Publications of Jianfeng Lu    :chronological  alphabetical  combined listing:

%% Papers Published   
@article{fds337144,
   Author = {Cao, Y and Lu, J},
   Title = {Stochastic dynamical low-rank approximation
             method},
   Journal = {Journal of Computational Physics},
   Volume = {372},
   Pages = {564-586},
   Year = {2018},
   Month = {November},
   url = {http://dx.doi.org/10.1016/j.jcp.2018.06.058},
   Abstract = {© 2018 Elsevier Inc. In this paper, we extend the dynamical
             low-rank approximation method to the space of finite signed
             measures. Under this framework, we derive stochastic
             low-rank dynamics for stochastic differential equations
             (SDEs) coming from classical stochastic dynamics or
             unraveling of Lindblad quantum master equations. We justify
             the proposed method by error analysis and also numerical
             examples for applications in solving high-dimensional SDE,
             stochastic Burgers' equation, and high-dimensional Lindblad
             equation.},
   Doi = {10.1016/j.jcp.2018.06.058},
   Key = {fds337144}
}

@article{fds337607,
   Author = {Li, X and Liu, J and Lu, J and Zhou, X},
   Title = {Moderate deviation for random elliptic PDE with small
             noise},
   Journal = {The Annals of Applied Probability},
   Volume = {28},
   Number = {5},
   Pages = {2781-2813},
   Year = {2018},
   Month = {October},
   url = {http://dx.doi.org/10.1214/17-AAP1373},
   Abstract = {© Institute of Mathematical Statistics, 2018. Partial
             differential equations with random inputs have become
             popular models to characterize physical systems with
             uncertainty coming from imprecise measurement and intrinsic
             randomness. In this paper, we perform asymptotic rare-event
             analysis for such elliptic PDEs with random inputs. In
             particular, we consider the asymptotic regime that the noise
             level converges to zero suggesting that the system
             uncertainty is low, but does exist. We develop sharp
             approximations of the probability of a large class of rare
             events.},
   Doi = {10.1214/17-AAP1373},
   Key = {fds337607}
}

@article{fds338041,
   Author = {Barthel, T and Lu, J},
   Title = {Fundamental Limitations for Measurements in Quantum
             Many-Body Systems.},
   Journal = {Physical Review Letters},
   Volume = {121},
   Number = {8},
   Pages = {080406},
   Year = {2018},
   Month = {August},
   url = {http://dx.doi.org/10.1103/physrevlett.121.080406},
   Abstract = {Dynamical measurement schemes are an important tool for the
             investigation of quantum many-body systems, especially in
             the age of quantum simulation. Here, we address the question
             whether generic measurements can be implemented efficiently
             if we have access to a certain set of experimentally
             realizable measurements and can extend it through time
             evolution. For the latter, two scenarios are considered:
             (a) evolution according to unitary circuits and
             (b) evolution due to Hamiltonians that we can control in a
             time-dependent fashion. We find that the time needed to
             realize a certain measurement to a predefined accuracy
             scales in general exponentially with the system size-posing
             a fundamental limitation. The argument is based on the
             construction of ϵ-packings for manifolds of observables
             with identical spectra and a comparison of their
             cardinalities to those of ϵ-coverings for quantum circuits
             and unitary time-evolution operators. The former is related
             to the study of Grassmann manifolds.},
   Doi = {10.1103/physrevlett.121.080406},
   Key = {fds338041}
}

@article{fds332859,
   Author = {Huang, Y and Lu, J and Ming, P},
   Title = {A Concurrent Global–Local Numerical Method for Multiscale
             PDEs},
   Journal = {Journal of Scientific Computing},
   Volume = {76},
   Number = {2},
   Pages = {1188-1215},
   Year = {2018},
   Month = {August},
   url = {http://dx.doi.org/10.1007/s10915-018-0662-5},
   Abstract = {© 2018 Springer Science+Business Media, LLC, part of
             Springer Nature We present a new hybrid numerical method for
             multiscale partial differential equations, which
             simultaneously captures the global macroscopic information
             and resolves the local microscopic events over regions of
             relatively small size. The method couples concurrently the
             microscopic coefficients in the region of interest with the
             homogenized coefficients elsewhere. The cost of the method
             is comparable to the heterogeneous multiscale method, while
             being able to recover microscopic information of the
             solution. The convergence of the method is proved for
             problems with bounded and measurable coefficients, while the
             rate of convergence is established for problems with rapidly
             oscillating periodic or almost-periodic coefficients.
             Numerical results are reported to show the efficiency and
             accuracy of the proposed method.},
   Doi = {10.1007/s10915-018-0662-5},
   Key = {fds332859}
}

