Math @ Duke

Papers Published
 Niu, X; Luo, T; Lu, J; Xiang, Y, Dislocation climb models from atomistic scheme to dislocation dynamics,
Journal of the Mechanics and Physics of Solids, vol. 99
(February, 2017),
pp. 242258 [doi]
 Mendl, CB; Lu, J; Lukkarinen, J, Thermalization of oscillator chains with onsite anharmonicity and comparison with kinetic theory,
Physical review. E, vol. 94 no. 6
(December, 2016) [doi]
 Yu, TQ; Lu, J; Abrams, CF; VandenEijnden, E, Multiscale implementation of infiniteswap replica exchange molecular dynamics.,
Proceedings of the National Academy of Sciences of USA, vol. 113 no. 42
(October, 2016),
pp. 1174411749 [abs]
 Lu, J; Zhou, Z, Improved sampling and validation of frozen Gaussian approximation with surface hopping algorithm for nonadiabatic dynamics.,
Journal of Chemical Physics, vol. 145 no. 12
(September, 2016),
pp. 124109 [doi] [abs]
 Li, X; Lu, J, Traction boundary conditions for molecular static simulations,
Computer Methods in Applied Mechanics and Engineering, vol. 308
(August, 2016),
pp. 310329 [doi]
 Lin, L; Lu, J, Decay estimates of discretized Green’s functions for Schrödinger type operators,
Science China Mathematics, vol. 59 no. 8
(August, 2016),
pp. 15611578 [doi]
 Lai, R; Lu, J, Localized density matrix minimization and linearscaling algorithms,
Journal of Computational Physics, vol. 315
(June, 2016),
pp. 194210 [doi]
 Lu, J; Ying, L, Sparsifying preconditioner for soliton calculations,
Journal of Computational Physics, vol. 315
(June, 2016),
pp. 458466 [doi]
 Lu, J; Wirth, B; Yang, H, Combining 2D synchrosqueezed wave packet transform with optimization for crystal image analysis,
Journal of the Mechanics and Physics of Solids, vol. 89
(2016),
pp. 194210, ISSN 00225096 [arXiv:1501.06254], [repository], [doi] [abs]
 Chen, J; Lu, J, Analysis of the divideandconquer method for electronic structure calculations,
Mathematics of Computation, vol. 85 no. 302
(January, 2016),
pp. 29192938 [doi]
 Delgadillo, R; Lu, J; Yang, X, GaugeInvariant Frozen Gaussian Approximation Method for the Schrödinger Equation with Periodic Potentials,
SIAM Journal on Scientific Computing, vol. 38 no. 4
(January, 2016),
pp. A2440A2463 [doi]
 Lu, J; Moroz, V; Muratov, CB, OrbitalFree Density Functional Theory of OutofPlane Charge Screening in Graphene,
Journal of Nonlinear Science, vol. 25 no. 6
(2015),
pp. 13911430, ISSN 09388974 [arXiv:1405.4949], [doi]
 Li, C; Lu, J; Yang, W, Gentlest ascent dynamics for calculating first excited state and exploring energy landscape of KohnSham density functionals.,
Journal of Chemical Physics, vol. 143 no. 22
(December, 2015),
pp. 224110, ISSN 00219606 [doi] [abs]
 Yang, H; Lu, J; Brown, WP; Daubechies, I; Ying, L, Quantitative Canvas Weave Analysis Using 2D Synchrosqueezed Transforms: Application of timefrequency analysis to art investigation,
IEEE Signal Processing Magazine, vol. 32 no. 4
(2015),
pp. 5563, ISSN 10535888 [repository], [doi]
 Li, Q; Lu, J; Sun, W, Diffusion approximations and domain decomposition method of linear transport equations: Asymptotics and numerics,
Journal of Computational Physics, vol. 292
(2015),
