Jianfeng Lu
Associate Professor of Mathematics
Jianfeng Lu is an applied mathematician interested in mathematical analysis and algorithm development for problems from computational physics, theoretical chemistry, materials science and other related fields.
More specifically, his current research focuses include:
Electronic structure and many body problems; quantum molecular dynamics; multiscale modeling and analysis; rare events and sampling techniques.
More specifically, his current research focuses include:
Electronic structure and many body problems; quantum molecular dynamics; multiscale modeling and analysis; rare events and sampling techniques.
Current Appointments & Affiliations
 Associate Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 2016
 Associate Professor of Chemistry, Chemistry, Trinity College of Arts & Sciences 2016
 Associate Professor of Physics, Physics, Trinity College of Arts & Sciences 2016
Contact Information
 242 Physics Bldg, 120 Science Drive, Durham, NC 27708
 Mathematics Department, Duke University, Box 90320, Durham, NC 27708
 jianfeng@math.duke.edu (919) 6602875
 Personal website
 Background

Education, Training, & Certifications
 Ph.D., Princeton University 2009

Duke Appointment History
 Assistant Professor in the Department of Mathematics, Mathematics, Trinity College of Arts & Sciences 2012  2016
 Assistant Professor in the Department of Physics, Physics, Trinity College of Arts & Sciences 2013  2016
 Assistant Professor in the Department of Chemistry, Chemistry, Trinity College of Arts & Sciences 2013  2016
 Recognition

In the News

Awards & Honors
 Expertise

Global Scholarship

Teaching

 Research

Selected Grants
 CAREER: Research and training in advanced computational methods for quantum and statistical mechanics awarded by National Science Foundation 2015  2020
 Collaborative Research: SI2SSI: ELSIInfrastructure for Scalable Electronic Structure Theory awarded by National Science Foundation 2015  2019
 Mathematical Problems for Electronic Structure Models awarded by National Science Foundation 2013  2016
 Publications & Artistic Works