@article{fds337608,
   Author = {You, Z and Li, L and Lu, J and Ge, H},
   Title = {Integrated tempering enhanced sampling method as the
             infinite switching limit of simulated tempering.},
   Journal = {The Journal of Chemical Physics},
   Volume = {149},
   Number = {8},
   Pages = {084114},
   Year = {2018},
   Month = {August},
   url = {http://dx.doi.org/10.1063/1.5045369},
   Abstract = {A fast and accurate sampling method is in high demand, in
             order to bridge the large gaps between molecular dynamic
             simulations and experimental observations. Recently, an
             integrated tempering enhanced sampling (ITS) method has been
             proposed and successfully applied to various biophysical
             examples, significantly accelerating conformational
             sampling. The mathematical validation for its effectiveness
             has not been elucidated yet. Here we show that the
             integrated tempering enhanced sampling method can be viewed
             as a reformulation of the infinite switching limit of the
             simulated tempering method over a mixed potential. Moreover,
             we demonstrate that the efficiency of simulated tempering
             molecular dynamics improves as the frequency of switching
             between the temperatures is increased, based on the large
             deviation principle of empirical distributions. Our theory
             provides the theoretical justification of the advantage of
             ITS. Finally, we illustrate the utility of the infinite
             switching simulated tempering method through several
             numerical examples.},
   Doi = {10.1063/1.5045369},
   Key = {fds337608}
}

@article{fds332860,
   Author = {Lu, J and Zhou, Z},
   Title = {Accelerated sampling by infinite swapping of path integral
             molecular dynamics with surface hopping.},
   Journal = {The Journal of Chemical Physics},
   Volume = {148},
   Number = {6},
   Pages = {064110},
   Year = {2018},
   Month = {February},
   url = {http://dx.doi.org/10.1063/1.5005024},
   Abstract = {To accelerate the thermal equilibrium sampling of
             multi-level quantum systems, the infinite swapping limit of
             a recently proposed multi-level ring polymer representation
             is investigated. In the infinite swapping limit, the ring
             polymer evolves according to an averaged Hamiltonian with
             respect to all possible surface index configurations of the
             ring polymer and thus connects the surface hopping approach
             to the mean-field path-integral molecular dynamics. A
             multiscale integrator for the infinite swapping limit is
             also proposed to enable efficient sampling based on the
             limiting dynamics. Numerical results demonstrate the huge
             improvement of sampling efficiency of the infinite swapping
             compared with the direct simulation of path-integral
             molecular dynamics with surface hopping.},
   Doi = {10.1063/1.5005024},
   Key = {fds332860}
}

@article{fds336984,
   Author = {Cai, Z and Lu, J},
   Title = {A Quantum Kinetic Monte Carlo Method for Quantum Many-Body
             Spin Dynamics},
   Journal = {Siam Journal on Scientific Computing},
   Volume = {40},
   Number = {3},
   Pages = {B706-B722},
   Year = {2018},
   Month = {January},
   url = {http://dx.doi.org/10.1137/17M1145446},
   Doi = {10.1137/17M1145446},
   Key = {fds336984}
}

@article{fds329344,
   Author = {Yu, VW-Z and Corsetti, F and García, A and Huhn, WP and Jacquelin, M and Jia, W and Lange, B and Lin, L and Lu, J and Mi, W and Seifitokaldani, A and Vázquez-Mayagoitia, Á and Yang, C and Yang, H and Blum,
             V},
   Title = {ELSI: A unified software interface for Kohn–Sham
             electronic structure solvers},
   Journal = {Computer Physics Communications},
   Volume = {222},
   Pages = {267-285},
   Year = {2018},
   Month = {January},
   url = {http://dx.doi.org/10.1016/j.cpc.2017.09.007},
   Doi = {10.1016/j.cpc.2017.09.007},
   Key = {fds329344}
}

@article{fds335540,
   Author = {Du, Q and Li, XH and Lu, J and Tian, X},
   Title = {A Quasi-nonlocal Coupling Method for Nonlocal and Local
             Diffusion Models},
   Journal = {Siam Journal on Numerical Analysis},
   Volume = {56},
   Number = {3},
   Pages = {1386-1404},
   Year = {2018},
   Month = {January},
   url = {http://dx.doi.org/10.1137/17M1124012},
   Doi = {10.1137/17M1124012},
   Key = {fds335540}
}

@article{fds332861,
   Author = {Dai, S and Li, B and Lu, J},
   Title = {Convergence of Phase-Field Free Energy and Boundary Force
             for Molecular Solvation},
   Journal = {Archive for Rational Mechanics and Analysis},
   Volume = {227},
   Number = {1},
   Pages = {105-147},
   Year = {2018},
   Month = {January},
   url = {http://dx.doi.org/10.1007/s00205-017-1158-4},
   Doi = {10.1007/s00205-017-1158-4},
   Key = {fds332861}
}

@article{fds335541,
   Author = {Zhu, W and Qiu, Q and Wang, B and Lu, J and Sapiro, G and Daubechies,
             I},
   Title = {Stop memorizing: A data-dependent regularization framework
             for intrinsic pattern learning.},
   Journal = {Corr},
   Volume = {abs/1805.07291},
   Year = {2018},
   Key = {fds335541}
}

