Math @ Duke

Papers Published
 with Lin Lin and Sihong Shao, Analysis of the time reversible BornOppenheimer molecular dynamics, edited by G. Ciccotti, M. Ferrario and Ch. Schuette,
Entropy, vol. 16
(2014),
pp. 110137 (Special issue on Molecular Dynamics Simulation.) [doi]
 with Robert V. Kohn, Ben Schweizer, Michael I. Weinstein, A variational perspective on cloaking by anomalous localized resonance,
Comm. Math. Phys., vol. 328 no. 1
(2014),
pp. 127 [doi]
 with Weinan E, Mathematical theory of solids: from quantum mechanics to continuum models,
Discret. Contin. Dyn. Sys., vol. 34
(2014),
pp. 50855097 [doi]
 with Weinan E, Yuan Yao, The Landscape of Complex Networks  Critical Nodes and a Hierarchical Decomposition,
Methods Appl. Anal., vol. 20 no. 4
(2013),
pp. 383404 (Special issue dedicated to Stan Osher's 70th birthday.) [doi]
 with Sergey Fomel, Xu Yang, Seismic modeling using the frozen Gaussian approximation,
in SEG Technical Program Expanded Abstracts 2013
(2013),
pp. 46774682 [arXiv:1304.3542]
 with Pingbing Ming, Convergence of a forcebased hybrid method for atomistic and continuum models in three dimension,
Comm. Pure Appl. Math., vol. 66
(2013),
pp. 83108 [doi]
 with Weinan E, The KohnSham equation for deformed crystals,
Mem. Amer. Math. Soc., vol. 221 no. 1040
(2013) [doi]
 with Eric VandenEijnden, Infinite swapping replica exchange molecular dynamics leads to a simple simulation patch using mixture potentials,
J. Chem. Phys., vol. 138
(2013),
pp. 084105 [doi]
 with Weinan E, Xu Yang, Asymptotic analysis of the quantum dynamics: BlochWigner transform and Bloch dynamics,
Acta Math. Appl. Sin. Engl. Ser., vol. 29
(2013),
pp. 465476 [doi]
 with Weinan E, Stability and the continuum limit of the spinpolarized ThomasFermiDiracvon Weizsacker model,
J. Math. Phys., vol. 53
(2012),
pp. 115615 [doi]
 with Weinan E, Lin Lin, Lexing Ying, Optimized local basis function for KohnSham density functional theory,
J. Comput. Phys., vol. 231
(2012),
pp. 4515
 with Xu Yang, Frozen Gaussian approximation for general linear strictly hyperbolic system: formulation and Eulerian methods,
Multiscale Model. Simul., vol. 10
(2012),
pp. 451 [doi]
 with Weinan E, Lin Lin, Lexing Ying, Adaptive local basis set for KohnSham density functional theory in a discontinuous Galerkin framework I: Total energy calculation,
J. Comput. Phys., vol. 231
(2012),
pp. 2140 [doi]
 with Xu Yang, Convergence of frozen Gaussian approximation for high frequency wave propagation,
Comm. Pure Appl. Math., vol. 65
(2012),
pp. 759 [doi]
 with Weinan E, Multiscale modeling,
Scholarpedia, vol. 6
(2011),
pp. 11527 [Multiscale_modeling]
 with Frank Noe, Marco Sarich, Christof Schutte, Eric VandenEijnden, Markov state models based on milestoning,
J. Chem. Phys., vol. 134
(2011),
pp. 204105 [doi]
 with Weinan E, Lin Lin, Chao Yang, Lexing Ying, A fast parallel algorithm for selected inversion of structured sparse matrix with application to 2D electronic structure calculations,
SIAM J. Sci. Comput., vol. 33
(2011),
pp. 1329
 with Lin Lin, Lexing Ying, Fast construction of hierarchical matrix representation from matrixvector multiplication,
J. Comput. Phys., vol. 230
(2011),
pp. 4071
 with Xu Yang, Frozen Gaussian approximation for high frequency wave propagation,
Commun. Math. Sci., vol. 9
(2011),
pp. 663 [doi]
 with Ingrid Daubechies, HauTieng Wu, Synchrosqueezed wavelet transforms: a tool for empirical mode decomposition,
Appl. Comp. Harmonic Anal., vol. 30
(2011),
pp. 243 [doi]
 with Weinan E, Xu Yang, Effective Maxwell equations from timedependent density functional theory,
Acta Math. Sin., vol. 32
(2011),
pp. 339
 with Weinan E, The electronic structure of smoothly deformed crystals: Wannier functions and the CauchyBorn rule,
