B/Fluids 10, #2 – Suppl., 145 (1991).
  4. M.R.E. Proctor and J. Lega, Secondary bifurcations and symmetry breaking as a route towards spatiotemporal disorder, Int. J. Bifurcation and Chaos 5, 841 (1995).
  5. J. Lega and T. Passot, Inverse cascade and energy transfer in forced low-Reynolds number two-dimensional turbulence, Fluid Dynamics Research 34, 289-297 (2004).

Modeling of Systems far from Equilibrium

  1. F. Daviaud, J. Lega, P. Bergé, P. Coullet and M. Dubois, Spatio-temporal intermittency in a 1-d convective pattern: theoretical model and experiments, Physica D 55, 287-308 (1992).
  2. J. Lega, S. Jucquois, B. Janiaud and V. Croquette, Localized phase jumps in wave trains, Phys. Rev. A 45, 5596-5604 (1992).
  3. J. Lega and J.M. Vince, Temporal forcing of traveling wave patterns, J. Phys. I France 6, 1417-1434 (1996).

Nonlinear Optics

  1. J.V. Moloney, P.K. Jakobsen, J. Lega, S.G. Wenden and A.C. Newell, Space-time complexity in nonlinear optics, Physica D 68, 127-134 (1993).
  2. P.K. Jakobsen, J. Lega, Q. Feng, M. Staley, J.V. Moloney, and A.C. Newell, Nonlinear transverse modes of large-aspect-ratio homogeneously broadened lasers: I. Analysis and numerical simulation, Phys. Rev. A 49, 4189-4200 (1994).
  3. J. Lega, P.K. Jakobsen, J.V. Moloney, and A.C. Newell, Nonlinear transverse modes of large-aspect-ratio homogeneously broadened lasers: II. Pattern analysis near and beyond threshold, Phys. Rev. A 49, 4201-4212 (1994).
  4. J. Lega, J.V. Moloney, and A.C. Newell, Swift-Hohenberg equation for lasers, Phys. Rev. Lett. 73, 2978-2981 (1994).
  5. J. B. Geddes, J. Lega, J.V. Moloney, R.A. Indik, E.M. Wright and W.J. Firth, Pattern selection in passive and active nonlinear optical systems, Chaos, Solitons and Fractals 4, 1261-1274 (1994).
  6. G. K. Harkness, J.C. Lega and G.L. Oppo, Correlation functions in the presence of optical vortices, Chaos, Solitons and Fractals 4, 1519-1533 (1994).
  7. J. Lega, J.V. Moloney, and A.C. Newell, Universal description of laser dynamics near threshold, Physica D 83, 478-498 (1995).
  8. G.K. Harkness, J. Lega, and G.L. Oppo, Measuring disorder with correlation functions of averaged patterns, Physica D 96, 26-29 (1996).
  9. D. Hochheiser, J.V. Moloney and J. Lega, Controlling optical turbulence, Phys. Rev. A 55, 4011-4014 (1997).
  10. O. G. Calderón, V. M. Pérez-García, J. Lega, and J. M. Guerra, Loss-induced transverse effects in lasers, Opt. Comm. 143, 315-321 (1997).

Coherent Structures

  1. J. Lega and S. Fauve, Traveling hole solutions to the complex Ginzburg-Landau equation as perturbations of Nonlinear Schrödinger dark solitons, Physica 102 D, 234-252 (1997).
  2. S. Bottin and J. Lega, Pulses of tunable size near a subcritical bifurcation, Eur. Phys. J. B 5, 299-308 (1998).
  3. J. Lega and A. Goriely, Pulses, fronts and oscillations of an elastic rod, Physica D 132, 374-392 (1999).
  4. S. Lafortune and J. Lega, Instability of local deformations of an elastic rod, Physica D 182, 103-124 (2003).
  5. S. Lafortune and J. Lega, Spectral stability of local deformations of an elastic rod: Hamiltonian formalism, SIAM J. Math. Anal. 36, 1726-1741 (2005).
  6. S. Lafortune, J. Lega, and S. Madrid, Instability of Local Deformations of an Elastic Rod: Numerical Evaluation of the Evans Function, SIAM J. Appl. Math. 71, 1653-1672 (2011).