@article{fds329343,
   Author = {Lu, J and Thicke, K},
   Title = {Cubic scaling algorithms for RPA correlation using
             interpolative separable density fitting},
   Journal = {Journal of Computational Physics},
   Volume = {351},
   Pages = {187-202},
   Year = {2017},
   Month = {December},
   url = {http://dx.doi.org/10.1016/j.jcp.2017.09.012},
   Doi = {10.1016/j.jcp.2017.09.012},
   Key = {fds329343}
}

@article{fds332172,
   Author = {Cao, Y and Lu, J},
   Title = {Lindblad equation and its semiclassical limit of the
             Anderson-Holstein model},
   Journal = {Journal of Mathematical Physics},
   Volume = {58},
   Number = {12},
   Pages = {122105-122105},
   Year = {2017},
   Month = {December},
   url = {http://dx.doi.org/10.1063/1.4993431},
   Abstract = {© 2017 Author(s). For multi-level open quantum systems, the
             interaction between different levels could pose a challenge
             to understand the quantum system both analytically and
             numerically. In this work, we study the approximation of the
             dynamics of the Anderson-Holstein model, as a model of the
             multi-level open quantum system, by Redfield and Lindblad
             equations. Both equations have a desirable property that if
             the density operators for different levels are diagonal
             initially, they remain to be diagonal for any time. Thanks
             to this nice property, the semiclassical limit of both
             Redfield and Lindblad equations could be derived explicitly;
             the resulting classical master equations share similar
             structures of transport and hopping terms. The Redfield and
             Lindblad equations are also compared from the angle of time
             dependent perturbation theory.},
   Doi = {10.1063/1.4993431},
   Key = {fds332172}
}

@article{fds337014,
   Author = {Lu, J and Zhou, Z},
   Title = {Frozen Gaussian approximation with surface hopping for mixed
             quantum-classical dynamics: A mathematical justification of
             fewest switches surface hopping algorithms},
   Journal = {Mathematics of Computation},
   Volume = {87},
   Number = {313},
   Pages = {2189-2232},
   Year = {2017},
   Month = {November},
   url = {http://dx.doi.org/10.1090/mcom/3310},
   Doi = {10.1090/mcom/3310},
   Key = {fds337014}
}

@article{fds328894,
   Author = {Li, L and Liu, J-G and Lu, J},
   Title = {Fractional Stochastic Differential Equations Satisfying
             Fluctuation-Dissipation Theorem},
   Journal = {Journal of Statistical Physics},
   Volume = {169},
   Number = {2},
   Pages = {316-339},
   Year = {2017},
   Month = {October},
   url = {http://dx.doi.org/10.1007/s10955-017-1866-z},
   Abstract = {© 2017 Springer Science+Business Media, LLC We propose in
             this work a fractional stochastic differential equation
             (FSDE) model consistent with the over-damped limit of the
             generalized Langevin equation model. As a result of the
             ‘fluctuation-dissipation theorem’, the differential
             equations driven by fractional Brownian noise to model
             memory effects should be paired with Caputo derivatives, and
             this FSDE model should be understood in an integral form. We
             establish the existence of strong solutions for such
             equations and discuss the ergodicity and convergence to
             Gibbs measure. In the linear forcing regime, we show
             rigorously the algebraic convergence to Gibbs measure when
             the ‘fluctuation-dissipation theorem’ is satisfied, and
             this verifies that satisfying ‘fluctuation-dissipation
             theorem’ indeed leads to the correct physical behavior. We
             further discuss possible approaches to analyze the
             ergodicity and convergence to Gibbs measure in the nonlinear
             forcing regime, while leave the rigorous analysis for future
             works. The FSDE model proposed is suitable for systems in
             contact with heat bath with power-law kernel and
             subdiffusion behaviors.},
   Doi = {10.1007/s10955-017-1866-z},
   Key = {fds328894}
}

@article{fds333283,
   Author = {Li, Q and Lu, J and Sun, W},
   Title = {A convergent method for linear half-space kinetic
             equations},
   Journal = {ESAIM. Mathematical modelling and numerical analysis =
             ESAIM. Modelisation mathematique et analyse numerique :
             M=2AN},
   Volume = {51},
   Number = {5},
   Pages = {1583-1615},
   Year = {2017},
   Month = {September},
   url = {http://dx.doi.org/10.1051/m2an/2016076},
   Doi = {10.1051/m2an/2016076},
   Key = {fds333283}
}

