Math @ Duke

Papers Published
 J Lu, B Wirth and H Yang, Combining 2D synchrosqueezed wave packet transform with optimization for crystal image analysis, edited by K Bhattacharya,
Journal of the Mechanics and Physics of Solids
(January, 2016), Elsevier [arXiv:1501.06254], [DukeSpace]
 C Li, J Lu and W Yang, Gentlest ascent dynamics for calculating first excited state and exploring energy landscape of KohnSham density functionals.,
The Journal of chemical physics, vol. 143 no. 22
(December, 2015),
pp. 224110, ISSN 00219606 [doi] [abs]
 J Lu, V Moroz and CB Muratov, 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]
 J Lu and L Ying, 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]
 H Yang, J Lu, WP Brown, I Daubechies and L Ying, 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 [doi]
 Q Li, J Lu and W Sun, 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]
 J Lu and CB Mendl, 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]
 W E, JF Lu and X Yang, Asymptotic analysis of quantum dynamics in crystals: The BlochWigner transform, Bloch dynamics and Berry phase,
Acta Mathematicae Applicatae Sinica, vol. 29 no. 3
(2013),
pp. 465476, ISSN 01689673 [doi] [abs]
 W E and J Lu, Mathematical theory of solids: From quantum mechanics to continuum models,
Discrete and Continuous Dynamical Systems, vol. 34 no. 12
(March, 2015),
pp. 50855097, ISSN 10780947 [doi]
 J Lu, JG Liu and D Margetis, 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]
 J Lu and J Nolen, 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]
 W E, J Lu and Y Yao, 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]
 J Liu, J Lu and X Zhou, 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]
 H Yang, J Lu and L Ying, Crystal Image Analysis Using 2D Synchrosqueezed Transforms,
Multiscale Modeling & Simulation, vol. 13 no. 4
(2015),
pp. 15421572, ISSN 15403459 [arXiv:1402.1262], [doi]
 R Lai, J Lu and S Osher, Density matrix minimization with ${\ell}_1$ regularization,
Communications in Mathematical Sciences, vol. 13 no. 8
(2015),
pp. 20972117, ISSN 15396746 [arXiv:1403.1525], [doi]
 J Lu and JL Marzuola, 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]
 J Lu and F Otto, Nonexistence of a Minimizer for ThomasFermiDiracvon Weizsäcker Model,
Communications on Pure and Applied Mathematics, vol. 67 no. 10
(2014),
pp. 16051617, ISSN 00103640 [doi]
 Y Yang, D Peng, J Lu and W Yang, Excitation energies from particleparticle random phase approximation: Davidson algorithm and benchmark studies,
The Journal of Chemical Physics, vol. 141 no. 12
(2014),
pp. 124104124104, ISSN 00219606 [doi]
 J Lu and E VandenEijnden, Exact dynamical coarsegraining without timescale separation,
The Journal of Chemical Physics, vol. 141 no. 4
(July, 2014),
pp. 044109044109, ISSN 00219606 [arXiv:1404.4225], [doi]
 RV Kohn, J Lu, B Schweizer and MI Weinstein, A Variational Perspective on Cloaking by Anomalous Localized Resonance,
Communications in Mathematical Physics, vol. 328 no. 1
(2014),
pp. 127, ISSN 00103616 [doi]
 L Lin, J Lu and S Shao, Analysis of Time Reversible BornOppenheimer Molecular Dynamics, edited by G. Ciccotti, M. Ferrario and Ch. Schuette,
Entropy, vol. 16 no. 1
(2014),
pp. 110137 (Special issue on Molecular Dynamics Simulation.) [doi]
 J Lu and P Ming, 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]
 J Lu and E VandenEijnden, Infinite swapping replica exchange molecular dynamics leads to a simple simulation patch using mixture potentials.,
J Chem Phys, vol. 138 no. 8
(2013),
pp. 084105 [23464138], [doi] [abs]
 W E, J Lu and X Yang, Effective Maxwell equations from timedependent density functional theory,
Acta Math. Sin., vol. 32
(2011),
pp. 339339
 W E and J Lu, Multiscale modeling,
Scholarpedia, vol. 6
(2011),
pp. 11527 [Multiscale_modeling]
 L Lin, J Lu, L Ying, R Car and W E, 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
 L Lin, J Lu, L Ying and W E, Polebased approximation of the FermiDirac function,
Chin. Ann. Math. Ser. B, vol. 30
(2009),
pp. 729742
 CJ GarciaCervera, W Ren, J Lu and W E, Sequential multiscale modelling using sparse representation,
Commun. Comput. Phys., vol. 4
(2008),
pp. 10251033
 J Lu and P Ming, Convergence of a ForceBased Hybrid Method in Three Dimensions,
Communications on Pure and Applied Mathematics, vol. 66 no. 1
(2013),
pp. 83108, ISSN 00103640 [doi]
 L Lin, J Lu, L Ying and W E, 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]
 L Lin, J Lu, L Ying and W E, 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]
 W E and J Lu, The KohnSham equation for deformed crystals,
Memoirs of the American Mathematical Society, vol. 221 no. 1040
(2013),
pp. 11, ISSN 00659266 [doi]