Transportation Networks

  1. C.A. Thompson, K. Saxberg, J. Lega, D. Tong, H.E. Brown, A cumulative gravity model for inter-urban spatial interaction at different scales, Journal of Transport Geography 79, 102461 (2019).

Analysis of Graphical Enumeration

  1. Nicholas Ercolani, Joceline Lega, and Brandon Tippings, Dynamics of Nonpolar Solutions to the Discrete Painlevé I Equation, SIAM J. Appl. Dyn. Sys. 21, 1322-1351 (2022).
  2. Nicholas Ercolani, Joceline Lega, and Brandon Tippings, Multiple scale asymptotics of map enumeration, Nonlinearity 36, 1663-1698 (2023).
  3. Nicholas Ercolani, Joceline Lega, and Brandon Tippings, Non-recursive counts of graphs on surfaces, ECA 3:3, Article S2R20 (2023). Link to PDF copy of the article.

Modeling of Biological Phenomena

  1. Y. Pomeau and J. Lega, Structures macroscopiques en spirales comme configurations d’équilibre d’un ensemble de molécules chirales, C. R. Acad. Sci. Paris II 311, 1135-1143 (1990).
  2. B.R. Schoene, J. Lega, K.W. Flessa, D.H. Goodwin and D.L. Dettman, Reconstructing daily temperatures from growth rates of the intertidal bivalve mollusk Chione cortezi (northern Gulf of California, Mexico), Palaeogeography, Palaeoclimatology, Palaeoecology 184, 131-146 (2002).
Bacterial colonies: bioconvection and colony dynamics
  1. N. Mendelson and J. Lega, A complex pattern of traveling stripes is produced by swimming cells of Bacillus subtilis, Journal of Bacteriology 180, 3285-3294 (1998).
  2. J. Lega and N. Mendelson, Control-parameter dependent Swift-Hohenberg equation as a model for bioconvection patterns, Phys. Rev. E 59, 6267-6274 (1999).
  3. J. Lega and T. Passot, Hydrodynamics of bacterial colonies: a model, Phys. Rev. E 67, 031906 1-18 (2003).
  4. J. Lega and T. Passot, Hydrodynamics of bacterial colonies: phase diagrams, Chaos 14, 562-570 (2004).
Neurophysiology
  1. T.A. Christensen, G. D’Alessandro, J. Lega and J.G. Hildebrand, Morphometric modeling of olfactory circuits in the insect antennal lobe: I. Simulations of spiking local interneurons, Biosystems 61, 143-153 (2001).
  2. M.A. Herrera-Valdez and J. Lega, Reduced models for the pacemaker dynamics of cardiac cells, J. Theoretical Biology 270, 164-176 (2011).
Mosquito abundance
  1. H. E. Brown, A. Young, J. Lega, T. G. Andreadis, J. Schurich, A. Comrie, Projection of Climate Change Influences on U.S. West Nile Virus Vectors, Earth Interact. 19, 1–18 (2015).
  2. H.E. Brown, R. Barrera, A.C. Comrie, J. Lega, Effect of temperature thresholds on modeled Aedes aegypti population dynamics, J. Med. Entomol. 54, 869–877 (2017).
  3. J. Lega, H.E. Brown, R. Barrera, Aedes aegypti (Diptera: Culicidae) abundance model improved with relative humidity and precipitation-driven egg hatching, J. Med. Entomol. 54, 1375–1384 (2017).
  4. J. Lega, H.E. Brown, R. Barrera, A 70% Reduction in Mosquito Populations Does Not Require Removal of 70% of Mosquitoes, J. Med. Entomol. 57, 1668–1670 (2020).
  5. A.C. Kinney, S. Current, J. Lega, Aedes-AI: Neural network models of mosquito abundance, PLoS Comput. Biol. 17, e1009467 (2021).
Disease forecasting
  1. J. Lega and H.E. Brown, Data-driven outbreak forecasting with a simple nonlinear growth model, Epidemics 17, 19–26 (2016).
  2. S.Y. Del Valle, B.H. McMahon, J. Asher, R. Hatchett, J.C. Lega, H.E. Brown, M.E. Leany, Y. Pantazis, D.J. Roberts, S. Moore, A.T. Peterson, L.E. Escobar, H. Qiao, N.W. Hengartner and H. Mukundan, Summary results of the 2014-2015 DARPA Chikungunya challenge, BMC Infectious Diseases 18, 245 (2018).
  3. J. McGowan, M. Biggerstaff, M. Johansson, K.M. Apfeldorf, M. Ben-Nun, L. Brooks, M. Convertino, M. Erraguntla, D.C. Farrow, J. Freeze, S. Ghosh, S. Hyun, S. Kandula, J. Lega, Y. Liu, N. Michaud, H. Morita, J. Niemi, N. Ramakrishnan, E.L. Ray, N.G. Reich, P. Riley, J. Shaman, R. Tibshirani, A. Vespignani, Q. Zhang, C. Reed & The Influenza Forecasting Working Group, Collaborative efforts to forecast seasonal influenza in the United States, 2015–2016, Scientific Reports 9, 683 (2019).
  4. J. Lega, Parameter estimation from ICC curves, Journal of Biological Dynamics 15, 195-212 (2021).
  5. E.Y. Cramer et al. (295 authors), Evaluation of individual and ensemble probabilistic forecasts of COVID-19 mortality in the United States, PNAS 119, e2113561119 (2022).
  6. E.Y. Cramer, Y. Huang, Y. Wang, Y. et al. (400+ authors), The United States COVID-19 Forecast Hub dataset, Scientific Data 9, 462 (2022).
  7. Faryad D. Sahneh, William Fries, Joseph C. Watkins, Joceline Lega, Epidemics from the Eye of the Pathogen, SIAM J. Appl. Math. 82, 2036-2056 (2022).