@article{fds328895,
   Author = {Lu, J and Steinerberger, S},
   Title = {A variation on the Donsker-Varadhan inequality for the
             principal eigenvalue.},
   Journal = {Proceedings. Mathematical, Physical, and Engineering
             Sciences},
   Volume = {473},
   Number = {2204},
   Pages = {20160877},
   Year = {2017},
   Month = {August},
   url = {http://dx.doi.org/10.1098/rspa.2016.0877},
   Abstract = {The purpose of this short paper is to give a variation on
             the classical Donsker-Varadhan inequality, which bounds the
             first eigenvalue of a second-order elliptic operator on a
             bounded domain Ω by the largest mean first exit time of the
             associated drift-diffusion process via [Formula: see
             text]Instead of looking at the mean of the first exit time,
             we study quantiles: let [Formula: see text] be the smallest
             time t such that the likelihood of exiting within that time
             is p, then [Formula: see text]Moreover, as [Formula: see
             text], this lower bound converges to λ1.},
   Doi = {10.1098/rspa.2016.0877},
   Key = {fds328895}
}

@article{fds325888,
   Author = {Lu, J and Yang, H},
   Title = {A cubic scaling algorithm for excited states calculations in
             particle–particle random phase approximation},
   Journal = {Journal of Computational Physics},
   Volume = {340},
   Pages = {297-308},
   Year = {2017},
   Month = {July},
   url = {http://dx.doi.org/10.1016/j.jcp.2017.03.055},
   Doi = {10.1016/j.jcp.2017.03.055},
   Key = {fds325888}
}

@article{fds326080,
   Author = {Gao, Y and Liu, J-G and Lu, J},
   Title = {Continuum Limit of a Mesoscopic Model with Elasticity of
             Step Motion on Vicinal Surfaces},
   Journal = {Journal of Nonlinear Science},
   Volume = {27},
   Number = {3},
   Pages = {873-926},
   Year = {2017},
   Month = {June},
   url = {http://dx.doi.org/10.1007/s00332-016-9354-1},
   Doi = {10.1007/s00332-016-9354-1},
   Key = {fds326080}
}

@article{fds326484,
   Author = {Li, C and Lu, J and Yang, W},
   Title = {On extending Kohn-Sham density functionals to systems with
             fractional number of electrons.},
   Journal = {The Journal of Chemical Physics},
   Volume = {146},
   Number = {21},
   Pages = {214109},
   Year = {2017},
   Month = {June},
   url = {http://dx.doi.org/10.1063/1.4982951},
   Abstract = {We analyze four ways of formulating the Kohn-Sham (KS)
             density functionals with a fractional number of electrons,
             through extending the constrained search space from the
             Kohn-Sham and the generalized Kohn-Sham (GKS)
             non-interacting v-representable density domain for integer
             systems to four different sets of densities for fractional
             systems. In particular, these density sets are (I) ensemble
             interacting N-representable densities, (II) ensemble
             non-interacting N-representable densities, (III)
             non-interacting densities by the Janak construction, and
             (IV) non-interacting densities whose composing orbitals
             satisfy the Aufbau occupation principle. By proving the
             equivalence of the underlying first order reduced density
             matrices associated with these densities, we show that sets
             (I), (II), and (III) are equivalent, and all reduce to the
             Janak construction. Moreover, for functionals with the
             ensemble v-representable assumption at the minimizer, (III)
             reduces to (IV) and thus justifies the previous use of the
             Aufbau protocol within the (G)KS framework in the study of
             the ground state of fractional electron systems, as defined
             in the grand canonical ensemble at zero temperature. By
             further analyzing the Aufbau solution for different density
             functional approximations (DFAs) in the (G)KS scheme, we
             rigorously prove that there can be one and only one
             fractional occupation for the Hartree Fock functional, while
             there can be multiple fractional occupations for general
             DFAs in the presence of degeneracy. This has been confirmed
             by numerical calculations using the local density
             approximation as a representative of general DFAs. This work
             thus clarifies important issues on density functional theory
             calculations for fractional electron systems.},
   Doi = {10.1063/1.4982951},
   Key = {fds326484}
}

@article{fds324707,
   Author = {Lu, J and Thicke, K},
   Title = {Orbital minimization method with ℓ 1 regularization},
   Journal = {Journal of Computational Physics},
   Volume = {336},
   Pages = {87-103},
   Year = {2017},
   Month = {May},
   url = {http://dx.doi.org/10.1016/j.jcp.2017.02.005},
   Doi = {10.1016/j.jcp.2017.02.005},
   Key = {fds324707}
}

@article{fds326081,
   Author = {Lu, J and Zhou, Z},
   Title = {Path integral molecular dynamics with surface hopping for
             thermal equilibrium sampling of nonadiabatic
             systems.},
   Journal = {The Journal of Chemical Physics},
   Volume = {146},
   Number = {15},
   Pages = {154110},
   Year = {2017},
   Month = {April},
   url = {http://dx.doi.org/10.1063/1.4981021},
   Abstract = {In this work, a novel ring polymer representation for a
             multi-level quantum system is proposed for thermal average
             calculations. The proposed representation keeps the
             discreteness of the electronic states: besides position and
             momentum, each bead in the ring polymer is also
             characterized by a surface index indicating the electronic
             energy surface. A path integral molecular dynamics with
             surface hopping (PIMD-SH) dynamics is also developed to
             sample the equilibrium distribution of the ring polymer
             configurational space. The PIMD-SH sampling method is
             validated theoretically and by numerical
             examples.},
   Doi = {10.1063/1.4981021},
   Key = {fds326081}
}