pp. 141167, ISSN 00219991 [arXiv:1409.0476], [doi] [abs]
 Lu, J; Mendl, CB, Numerical scheme for a spatially inhomogeneous matrixvalued quantum Boltzmann equation,
Journal of Computational Physics, vol. 291
(2015),
pp. 303316, ISSN 00219991 [arXiv:1408.1782], [doi]
 Lu, J; Liu, JG; 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, vol. 91 no. 3
(2015),
pp. 032403, ISSN 15393755 [arXiv:1409.0046], [doi] [abs]
 Lu, J; Nolen, J, Reactive trajectories and the transition path process,
Probability Theory and Related Fields, vol. 161 no. 12
(February, 2015),
pp. 195244, ISSN 01788051 ([erratum].) [arXiv:1303.1744], [doi]
 Liu, J; Lu, J; Zhou, X, Efficient Rare Event Simulation for Failure Problems in Random Media,
SIAM Journal on Scientific Computing, vol. 37 no. 2
(2015),
pp. A609A624, ISSN 10648275 [arXiv:1404.4729], [doi]
 Yang, H; Lu, J; Ying, L, Crystal Image Analysis Using 2D Synchrosqueezed Transforms,
Multiscale Modeling & Simulation, vol. 13 no. 4
(2015),
pp. 15421572, ISSN 15403459 [arXiv:1402.1262], [repository], [doi]
 Lu, J; Ying, L, Compression of the electron repulsion integral tensor in tensor hypercontraction format with cubic scaling cost,
Journal of Computational Physics, vol. 302
(2015),
pp. 329335, ISSN 00219991 [arXiv:1410.7757], [doi] [abs]
 Lai, R; Lu, J; Osher, S, Density matrix minimization with ${\ell}_1$ regularization,
Communications in Mathematical Sciences, vol. 13 no. 8
(2015),
pp. 20972117, ISSN 15396746 [arXiv:1403.1525], [doi]
 Lu, J; Marzuola, JL, Strang splitting methods for a quasilinear Schrödinger equation: convergence, instability, and dynamics,
Communications in Mathematical Sciences, vol. 13 no. 5
(2015),
pp. 10511074, ISSN 15396746 [arXiv:1305.7205], [doi]
 Lu, J; Otto, F, Nonexistence of a Minimizer for ThomasFermiDiracvon Weizsäcker Model,
Communications on Pure & Applied Mathematics, vol. 67 no. 10
(2014),
pp. 16051617, ISSN 00103640 [doi]
 Yang, Y; Peng, D; Lu, J; Yang, W, Excitation energies from particleparticle random phase approximation: Davidson algorithm and benchmark studies.,
Journal of Chemical Physics, vol. 141 no. 12
(2014),
pp. 124104, ISSN 00219606 [doi] [abs]
 Lu, J; VandenEijnden, E, Exact dynamical coarsegraining without timescale separation,
Journal of Chemical Physics, vol. 141 no. 4
(July, 2014),
pp. 044109044109, ISSN 00219606 [arXiv:1404.4225], [doi]
 E, W; Lu, J, Mathematical theory of solids: From quantum mechanics to continuum models,
Discrete and Continuous Dynamical Systems, vol. 34 no. 12
(June, 2014),
pp. 50855097, ISSN 10780947 [doi]
 Kohn, RV; Lu, J; Schweizer, B; Weinstein, MI, A Variational Perspective on Cloaking by Anomalous Localized Resonance,
Communications in Mathematical Physics, vol. 328 no. 1
(2014),
pp. 127, ISSN 00103616 [doi]
 Lin, L; Lu, J; Shao, S, Analysis of Time Reversible BornOppenheimer Molecular Dynamics, edited by G. Ciccotti, M. Ferrario and Ch. Schuette,
Entropy (Basel, Switzerland), vol. 16 no. 1
(2014),
pp. 110137 (Special issue on Molecular Dynamics Simulation.) [doi]
 Lu, J; Ming, P, Stability Of A ForceBased Hybrid Method With Planar Sharp Interface,
SIAM Journal on Numerical Analysis, vol. 52 no. 4
(2014),