Selected Publications

Journal Articles
 Lu, J, and Yang, H. "A cubic scaling algorithm for excited states calculations in particle–particle random phase approximation." Journal of Computational Physics 340 (July 2017): 297308. Full Text Open Access Copy
 Gao, Y, Liu, JG, and Lu, J. "Continuum Limit of a Mesoscopic Model with Elasticity of Step Motion on Vicinal Surfaces." Journal of Nonlinear Science 27, no. 3 (June 2017): 873926. Full Text Open Access Copy
 Li, C, Lu, J, and Yang, W. "On extending KohnSham density functionals to systems with fractional number of electrons." The Journal of chemical physics 146, no. 21 (June 2017): 214109. Full Text
 Lu, J, and Thicke, K. "Orbital minimization method with ℓ 1 regularization." Journal of Computational Physics 336 (May 2017): 87103. Full Text Open Access Copy
 Lu, J, and Zhou, Z. "Path integral molecular dynamics with surface hopping for thermal equilibrium sampling of nonadiabatic systems." The Journal of chemical physics 146, no. 15 (April 2017): 154110. Full Text Open Access Copy
 Niu, X, Luo, T, Lu, J, and Xiang, Y. "Dislocation climb models from atomistic scheme to dislocation dynamics." Journal of the Mechanics and Physics of Solids 99 (February 2017): 242258. Full Text Open Access Copy
 Watson, AB, Lu, J, and Weinstein, MI. "Wavepackets in inhomogeneous periodic media: Effective particlefield dynamics and Berry curvature." Journal of Mathematical Physics 58, no. 2 (February 2017): 021503021503. Full Text Open Access Copy
 Cornelis, B, Yang, H, Goodfriend, A, Ocon, N, Lu, J, and Daubechies, I. "Removal of Canvas Patterns in Digital Acquisitions of Paintings." IEEE transactions on image processing : a publication of the IEEE Signal Processing Society 26, no. 1 (January 2017): 160171. Full Text Open Access Copy
 Gao, Y, Liu, JG, and Lu, J. "Weak Solution of a Continuum Model For Vicinal Surface in The AttachmentDetachmentLimited Regime." SIAM Journal on Mathematical Analysis 49, no. 3 (January 2017): 17051731. Full Text Open Access Copy
 Li, Q, Lu, J, and Sun, W. "Validity and Regularization of Classical HalfSpace Equations." Journal of Statistical Physics 166, no. 2 (January 2017): 398433. Full Text Open Access Copy
 Lu, J, and Yang, H. "Preconditioning Orbital Minimization Method for Planewave Discretization." Multiscale Modeling & Simulation 15, no. 1 (January 2017): 254273. Full Text Open Access Copy
 Mendl, CB, Lu, J, and Lukkarinen, J. "Thermalization of oscillator chains with onsite anharmonicity and comparison with kinetic theory." Physical review. E 94, no. 61 (December 2, 2016): 062104. Full Text Open Access Copy
 Li, Q, Lu, J, and Sun, W. "Halfspace kinetic equations with general boundary conditions." Mathematics of Computation 86, no. 305 (October 12, 2016): 12691301. Full Text Open Access Copy
 Yu, TQ, Lu, J, Abrams, CF, and VandenEijnden, E. "Multiscale implementation of infiniteswap replica exchange molecular dynamics." Proceedings of the National Academy of Sciences of the United States of America 113, no. 42 (October 3, 2016): 1174411749. Full Text
 Lu, J, and Zhou, Z. "Improved sampling and validation of frozen Gaussian approximation with surface hopping algorithm for nonadiabatic dynamics." The Journal of chemical physics 145, no. 12 (September 2016): 124109. Full Text Open Access Copy
 Li, X, and Lu, J. "Traction boundary conditions for molecular static simulations." Computer Methods in Applied Mechanics and Engineering 308 (August 2016): 310329. Full Text Open Access Copy
 Lin, L, and Lu, J. "Decay estimates of discretized Green’s functions for Schrödinger type operators." Science China Mathematics 59, no. 8 (August 2016): 15611578. Full Text Open Access Copy
 Lai, R, and Lu, J. "Localized density matrix minimization and linearscaling algorithms." Journal of Computational Physics 315 (June 2016): 194210. Full Text Open Access Copy