@article{fds325889,
   Author = {Watson, AB and Lu, J and Weinstein, MI},
   Title = {Wavepackets in inhomogeneous periodic media: Effective
             particle-field dynamics and Berry curvature},
   Journal = {Journal of Mathematical Physics},
   Volume = {58},
   Number = {2},
   Pages = {021503-021503},
   Year = {2017},
   Month = {February},
   url = {http://dx.doi.org/10.1063/1.4976200},
   Doi = {10.1063/1.4976200},
   Key = {fds325889}
}

@article{fds320926,
   Author = {Niu, X and Luo, T and Lu, J and Xiang, Y},
   Title = {Dislocation climb models from atomistic scheme to
             dislocation dynamics},
   Journal = {Journal of the Mechanics and Physics of Solids},
   Volume = {99},
   Pages = {242-258},
   Year = {2017},
   Month = {February},
   url = {http://dx.doi.org/10.1016/j.jmps.2016.11.012},
   Doi = {10.1016/j.jmps.2016.11.012},
   Key = {fds320926}
}

@article{fds330519,
   Author = {Li, XH and Lu, J},
   Title = {Quasi-nonlocal Coupling of Nonlocal Diffusions},
   Journal = {Siam Journal on Numerical Analysis},
   Volume = {55},
   Number = {5},
   Pages = {2394-2415},
   Year = {2017},
   Month = {January},
   url = {http://dx.doi.org/10.1137/16M1086443},
   Doi = {10.1137/16M1086443},
   Key = {fds330519}
}

@article{fds325890,
   Author = {Lu, J and Yang, H},
   Title = {Preconditioning Orbital Minimization Method for Planewave
             Discretization},
   Journal = {Multiscale Modeling & Simulation},
   Volume = {15},
   Number = {1},
   Pages = {254-273},
   Year = {2017},
   Month = {January},
   url = {http://dx.doi.org/10.1137/16M1068670},
   Doi = {10.1137/16M1068670},
   Key = {fds325890}
}

@article{fds333284,
   Author = {Lin, L and Lu, J and Vanden-Eijnden, E},
   Title = {A Mathematical Theory of Optimal Milestoning (with a Detour
             via Exact Milestoning)},
   Journal = {Communications on Pure and Applied Mathematics},
   Year = {2017},
   Month = {January},
   url = {http://dx.doi.org/10.1002/cpa.21725},
   Abstract = {© 2017 Wiley Periodicals, Inc. Milestoning is a
             computational procedure that reduces the dynamics of complex
             systems to memoryless jumps between intermediates, or
             milestones, and only retains some information about the
             probability of these jumps and the time lags between them.
             Here we analyze a variant of this procedure, termed optimal
             milestoning, which relies on a specific choice of milestones
             to capture exactly some kinetic features of the original
             dynamical system. In particular, we prove that optimal
             milestoning permits the exact calculation of the mean first
             passage times (MFPT) between any two milestones. In so
             doing, we also analyze another variant of the method, called
             exact milestoning, which also permits the exact calculation
             of certain MFPTs, but at the price of retaining more
             information about the original system's dynamics. Finally,
             we discuss importance sampling strategies based on optimal
             and exact milestoning that can be used to bypass the
             simulation of the original system when estimating the
             statistical quantities used in these methods.},
   Doi = {10.1002/cpa.21725},
   Key = {fds333284}
}

@article{fds323661,
   Author = {Li, Q and Lu, J and Sun, W},
   Title = {Validity and Regularization of Classical Half-Space
             Equations},
   Journal = {Journal of Statistical Physics},
   Volume = {166},
   Number = {2},
   Pages = {398-433},
   Year = {2017},
   Month = {January},
   url = {http://dx.doi.org/10.1007/s10955-016-1688-4},
   Doi = {10.1007/s10955-016-1688-4},
   Key = {fds323661}
}

@article{fds332173,
   Author = {Li, Q and Lu, J},
   Title = {An asymptotic preserving method for transport equations with
             oscillatory scattering coefficients},
   Journal = {Multiscale Modeling & Simulation},
   Volume = {15},
   Number = {4},
   Pages = {1694-1718},
   Year = {2017},
   Month = {January},
   url = {http://dx.doi.org/10.1137/16M109212X},
   Abstract = {© 2017 Society for Industrial and Applied Mathematics. We
             design a numerical scheme for transport equations with
             oscillatory periodic scattering coefficients. The scheme is
             asymptotic preserving in the diffusion limit as the Knudsen
             number goes to zero. It also captures the homogenization
             limit as the length scale of the scattering coefficient goes
             to zero. The proposed method is based on the construction of
             multiscale finite element basis and a Galerkin projection
             based on the even-odd decomposition. The method is analyzed
             in the asymptotic regime, as well as validated
             numerically.},
   Doi = {10.1137/16M109212X},
   Key = {fds332173}
}