pp. 20052026, ISSN 00361429 [doi]
 Lu, J; Otto, F, Nonexistence of a minimizer for ThomasFermiDiracvon Weizsäcker model,
Communications on Pure & Applied Mathematics, vol. 67 no. 10
(2014),
pp. 16051617 [doi]
 Lu, J; VandenEijnden, E, Infinite swapping replica exchange molecular dynamics leads to a simple simulation patch using mixture potentials.,
Journal of Chemical Physics, vol. 138 no. 8
(2013),
pp. 084105 [23464138], [doi] [abs]
 Lu, J; Ming, P, Convergence of a ForceBased Hybrid Method in Three Dimensions,
Communications on Pure & Applied Mathematics, vol. 66 no. 1
(2013),
pp. 83108, ISSN 00103640 [doi]
 E, W; Lu, JF; Yang, X, Asymptotic analysis of quantum dynamics in crystals: The BlochWigner transform, Bloch dynamics and Berry phase,
Acta Mathematicae Applicatae Sinica, English Series, vol. 29 no. 3
(2013),
pp. 465476, ISSN 01689673 [doi] [abs]
 E, W; Lu, J; Yao, Y, The landscape of complex networks: Critical nodes and a hierarchical decomposition,
Methods and Applications of Analysis, vol. 20 no. 4
(2013),
pp. 383404, ISSN 10732772 (Special issue dedicated to Stan Osher's 70th birthday.) [doi]
 E, W; Lu, J, Stability and the continuum limit of the spinpolarized ThomasFermiDiracvon Weizsäcker model,
Journal of Mathematical Physics, vol. 53 no. 11
(November, 2012),
pp. 115615115615, ISSN 00222488 [doi]
 Lin, L; Lu, J; Ying, L; E, W, Optimized local basis set for Kohn–Sham density functional theory,
Journal of Computational Physics, vol. 231 no. 13
(May, 2012),
pp. 45154529, ISSN 00219991 [doi]
 Lin, L; Lu, J; Ying, L; 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, vol. 231 no. 4
(February, 2012),
pp. 21402154, ISSN 00219991 [doi]
 E, W; Lu, J, The KohnSham equation for deformed crystals,
Memoirs of the American Mathematical Society, vol. 221 no. 1040
(2013),
pp. 11, ISSN 00659266 [doi]
 Lu, J; Yang, X, Convergence of frozen Gaussian approximation for highfrequency wave propagation,
Communications on Pure & Applied Mathematics, vol. 65 no. 6
(2012),
pp. 759789, ISSN 00103640 [doi] [abs]
 Lu, J; Yang, X, Frozen gaussian approximation for general linear strictly hyperbolic systems: Formulation and eulerian methods,
Multiscale Modeling & Simulation, vol. 10 no. 2
(2012),
pp. 451472, ISSN 15403459 [doi] [abs]
 Daubechies, I; Lu, J; Wu, HT, Synchrosqueezed wavelet transforms: An empirical mode decompositionlike tool,
Applied and Computational Harmonic Analysis, vol. 30 no. 2
(2011),
pp. 243261, ISSN 10635203 [doi] [abs]
 Lin, L; Yang, C; Meza, JC; Lu, J; Ying, L; E, W, SelInvAn Algorithm for Selected Inversion of a Sparse Symmetric Matrix,
ACM Transactions on Mathematical Software, vol. 37 no. 4
(2011),
pp. 119, ISSN 00983500 [doi]
 E, W; Lu, J, The Electronic Structure of Smoothly Deformed Crystals: Wannier Functions and the Cauchy–Born Rule,
Archive for Rational Mechanics and Analysis, vol. 199 no. 2
(2011),
pp. 407433, ISSN 00039527 [doi]
 Lin, L; Yang, C; Lu, J; Ying, L; 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, vol. 33 no. 3
(2011),
pp. 13291351, ISSN 10648275 [doi]
 E, W; Lu, J; Yang, X, Effective Maxwell equations from timedependent density functional theory,
