Math @ Duke

Papers Published
 with Lexing 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]
 Haizhao Yang, Jianfeng Lu, William Brown, Ingrid Daubechies, Lexing 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]
 with Qin Li and Weiran 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]
 with Vitaly Moroz, Cyrill B. Muratov, OrbitalFree Density Functional Theory of OutofPlane Charge Screening in Graphene,
Journal of Nonlinear Science, vol. 25
(2015),
pp. 13911430, ISSN 09388974 [arXiv:1405.4949], [doi]
 with Christian B. 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]
 with JianGuo Liu and Dionisios 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 [doi]
 with Jingchen Liu, Xiang 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]
 with James Nolen, Reactive trajectories and the transition path processes,
Probab. Theory Related Fields, vol. 161 no. 12
(2015),
pp. 195244 ([erratum].) [arXiv:1303.1744], [doi]
 with Rongjie Lai, Stanley 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]
 with Jeremy L. 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]
 with Felix 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]
 Yang Yang, Degao Peng, Jianfeng Lu, Weitao 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]
 with Eric 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]
 with Weinan E, 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]
 with Robert V. Kohn, Ben Schweizer, Michael I. Weinstein, A Variational Perspective on Cloaking by Anomalous Localized Resonance,
Communications in Mathematical Physics, vol. 328 no. 1
(2014),
pp. 127, ISSN 00103616 [doi]
 with Lin Lin and Sihong 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]
 with Pingbing 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]
 with Eric 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]
 with Pingbing 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]
 with Weinan E, Xu 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]
 with Weinan E, Yuan 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]
 with Weinan E, Lin Lin, Lexing Ying, 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]
 with Weinan E, Lin Lin, Lexing Ying, 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]
 with Weinan E, The KohnSham equation for deformed crystals,
Memoirs of the American Mathematical Society, vol. 221 no. 1040
(2013),
pp. 11, ISSN 00659266 [doi]
 with Xu 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]
 with Xu 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]
 with Weinan E, 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]
 with Ingrid Daubechies, HauTieng Wu, Synchrosqueezed wavelet transforms: An empirical mode decompositionlike tool,
Applied and Computational Harmonic Analysis, vol. 30 no. 2
(2011),
pp. 243261, ISSN 10635203 [doi]
 with Weinan E, Lin Lin, Juan Meza, Chao Yang, Lexing Ying, 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]
 with Weinan E, 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]
 with Weinan E, Lin Lin, Chao Yang, Lexing Ying, 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]
 with Weinan E, Xu Yang, Effective Maxwell equations from timedependent density functional theory,
Acta Math. Sin., vol. 32
(2011),
pp. 339
 with Lin Lin, Lexing 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]
 with Xu Yang, Frozen Gaussian approximation for high frequency wave propagation,
Communications in Mathematical Sciences, vol. 9 no. 3
(2011),
pp. 663683, ISSN 15396746 [doi] [abs]
 with Frank Noe, Marco Sarich, Christof Schutte, Eric VandenEijnden, Markov state models based on milestoning,
The Journal of Chemical Physics, vol. 134 no. 20
(2011),
pp. 204105204105, ISSN 00219606 [doi]
 with Weinan E, Multiscale modeling,
Scholarpedia, vol. 6
(2011),
pp. 11527 [Multiscale_modeling]
 with Weinan E, 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]
 with Weinan E, Tiejun Li, Localized bases of eigensubspaces and operator compression,
Proceedings of the National Academy of Sciences, vol. 107 no. 4
(2010),
pp. 12731278, ISSN 00278424 [doi]
 with Weinan E, Carlos J. GarciaCervera, Yulin Xuan, 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]
 with Roberto Car, Weinan E, Lin Lin, 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]
 with Roberto Car, Weinan E, Lin Lin, Lexing Ying, 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
 with Weinan E, Lin Lin, Lexing Ying, Polebased approximation of the FermiDirac function,
Chin. Ann. Math. Ser. B, vol. 30
(2009),
pp. 729742
 with Weinan E, Carlos J. GarciaCervera, Weiqing Ren, Sequential multiscale modelling using sparse representation,
Commun. Comput. Phys., vol. 4
(2008),
pp. 10251033
 with Weinan E, 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]
 with Weinan E, Carlos J. GarciaCervera, 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]
 with Weinan E, Seamless multiscale modeling via dynamics on fiber bundles,
Communications in Mathematical Sciences, vol. 5 no. 3
(2007),
pp. 649663, ISSN 15396746 [doi]
 with Weinan E, 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]
 with Weinan E, Jerry Z. Yang, Uniform accuracy of the quasicontinuum method,
Physical Review B, vol. 74 no. 21
(2006),
pp. 214115, ISSN 10980121 [doi]
Papers Accepted
 with Chen Li and Weitao Yang, Gentlest ascent dynamics for calculating first excited state and exploring energy landscape of KohnSham density functionals,
J. Chem. Phys.
(2015)
 with Jingrun Chen, Analysis of the divideandconquer method for electronic structure calculations,
Math. Comp.
(2014) [arXiv:1411.0066]
 with Haizhao Yang, Lexing Ying, Crystal image analysis using 2D synchrosqueezed transforms,
Multiscale Model. Simul.
(2014) [arXiv:1402.1262]
Papers Submitted
 with Lin Lin, Sharp decay estimates of discretized Green's functions for Schrodinger type operators
(2015)
 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 Rongjie Lai, Localized density matrix minimization and linear scaling algorithms
(2015) [arXiv:1506.01610]
 with Xiantao Li, Traction boundary conditions for molecular static simulations
(2015) [arXiv:1503.03555]
 with Benedikt Wirth and Haizhao Yang, Combining 2D synchrosqueezed wave packet transform with optimization for crystal image analysis
(2015) [arXiv:1501.06254]
 with Qin Li and Weiran Sun, A convergent method for linear halfspace kinetic equation
(2014) [arXiv:1408.6630]
 with Bin Hu, Dynamic production capacity management with price skimming
(2014)


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