Interacting Particles

  1. Joceline Lega, Collective behaviors in two-dimensional systems of interacting particles, SIAM J. Appl. Dyn. Sys. 10, 1213-1231 (2011).
    Erratum: SIAM J. Appl. Dyn. Sys. 12, 2093–2093 (2013).
  2. Joceline Lega, Sunder Sethuraman, Alexander L. Young, On Collisions Times of ‘Self-Sorting’ Interacting Particles in One-Dimension with Random Initial Positions and Velocities, Journal of Statistical Physics 170, 1088-1122 (2018).

Thin Films, Thin Elastic Plates, and Membranes

Thin films
  1. D. Moulton and J. Lega, Reverse draining of a magnetic soap film – Analysis and simulation of thin film equation with non-uniform forcing, Physica D 238, 2153-2165 (2009).
  2. D.E. Moulton and J. Lega, Effect of disjoining pressure in a thin film equation with non-uniform forcing, Euro. Jnl of Applied Mathematics 24, 887-920 (2013).
Microelectromechanical devices (MEMS)
  1. A.E. Lindsay and J. Lega, Multiple Quenching Solutions of a Fourth Order Parabolic PDE with a Singular Nonlinearity Modeling a MEMS Capacitor, SIAM J. Appl. Math. 72, 935-958 (2012).
  2. A.E. Lindsay, J. Lega, F.J. Sayas, The Quenching Set of a MEMS Capacitor in Two-Dimensional Geometries, J. Nonlinear Sci. 23, 807-834 (2013).
  3. A.E. Lindsay, J. Lega, K.B. Glasner, Regularized model of post-touchdown configurations in electrostatic MEMS: Equilibrium analysis, Physica D 280-281, 95–108 (2014).
  4. A.E. Lindsay, J. Lega, K. B. Glasner, Regularized model of post-touchdown configurations in electrostatic MEMS: interface dynamics, IMA Journal of Applied Mathematics,
    doi: 10.1093/imamat/hxv011 (2015).
Capillary origami
  1. N.D. Brubaker and J. Lega, Two-dimensional capillary origami with pinned contact line, SIAM J. Appl. Math. 75, 1275-1300 (2015).
  2. N.D. Brubaker and J. Lega, Two-dimensional capillary origami, Phys. Lett. A 380, 83-87 (2016).
    Featured in the Virtual Special Issue on Women in Physics 2017
  3. N.D. Brubaker and J. Lega, Capillary induced deformations of a thin elastic sheet, Phil. Trans. R. Soc. A 374, 20150169 (2016).

Teaching

  1. J.C. Lega, S. Buxner, B. Blonder, F. Tama, Explorations in Integrated Science, Journal of College Science Teaching 43, 55-60 (2014).
    Link to supplementary materials (PDF)