 Lu, J, and Ying, L. "Sparsifying preconditioner for soliton calculations." Journal of Computational Physics 315 (June 2016): 458466. Full Text Open Access Copy
 Lu, J, Wirth, B, and Yang, H. "Combining 2D synchrosqueezed wave packet transform with optimization for crystal image analysis." Journal of the Mechanics and Physics of Solids 89 (April 1, 2016): 194210. Full Text Open Access Copy
 Chen, J, and Lu, J. "Analysis of the divideandconquer method for electronic structure calculations." Mathematics of Computation 85, no. 302 (January 28, 2016): 29192938. Full Text Open Access Copy
 Delgadillo, R, Lu, J, and Yang, X. "GaugeInvariant Frozen Gaussian Approximation Method for the Schrödinger Equation with Periodic Potentials." SIAM Journal on Scientific Computing 38, no. 4 (January 2016): A2440A2463. Full Text Open Access Copy
 Li, C, Lu, J, and Yang, W. "Gentlest ascent dynamics for calculating first excited state and exploring energy landscape of KohnSham density functionals." The Journal of chemical physics 143, no. 22 (December 2015): 224110. Full Text
 Lu, J, Moroz, V, and Muratov, CB. "OrbitalFree Density Functional Theory of OutofPlane Charge Screening in Graphene." Journal of Nonlinear Science 25, no. 6 (December 2015): 13911430. Full Text Open Access Copy
 Li, Q, Lu, J, and Sun, W. "Diffusion approximations and domain decomposition method of linear transport equations: Asymptotics and numerics." Journal of Computational Physics 292 (July 1, 2015): 141167. Full Text Open Access Copy
 Yang, H, Lu, J, Brown, WP, Daubechies, I, and Ying, L. "Quantitative Canvas Weave Analysis Using 2D Synchrosqueezed Transforms: Application of timefrequency analysis to art investigation." IEEE Signal Processing Magazine 32, no. 4 (July 2015): 5563. Full Text Open Access Copy
 Lu, J, and Mendl, CB. "Numerical scheme for a spatially inhomogeneous matrixvalued quantum Boltzmann equation." Journal of Computational Physics 291 (June 2015): 303316. Full Text Open Access Copy
 Lu, J, Liu, JG, and Margetis, D. "Emergence of step flow from an atomistic scheme of epitaxial growth in 1+1 dimensions." Physical review. E, Statistical, nonlinear, and soft matter physics 91, no. 3 (March 4, 2015): 032403. Full Text Open Access Copy
 Lu, J, and Nolen, J. "Reactive trajectories and the transition path process." Probability Theory and Related Fields 161, no. 12 (February 2015): 195244. Full Text Open Access Copy
 Lai, R, Lu, J, and Osher, S. "Density matrix minimization with ${\ell}_1$ regularization." Communications in Mathematical Sciences 13, no. 8 (2015): 20972117. Full Text Open Access Copy
 Liu, J, Lu, J, and Zhou, X. "Efficient Rare Event Simulation for Failure Problems in Random Media." SIAM Journal on Scientific Computing 37, no. 2 (January 2015): A609A624. Full Text Open Access Copy
 Lu, J, and Marzuola, JL. "Strang splitting methods for a quasilinear Schrödinger equation: convergence, instability, and dynamics." Communications in Mathematical Sciences 13, no. 5 (2015): 10511074. Full Text Open Access Copy
 Lu, J, and Ying, L. "Compression of the electron repulsion integral tensor in tensor hypercontraction format with cubic scaling cost." Journal of Computational Physics 302 (2015): 329335. Full Text Open Access Copy
 Yang, H, Lu, J, and Ying, L. "Crystal Image Analysis Using 2D Synchrosqueezed Transforms." Multiscale Modeling & Simulation 13, no. 4 (January 2015): 15421572. Full Text Open Access Copy
 Lu, J, and Otto, F. "Nonexistence of a Minimizer for ThomasFermiDiracvon Weizsäcker Model." Communications on Pure and Applied Mathematics 67, no. 10 (October 2014): 16051617. Full Text
 Yang, Y, Peng, D, Lu, J, and Yang, W. "Excitation energies from particleparticle random phase approximation: Davidson algorithm and benchmark studies." The Journal of chemical physics 141, no. 12 (September 2014): 124104. Full Text