@article{fds327371,
   Author = {Gao, Y and Liu, J-G and Lu, J},
   Title = {Weak Solution of a Continuum Model For Vicinal Surface in
             The Attachment-Detachment-Limited Regime},
   Journal = {Siam Journal on Mathematical Analysis},
   Volume = {49},
   Number = {3},
   Pages = {1705-1731},
   Year = {2017},
   Month = {January},
   url = {http://dx.doi.org/10.1137/16M1094543},
   Abstract = {© 2017 Society for Industrial and Applied Mathematics. We
             study in this work a continuum model derived from a
             one-dimensional attachmentdetachment-limited type step flow
             on a vicinal surface, u t = -u 2 (u 3 ) hhhh , where u,
             considered as a function of step height h, is the step slope
             of the surface. We formulate a notion of a weak solution to
             this continuum model and prove the existence of a global
             weak solution, which is positive almost everywhere. We also
             study the long time behavior of the weak solution and prove
             it converges to a constant solution as time goes to
             infinity. The space-time Hölder continuity of the weak
             solution is also discussed as a byproduct.},
   Doi = {10.1137/16M1094543},
   Key = {fds327371}
}

@article{fds325467,
   Author = {Cornelis, B and Yang, H and Goodfriend, A and Ocon, N and Lu, J and Daubechies, I},
   Title = {Removal of Canvas Patterns in Digital Acquisitions of
             Paintings.},
   Journal = {Ieee Transactions on Image Processing : a Publication of the
             Ieee Signal Processing Society},
   Volume = {26},
   Number = {1},
   Pages = {160-171},
   Year = {2017},
   Month = {January},
   url = {http://dx.doi.org/10.1109/tip.2016.2621413},
   Abstract = {We address the removal of canvas artifacts from
             high-resolution digital photographs and X-ray images of
             paintings on canvas. Both imaging modalities are common
             investigative tools in art history and art conservation.
             Canvas artifacts manifest themselves very differently
             according to the acquisition modality; they can hamper the
             visual reading of the painting by art experts, for instance,
             in preparing a restoration campaign. Computer-aided canvas
             removal is desirable for restorers when the painting on
             canvas they are preparing to restore has acquired over the
             years a much more salient texture. We propose a new
             algorithm that combines a cartoon-texture decomposition
             method with adaptive multiscale thresholding in the
             frequency domain to isolate and suppress the canvas
             components. To illustrate the strength of the proposed
             method, we provide various examples, for acquisitions in
             both imaging modalities, for paintings with different types
             of canvas and from different periods. The proposed algorithm
             outperforms previous methods proposed for visual photographs
             such as morphological component analysis and Wiener
             filtering and it also works for the digital removal of
             canvas artifacts in X-ray images.},
   Doi = {10.1109/tip.2016.2621413},
   Key = {fds325467}
}

@article{fds321515,
   Author = {Mendl, CB and Lu, J and Lukkarinen, J},
   Title = {Thermalization of oscillator chains with onsite
             anharmonicity and comparison with kinetic
             theory.},
   Journal = {Physical Review. E},
   Volume = {94},
   Number = {6-1},
   Pages = {062104},
   Year = {2016},
   Month = {December},
   url = {http://dx.doi.org/10.1103/physreve.94.062104},
   Abstract = {We perform microscopic molecular dynamics simulations of
             particle chains with an onsite anharmonicity to study
             relaxation of spatially homogeneous states to equilibrium,
             and directly compare the simulations with the corresponding
             Boltzmann-Peierls kinetic theory. The Wigner function serves
             as a common interface between the microscopic and kinetic
             level. We demonstrate quantitative agreement after an
             initial transient time interval. In particular, besides
             energy conservation, we observe the additional
             quasiconservation of the phonon density, defined via an
             ensemble average of the related microscopic field variables
             and exactly conserved by the kinetic equations. On
             superkinetic time scales, density quasiconservation is lost
             while energy remains conserved, and we find evidence for
             eventual relaxation of the density to its canonical ensemble
             value. However, the precise mechanism remains unknown and is
             not captured by the Boltzmann-Peierls equations.},
   Doi = {10.1103/physreve.94.062104},
   Key = {fds321515}
}

@article{fds325891,
   Author = {Li, Q and Lu, J and Sun, W},
   Title = {Half-space kinetic equations with general boundary
             conditions},
   Journal = {Mathematics of Computation},
   Volume = {86},
   Number = {305},
   Pages = {1269-1301},
   Year = {2016},
   Month = {October},
   url = {http://dx.doi.org/10.1090/mcom/3155},
   Doi = {10.1090/mcom/3155},
   Key = {fds325891}
}