 J Lu and X Yang, Convergence of frozen Gaussian approximation for highfrequency wave propagation,
Communications on Pure and Applied Mathematics, vol. 65 no. 6
(2012),
pp. 759789, ISSN 00103640 [doi] [abs]
 J Lu and X Yang, Frozen gaussian approximation for general linear strictly hyperbolic systems: Formulation and eulerian methods,
Multiscale Modeling and Simulation, vol. 10 no. 2
(2012),
pp. 451472, ISSN 15403459 [doi] [abs]
 W E and J Lu, Stability and the continuum limit of the spinpolarized ThomasFermiDiracvon Weizsäcker model,
Journal of Mathematical Physics, vol. 53 no. 11
(2012),
pp. 115615115615, ISSN 00222488 [doi]
 I Daubechies, J Lu and HT Wu, Synchrosqueezed wavelet transforms: An empirical mode decompositionlike tool,
Applied and Computational Harmonic Analysis, vol. 30 no. 2
(2011),
pp. 243261, ISSN 10635203 [doi]
 L Lin, C Yang, JC Meza, J Lu, L Ying and W E, 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]
 W E and J Lu, 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]
 L Lin, C Yang, J Lu, L Ying and W E, 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]
 L Lin, J Lu and L Ying, Fast construction of hierarchical matrix representation from matrixvector multiplication,
Journal of Computational Physics, vol. 230 no. 10
(2011),
pp. 40714087, ISSN 00219991 [doi] [abs]
 J Lu and X Yang, Frozen Gaussian approximation for high frequency wave propagation,
Communications in Mathematical Sciences, vol. 9 no. 3
(2011),
pp. 663683, ISSN 15396746 [doi] [abs]
 C Schütte, F Noé, J Lu, M Sarich and E VandenEijnden, Markov state models based on milestoning,
The Journal of Chemical Physics, vol. 134 no. 20
(2011),
pp. 204105204105, ISSN 00219606 [doi]
 W E and J Lu, Electronic structure of smoothly deformed crystals: Cauchyborn rule for the nonlinear tightbinding model,
Communications on Pure and Applied Mathematics, vol. 63 no. 11
(2010),
pp. 14321468, ISSN 00103640 [doi]
 W E, T Li and J Lu, Localized bases of eigensubspaces and operator compression,
Proceedings of the National Academy of Sciences, vol. 107 no. 4
(2010),
pp. 12731278, ISSN 00278424 [doi]
 CJ GarcíaCervera, J Lu, Y Xuan and W E, Linearscaling subspaceiteration algorithm with optimally localized nonorthogonal wave functions for KohnSham density functional theory,
Physical Review B, vol. 79 no. 11
(2009),
pp. 115110, ISSN 10980121 [doi]
 L Lin, J Lu, R Car and W E, Multipole representation of the Fermi operator with application to the electronic structure analysis of metallic systems,
Physical Review B, vol. 79 no. 11
(2009),
pp. 115133, ISSN 10980121 [doi]
 W E and J Lu, 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]
 W E, CJ GarcíaCervera and J Lu, 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]
 W E and J Lu, Seamless multiscale modeling via dynamics on fiber bundles,
Communications in Mathematical Sciences, vol. 5 no. 3
(2007),
pp. 649663, ISSN 15396746 [doi]
 W E and J Lu, 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]
 W E, J Lu and JZ Yang, Uniform accuracy of the quasicontinuum method,
Physical Review B, vol. 74 no. 21
(2006),
pp. 214115, ISSN 10980121 [doi]
Papers Accepted
 with Jingrun Chen, Analysis of the divideandconquer method for electronic structure calculations,
Math. Comp.
(2015) [arXiv:1411.0066]
 with Rongjie Lai, Localized density matrix minimization and linear scaling algorithms,
J. Comput. Phys.
(2015) [arXiv:1506.01610]
Papers Submitted
 with Zhennan Zhou, Bloch dynamics with second order Berry phase correction
(2015) [arXiv:1512.07357]
 with Lexing Ying, Fast algorithm for periodic density fitting for Bloch waves
(2015) [arXiv:1512.00432]
 with Lin Lin, Sharp decay estimates of discretized Green's functions for Schrodinger type operators
(2015) [arXiv:1511.07957]
 with Lexing Ying, Sparsifying preconditioner for soliton calculations
(2015) [arXiv:1511.03756]
 with Qin Li and Weiran Sun, Halfspace kinetic equations with general boundary conditions
(2015) [arXiv:1509.03225]
 with Ricardo Delgadillo and Xu Yang, Gaugeinvariant frozen Gaussian approximation method for the Schrodinger equation with periodic potentials
(2015) [arXiv:1509.05552]
 with Felix Otto, An isoperimetric problem with Coulomb repulsion and attraction to a background nucleus
(2015) [arXiv:1508.07172]
 with Ricardo Delgadillo and Xu Yang, Frozen Gaussian approximation for high frequency wave propagation in periodic media
(2015) [arXiv:1504.08051]
 with Xiantao Li, Traction boundary conditions for molecular static simulations
(2015) [arXiv:1503.03555]
 with Qin Li and Weiran Sun, A convergent method for linear halfspace kinetic equation
(2014) [arXiv:1408.6630]


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