 Lu, J, and VandenEijnden, E. "Exact dynamical coarsegraining without timescale separation." The Journal of Chemical Physics 141, no. 4 (July 28, 2014): 044109044109. Full Text
 E, W, and Lu, J. "Mathematical theory of solids: From quantum mechanics to continuum models." Discrete and Continuous Dynamical Systems 34, no. 12 (June 2014): 50855097. Full Text
 Kohn, RV, Lu, J, Schweizer, B, and Weinstein, MI. "A Variational Perspective on Cloaking by Anomalous Localized Resonance." Communications in Mathematical Physics 328, no. 1 (May 2014): 127. Full Text Open Access Copy
 Lin, L, Lu, J, and Shao, S. "Analysis of Time Reversible BornOppenheimer Molecular Dynamics." Entropy 16, no. 1 (January 2014): 110137. Full Text Open Access Copy
 Lu, J, and Ming, P. "Stability Of A ForceBased Hybrid Method With Planar Sharp Interface." SIAM Journal on Numerical Analysis 52, no. 4 (January 2014): 20052026. Full Text Open Access Copy
 Lu, J, and Otto, F. "Nonexistence of a minimizer for ThomasFermiDiracvon Weizsäcker model." Communications on Pure and Applied Mathematics 67, no. 10 (2014): 16051617. Full Text
 Lu, J, and VandenEijnden, E. "Infinite swapping replica exchange molecular dynamics leads to a simple simulation patch using mixture potentials." J Chem Phys 138, no. 8 (February 28, 2013): 084105. Full Text Open Access Copy Link to Item
 E, W, Lu, J, and Yao, Y. "The landscape of complex networks: Critical nodes and a hierarchical decomposition." Methods and Applications of Analysis 20, no. 4 (2013): 383404. Full Text
 E, W, Lu, JF, and Yang, X. "Asymptotic analysis of quantum dynamics in crystals: The BlochWigner transform, Bloch dynamics and Berry phase." Acta Mathematicae Applicatae Sinica 29, no. 3 (2013): 465476. Full Text
 Lu, J, and Ming, P. "Convergence of a ForceBased Hybrid Method in Three Dimensions." Communications on Pure and Applied Mathematics 66, no. 1 (January 2013): 83108. Full Text Open Access Copy
 E, W, and Lu, J. "Stability and the continuum limit of the spinpolarized ThomasFermiDiracvon Weizsäcker model." Journal of Mathematical Physics 53, no. 11 (November 2012): 115615115615. Full Text Open Access Copy
 Lin, L, Lu, J, Ying, L, and E, W. "Optimized local basis set for Kohn–Sham density functional theory." Journal of Computational Physics 231, no. 13 (May 2012): 45154529. Full Text
 Lin, L, Lu, J, Ying, L, and E, W. "Adaptive local basis set for Kohn–Sham density functional theory in a discontinuous Galerkin framework I: Total energy calculation." Journal of Computational Physics 231, no. 4 (February 2012): 21402154. Full Text Open Access Copy
 E, W, and Lu, J. "The KohnSham equation for deformed crystals." Memoirs of the American Mathematical Society 221, no. 1040 (2012): 11. Full Text
 Lu, J, and Yang, X. "Frozen gaussian approximation for general linear strictly hyperbolic systems: Formulation and eulerian methods." Multiscale Modeling and Simulation 10, no. 2 (2012): 451472. Full Text Open Access Copy
 Lu, J, and Yang, X. "Convergence of frozen Gaussian approximation for highfrequency wave propagation." Communications on Pure and Applied Mathematics 65, no. 6 (2012): 759789. Full Text Open Access Copy
 Schütte, C, Noé, F, Lu, J, Sarich, M, and VandenEijnden, E. "Markov state models based on milestoning." The Journal of Chemical Physics 134, no. 20 (May 28, 2011): 204105204105. Full Text
 E, W, and Lu, J. "The Electronic Structure of Smoothly Deformed Crystals: Wannier Functions and the Cauchy–Born Rule." Archive for Rational Mechanics and Analysis 199, no. 2 (February 2011): 407433. Full Text
 Lin, L, Yang, C, Meza, JC, Lu, J, Ying, L, and E, W. "SelInvAn Algorithm for Selected Inversion of a Sparse Symmetric Matrix." ACM Transactions on Mathematical Software 37, no. 4 (February 1, 2011): 119. Full Text