Acta Math. Sin., vol. 32
(2011),
pp. 339339
 Lin, L; Lu, J; Ying, L, Fast construction of hierarchical matrix representation from matrixvector multiplication,
Journal of Computational Physics, vol. 230 no. 10
(2011),
pp. 40714087, ISSN 00219991 [doi] [abs]
 Lu, J; Yang, X, Frozen Gaussian approximation for high frequency wave propagation,
Communications in Mathematical Sciences, vol. 9 no. 3
(2011),
pp. 663683, ISSN 15396746 [doi] [abs]
 Schütte, C; Noé, F; Lu, J; Sarich, M; VandenEijnden, E, Markov state models based on milestoning,
Journal of Chemical Physics, vol. 134 no. 20
(2011),
pp. 204105204105, ISSN 00219606 [doi]
 E, W; Lu, J, Multiscale modeling,
Scholarpedia, vol. 6
(2011),
pp. 11527 [Multiscale_modeling]
 E, W; Lu, J, Electronic structure of smoothly deformed crystals: Cauchyborn rule for the nonlinear tightbinding model,
Communications on Pure & Applied Mathematics, vol. 63 no. 11
(2010),
pp. 14321468, ISSN 00103640 [doi]
 E, W; Li, T; Lu, J, Localized bases of eigensubspaces and operator compression,
Proceedings of the National Academy of Sciences of USA, vol. 107 no. 4
(2010),
pp. 12731278, ISSN 00278424 [doi]
 GarcíaCervera, CJ; Lu, J; Xuan, Y; E, W, Linearscaling subspaceiteration algorithm with optimally localized nonorthogonal wave functions for KohnSham density functional theory,
Physical Review B  Condensed Matter and Materials Physics, vol. 79 no. 11
(2009),
pp. 115110, ISSN 10980121 [doi]
 Lin, L; Lu, J; Car, R; E, W, Multipole representation of the Fermi operator with application to the electronic structure analysis of metallic systems,
Physical Review B  Condensed Matter and Materials Physics, vol. 79 no. 11
(2009),
pp. 115133, ISSN 10980121 [doi]
 Lin, L; Lu, J; Ying, L; Car, R; 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., vol. 7
(2009),
pp. 755777
 Lin, L; Lu, J; Ying, L; E, W, Polebased approximation of the FermiDirac function,
Chin. Ann. Math. Ser. B, vol. 30
(2009),
pp. 729742
 GarciaCervera, CJ; Ren, W; Lu, J; E, W, Sequential multiscale modelling using sparse representation,
Commun. Comput. Phys., vol. 4
(2008),
pp. 10251033
 E, W; Lu, J, The Elastic Continuum Limit of the Tight Binding Model*,
Chinese Annals of Mathematics  Series B, vol. 28 no. 6
(2007),
pp. 665676, ISSN 02529599 [doi]
 E, W; GarcíaCervera, CJ; Lu, J, A sublinear scaling algorithm for computing the electronic structure of materials,
Communications in Mathematical Sciences, vol. 5 no. 4
(2007),
pp. 9991026, ISSN 15396746 [doi]
 E, W; Lu, J, Seamless multiscale modeling via dynamics on fiber bundles,
Communications in Mathematical Sciences, vol. 5 no. 3
(2007),
pp. 649663, ISSN 15396746 [doi]
 E, W; Lu, J, The continuum limit and QMcontinuum approximation of quantum mechanical models of solids,
Communications in Mathematical Sciences, vol. 5 no. 3
(2007),
pp. 679696, ISSN 15396746 [doi]
 E, W; Lu, J; Yang, JZ, Uniform accuracy of the quasicontinuum method,
Physical Review B  Condensed Matter and Materials Physics, vol. 74 no. 21
(2006),
pp. 214115, ISSN 10980121 [doi]


dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
 
Mathematics Department
Duke University, Box 90320
Durham, NC 277080320