@article{fds320186,
   Author = {Yu, T-Q and Lu, J and Abrams, CF and Vanden-Eijnden,
             E},
   Title = {Multiscale implementation of infinite-swap replica exchange
             molecular dynamics.},
   Journal = {Proceedings of the National Academy of Sciences of the
             United States of America},
   Volume = {113},
   Number = {42},
   Pages = {11744-11749},
   Year = {2016},
   Month = {October},
   url = {http://dx.doi.org/10.1073/pnas.1605089113},
   Abstract = {Replica exchange molecular dynamics (REMD) is a popular
             method to accelerate conformational sampling of complex
             molecular systems. The idea is to run several replicas of
             the system in parallel at different temperatures that are
             swapped periodically. These swaps are typically attempted
             every few MD steps and accepted or rejected according to a
             Metropolis-Hastings criterion. This guarantees that the
             joint distribution of the composite system of replicas is
             the normalized sum of the symmetrized product of the
             canonical distributions of these replicas at the different
             temperatures. Here we propose a different implementation of
             REMD in which (i) the swaps obey a continuous-time Markov
             jump process implemented via Gillespie's stochastic
             simulation algorithm (SSA), which also samples exactly the
             aforementioned joint distribution and has the advantage of
             being rejection free, and (ii) this REMD-SSA is combined
             with the heterogeneous multiscale method to accelerate the
             rate of the swaps and reach the so-called infinite-swap
             limit that is known to optimize sampling efficiency. The
             method is easy to implement and can be trivially
             parallelized. Here we illustrate its accuracy and efficiency
             on the examples of alanine dipeptide in vacuum and
             C-terminal β-hairpin of protein G in explicit solvent. In
             this latter example, our results indicate that the landscape
             of the protein is a triple funnel with two folded structures
             and one misfolded structure that are stabilized by
             H-bonds.},
   Doi = {10.1073/pnas.1605089113},
   Key = {fds320186}
}

@article{fds320187,
   Author = {Lu, J and Zhou, Z},
   Title = {Improved sampling and validation of frozen Gaussian
             approximation with surface hopping algorithm for
             nonadiabatic dynamics.},
   Journal = {The Journal of Chemical Physics},
   Volume = {145},
   Number = {12},
   Pages = {124109},
   Year = {2016},
   Month = {September},
   url = {http://dx.doi.org/10.1063/1.4963107},
   Abstract = {In the spirit of the fewest switches surface hopping, the
             frozen Gaussian approximation with surface hopping (FGA-SH)
             method samples a path integral representation of the
             non-adiabatic dynamics in the semiclassical regime. An
             improved sampling scheme is developed in this work for
             FGA-SH based on birth and death branching processes. The
             algorithm is validated for the standard test examples of
             non-adiabatic dynamics.},
   Doi = {10.1063/1.4963107},
   Key = {fds320187}
}

@article{fds318293,
   Author = {Li, X and Lu, J},
   Title = {Traction boundary conditions for molecular static
             simulations},
   Journal = {Computer Methods in Applied Mechanics and
             Engineering},
   Volume = {308},
   Pages = {310-329},
   Year = {2016},
   Month = {August},
   url = {http://dx.doi.org/10.1016/j.cma.2016.05.002},
   Doi = {10.1016/j.cma.2016.05.002},
   Key = {fds318293}
}

@article{fds318294,
   Author = {Lin, L and Lu, J},
   Title = {Decay estimates of discretized Green’s functions for
             Schrödinger type operators},
   Journal = {Science China Mathematics},
   Volume = {59},
   Number = {8},
   Pages = {1561-1578},
   Year = {2016},
   Month = {August},
   url = {http://dx.doi.org/10.1007/s11425-016-0311-4},
   Doi = {10.1007/s11425-016-0311-4},
   Key = {fds318294}
}

@article{fds318295,
   Author = {Lai, R and Lu, J},
   Title = {Localized density matrix minimization and linear-scaling
             algorithms},
   Journal = {Journal of Computational Physics},
   Volume = {315},
   Pages = {194-210},
   Year = {2016},
   Month = {June},
   url = {http://dx.doi.org/10.1016/j.jcp.2016.02.076},
   Doi = {10.1016/j.jcp.2016.02.076},
   Key = {fds318295}
}

@article{fds318296,
   Author = {Lu, J and Ying, L},
   Title = {Sparsifying preconditioner for soliton calculations},
   Journal = {Journal of Computational Physics},
   Volume = {315},
   Pages = {458-466},
   Year = {2016},
   Month = {June},
   url = {http://dx.doi.org/10.1016/j.jcp.2016.03.061},
   Doi = {10.1016/j.jcp.2016.03.061},
   Key = {fds318296}
}