 E, W, Lu, J, and Yang, X. "Effective Maxwell equations from timedependent density functional theory." Acta Math. Sin. 32 (2011): 339339. Open Access Copy
 E, W, and Lu, J. "Multiscale modeling." Scholarpedia 6 (2011): 11527. (Review) Link to Item
 Lin, L, Lu, J, and Ying, L. "Fast construction of hierarchical matrix representation from matrixvector multiplication." Journal of Computational Physics 230, no. 10 (2011): 40714087. Full Text Open Access Copy
 Lin, L, Yang, C, Lu, J, Ying, L, and E, W. "A Fast Parallel Algorithm for Selected Inversion of Structured Sparse Matrices with Application to 2D Electronic Structure Calculations." SIAM Journal on Scientific Computing 33, no. 3 (January 2011): 13291351. Full Text
 Lu, J, and Yang, X. "Frozen Gaussian approximation for high frequency wave propagation." Communications in Mathematical Sciences 9, no. 3 (2011): 663683.
 E, W, and Lu, J. "Electronic structure of smoothly deformed crystals: Cauchyborn rule for the nonlinear tightbinding model." Communications on Pure and Applied Mathematics 63, no. 11 (November 2010): 14321468. Full Text
 E, W, Li, T, and Lu, J. "Localized bases of eigensubspaces and operator compression." Proceedings of the National Academy of Sciences 107, no. 4 (January 26, 2010): 12731278. Full Text
 GarcíaCervera, CJ, Lu, J, Xuan, Y, and E, W. "Linearscaling subspaceiteration algorithm with optimally localized nonorthogonal wave functions for KohnSham density functional theory." Physical Review B 79, no. 11 (March 2009). Full Text
 Lin, L, Lu, J, Car, R, and E, W. "Multipole representation of the Fermi operator with application to the electronic structure analysis of metallic systems." Physical Review B 79, no. 11 (March 2009). Full Text Open Access Copy
 Lin, L, Lu, J, Ying, L, Car, R, and E, W. "Fast algorithm for extracting the diagonal of the inverse matrix with application to the electronic structure analysis of metallic systems." Commun. Math. Sci. 7 (2009): 755777.
 Lin, L, Lu, J, Ying, L, and E, W. "Polebased approximation of the FermiDirac function." Chin. Ann. Math. Ser. B 30 (2009): 729742. Open Access Copy
 GarciaCervera, CJ, Ren, W, Lu, J, and E, W. "Sequential multiscale modelling using sparse representation." Commun. Comput. Phys. 4 (2008): 10251033.
 E, W, and Lu, J. "The Elastic Continuum Limit of the Tight Binding Model*." Chinese Annals of Mathematics, Series B 28, no. 6 (December 2007): 665676. Full Text
 E, W, GarcíaCervera, CJ, and Lu, J. "A sublinear scaling algorithm for computing the electronic structure of materials." Communications in Mathematical Sciences 5, no. 4 (2007): 9991026. Full Text
 E, W, and Lu, J. "Seamless multiscale modeling via dynamics on fiber bundles." Communications in Mathematical Sciences 5, no. 3 (2007): 649663. Full Text
 E, W, and Lu, J. "The continuum limit and QMcontinuum approximation of quantum mechanical models of solids." Communications in Mathematical Sciences 5, no. 3 (2007): 679696. Full Text
 E, W, Lu, J, and Yang, JZ. "Uniform accuracy of the quasicontinuum method." Physical Review B 74, no. 21 (December 2006). Full Text
 Cai, Z, and Lu, J. "A Surface Hopping Gaussian Beam Method for HighDimensional Transport Systems." Open Access Copy Link to Item
 Cao, Y, and Lu, J. "Lindblad equation and its semiclassical limit of the AndersonHolstein model." Open Access Copy Link to Item
 Chen, H, Lu, J, and Ortner, C. "Thermodynamic Limit of Crystal Defects with Finite Temperature Tight Binding." Open Access Copy Link to Item
 Dai, S, Li, B, and Lu, J. "Convergence of PhaseField Free Energy and Boundary Force for Molecular Solvation." Open Access Copy Link to Item
 Daubechies, I, Lu, J, and Wu, HT. "Synchrosqueezed Wavelet Transforms: a Tool for Empirical Mode Decomposition." Link to Item