Arch. Ration. Mech. Anal., vol. 199
(2011),
pp. 407 [doi]
 with Weinan E, Lin Lin, Juan Meza, Chao Yang, Lexing Ying, SelInv  an algorithm for selected inversion of a sparse symmetric matrix,
ACM Trans. Math. Software, vol. 37 no. 40
(2011)
 with Weinan E, The electronic structure of smoothly deformed crystals: CauchyBorn rule for nonlinear tightbinding model,
Comm. Pure Appl. Math., vol. 63
(2010),
pp. 1432
 with Weinan E, Tiejun Li, Localized basis of eigensubspaces and operator compression,
Proc. Natl. Acad. Sci. USA, vol. 107
(2010),
pp. 1273
 with Roberto Car, Weinan E, Lin Lin, Multipole representation of the Fermi operator with application to the electronic structure analysis of metallic systems,
Phys. Rev. B, vol. 79
(2009),
pp. 115133
 with Weinan E, Lin Lin, Lexing Ying, Polebased approximation of the FermiDirac function,
Chin. Ann. Math. Ser. B, vol. 30
(2009),
pp. 729742
 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, Carlos J. GarciaCervera, Yulin Xuan, A linear scaling subspace iteration algorithm with optimally localized nonorthogonal wave functions for KohnSham density functional theory,
Phys. Rev. B, vol. 79
(2009),
pp. 115110
 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, Carlos J. GarciaCervera, Asymptoticsbased sublinear scaling algorithms and application to the study of the electronic structure of materials,
Commun. Math. Sci., vol. 5
(2007),
pp. 9991024
 with Weinan E, The continuum limit and QMcontinuum approximation of quantum mechanical models of solids,
Commun. Math. Sci., vol. 5
(2007),
pp. 679696
 with Weinan E, Seamless multiscale modelling via dynamics on fiber bundles,
Commun. Math. Sci., vol. 5
(2007),
pp. 649663
 with Weinan E, The elastic continuum limit of the tight binding model,
Chin. Ann. Math. Ser. B, vol. 28
(2007),
pp. 665675
 with Weinan E, Jerry Z. Yang, Uniform accuracy of the quasicontinuum method,
Phys. Rev. B, vol. 74
(2006),
pp. 214115
Papers Accepted
 with Felix Otto, Nonexistence of minimizer for ThomasFermiDiracvon Weizsacker model,
Comm. Pure Appl. Math.
(2014)
 with James Nolen, Reactive trajectories and the transition path processes,
Probab. Theory Related Fields
(2014)
 with Eric VandenEijnden, Exact dynamical coarsegraining without timescale separation,
J. Chem. Phys.
(2014) [arXiv:1404.4225]
 with Jeremy L. Marzuola, Strang splitting methods for a quasilinear Schrodinger equation  convergence, instability and dynamics,
Commun. Math. Sci.
(2013)
 with Pingbing Ming, Stability of a forcebased hybrid method in three dimension with sharp interface,
SIAM J. Numer. Anal.
(2012)
Papers Submitted
 with Qin Li and Weiran Sun, Diffusion approximations of linear transport equations: Asymptotics and numerics
(2014) [arXiv:1409.0476]
 with JianGuo Liu and Dionisios Margetis, Emergence of step flow from atomistic scheme of epitaxial growth in 1+1 dimensions
(2014) [arXiv:1409.0046]
 with Christian B. Mendl, Numerical scheme for a spatially inhomogeneous matrixvalued quantum Boltzmann equation
(2014) [arXiv:1408.1782]
 with Qin Li, 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)
 with Rongjie Lai, Stanley Osher, Density matrix minimization with $\ell_1$ regularization
(2014) [arXiv:1403.1525]
 with Haizhao Yang, Lexing Ying, Crystal image analysis using 2D synchrosqueezing transforms
(2014) [arXiv:1402.1262]
 with Jingchen Liu, Xiang Zhou, Efficient rare event simulation for failure problems in random media
(2014) [arXiv:1404.4729]
 with Vitaly Moroz, Cyrill B. Muratov, Orbitalfree density functional theory of outofplane charge screening in graphene
(2014) [arXiv:1405.4949]


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