 Delgadillo, R, Lu, J, and Yang, X. "Frozen Gaussian approximation for high frequency wave propagation in periodic media." Open Access Copy Link to Item
 Du, Q, Li, XH, Lu, J, and Tian, X. "A quasinonlocal coupling method for nonlocal and local diffusion models." Open Access Copy Link to Item
 Fang, D, and Lu, J. "A Diabatic Surface Hopping Algorithm based on Time Dependent Perturbation Theory and Semiclassical Analysis." Link to Item
 Huang, Y, Lu, J, and Ming, P. "A Concurrent Globallocal Numerical Method for Multiscale PDEs." Open Access Copy Link to Item
 Khoo, Y, Lu, J, and Ying, L. "Solving parametric PDE problems with artificial neural networks." Link to Item
 Lai, R, and Lu, J. "Point cloud discretization of FokkerPlanck operators for committor functions." Open Access Copy Link to Item
 Li, L, Liu, JG, and Lu, J. "Fractional stochastic differential equations satisfying fluctuationdissipation theorem." Open Access Copy Link to Item
 Li, Q, Lu, J, and Sun, W. "A convergent method for linear halfspace kinetic equations." Open Access Copy Link to Item
 Li, Q, and Lu, J. "An asymptotic preserving method for transport equations with oscillatory scattering coefficients." Open Access Copy Link to Item
 Li, X, Lin, L, and Lu, J. "PEXSI$Σ$: A Green's function embedding method for KohnSham density functional theory." Open Access Copy Link to Item
 Li, X, Liu, J, Lu, J, and Zhou, X. "Moderate Deviation for Random Elliptic PDEs with Small Noise." Open Access Copy Link to Item
 Li, XH, and Lu, J. "Quasinonlocal coupling of nonlocal diffusions." Open Access Copy Link to Item
 Lin, L, Lu, J, and VandenEijnden, E. "A Mathematical Theory of Optimal Milestoning (with a Detour via Exact Milestoning)." Open Access Copy Link to Item
 Liu, JG, Lu, J, Margetis, D, and Marzuola, JL. "Asymmetry in crystal facet dynamics of homoepitaxy by a continuum model." Open Access Copy Link to Item
 Lu, J, and Otto, F. "An isoperimetric problem with Coulomb repulsion and attraction to a background nucleus." Open Access Copy Link to Item
 Lu, J, and Spiliopoulos, K. "Multiscale integrators for stochastic differential equations and irreversible Langevin samplers." Open Access Copy Link to Item
 Lu, J, and Steinerberger, S. "A Variation on the DonskerVaradhan Inequality for the Principial Eigenvalue." Open Access Copy Link to Item
 Lu, J, and Thicke, K. "Cubic scaling algorithms for RPA correlation using interpolative separable density fitting." Open Access Copy Link to Item
 Lu, J, and Ying, L. "Fast algorithm for periodic density fitting for Bloch waves." Open Access Copy Link to Item
 Lu, J, and Zhou, Z. "Frozen Gaussian approximation with surface hopping for mixed quantumclassical dynamics: A mathematical justification of fewest switches surface hopping algorithms." Open Access Copy Link to Item
 Lu, J, and Zhou, Z. "Bloch dynamics with second order Berry phase correction." Open Access Copy Link to Item
 Nishimura, A, Dunson, D, and Lu, J. "Discontinuous Hamiltonian Monte Carlo for sampling discrete parameters." Link to Item
 Yang, H, and Lu, J. "Phase Space Sketching for Crystal Image Analysis based on Synchrosqueezed Transforms." Open Access Copy Link to Item
 Yu, VWZ, Corsetti, F, García, A, Huhn, WP, Jacquelin, M, Jia, W, Lange, B, Lin, L, Lu, J, Mi, W, Seifitokaldani, A, VázquezMayagoitia, Á, Yang, C, Yang, H, and Blum, V. "ELSI: A Unified Software Interface for KohnSham Electronic Structure Solvers." Open Access Copy Link to Item

 Teaching & Mentoring

Recent Courses
 MATH 356: Elementary Differential Equations 2017
 MATH 631: Real Analysis 2017
 MATH 493: Research Independent Study 2016
 MATH 563: Applied Computational Analysis 2016
 MATH 79090: Minicourse in Advanced Topics 2016
 MATH 393: Research Independent Study 2015
 MATH 635: Functional Analysis 2015
 MATH 799: Special Readings 2015
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