@article{fds316401,
   Author = {Lu, J and Wirth, B and Yang, H},
   Title = {Combining 2D synchrosqueezed wave packet transform with
             optimization for crystal image analysis},
   Journal = {Journal of the Mechanics and Physics of Solids},
   Volume = {89},
   Pages = {194-210},
   Year = {2016},
   Month = {April},
   ISSN = {0022-5096},
   url = {http://hdl.handle.net/10161/11296 Duke open
             access},
   Abstract = {© 2016 Elsevier Ltd. All rights reserved. We develop a
             variational optimization method for crystal analysis in
             atomic resolution images, which uses information from a 2D
             synchrosqueezed transform (SST) as input. The
             synchrosqueezed transform is applied to extract initial
             information from atomic crystal images: crystal defects,
             rotations and the gradient of elastic deformation. The
             deformation gradient estimate is then improved outside the
             identified defect region via a variational approach, to
             obtain more robust results agreeing better with the physical
             constraints. The variational model is optimized by a
             nonlinear projected conjugate gradient method. Both examples
             of images from computer simulations and imaging experiments
             are analyzed, with results demonstrating the effectiveness
             of the proposed method.},
   Doi = {10.1016/j.jmps.2016.01.002},
   Key = {fds316401}
}

@article{fds318297,
   Author = {Chen, J and Lu, J},
   Title = {Analysis of the divide-and-conquer method for electronic
             structure calculations},
   Journal = {Mathematics of Computation},
   Volume = {85},
   Number = {302},
   Pages = {2919-2938},
   Year = {2016},
   Month = {January},
   url = {http://dx.doi.org/10.1090/mcom/3066},
   Doi = {10.1090/mcom/3066},
   Key = {fds318297}
}

@article{fds320188,
   Author = {Delgadillo, R and Lu, J and Yang, X},
   Title = {Gauge-Invariant Frozen Gaussian Approximation Method for the
             Schrödinger Equation with Periodic Potentials},
   Journal = {Siam Journal on Scientific Computing},
   Volume = {38},
   Number = {4},
   Pages = {A2440-A2463},
   Year = {2016},
   Month = {January},
   url = {http://dx.doi.org/10.1137/15M1040384},
   Doi = {10.1137/15M1040384},
   Key = {fds320188}
}

@article{fds243728,
   Author = {Lu, J and Moroz, V and Muratov, CB},
   Title = {Orbital-Free Density Functional Theory of Out-of-Plane
             Charge Screening in Graphene},
   Journal = {Journal of Nonlinear Science},
   Volume = {25},
   Number = {6},
   Pages = {1391-1430},
   Year = {2015},
   Month = {December},
   ISSN = {0938-8974},
   url = {http://dx.doi.org/10.1007/s00332-015-9259-4},
   Doi = {10.1007/s00332-015-9259-4},
   Key = {fds243728}
}

@article{fds305048,
   Author = {Li, C and Lu, J and Yang, W},
   Title = {Gentlest ascent dynamics for calculating first excited state
             and exploring energy landscape of Kohn-Sham density
             functionals.},
   Journal = {The Journal of Chemical Physics},
   Volume = {143},
   Number = {22},
   Pages = {224110},
   Year = {2015},
   Month = {December},
   ISSN = {0021-9606},
   url = {http://dx.doi.org/10.1063/1.4936411},
   Abstract = {We develop the gentlest ascent dynamics for Kohn-Sham
             density functional theory to search for the index-1 saddle
             points on the energy landscape of the Kohn-Sham density
             functionals. These stationary solutions correspond to
             excited states in the ground state functionals. As shown by
             various examples, the first excited states of many chemical
             systems are given by these index-1 saddle points. Our novel
             approach provides an alternative, more robust way to obtain
             these excited states, compared with the widely used ΔSCF
             approach. The method can be easily generalized to target
             higher index saddle points. Our results also reveal the
             physical interest and relevance of studying the Kohn-Sham
             energy landscape.},
   Doi = {10.1063/1.4936411},
   Key = {fds305048}
}

@article{fds243731,
   Author = {Yang, H and Lu, J and Brown, WP and Daubechies, I and Ying,
             L},
   Title = {Quantitative Canvas Weave Analysis Using 2-D Synchrosqueezed
             Transforms: Application of time-frequency analysis to art
             investigation},
   Journal = {Ieee Signal Processing Magazine},
   Volume = {32},
   Number = {4},
   Pages = {55-63},
   Year = {2015},
   Month = {July},
   ISSN = {1053-5888},
   url = {http://hdl.handle.net/10161/12009 Duke open
             access},
   Doi = {10.1109/MSP.2015.2406882},
   Key = {fds243731}
}

@article{fds243732,
   Author = {Li, Q and Lu, J and Sun, W},
   Title = {Diffusion approximations and domain decomposition method of
             linear transport equations: Asymptotics and
             numerics},
   Journal = {Journal of Computational Physics},
   Volume = {292},
   Pages = {141-167},
   Year = {2015},
   Month = {July},
   ISSN = {0021-9991},
   url = {http://dx.doi.org/10.1016/j.jcp.2015.03.014},
   Abstract = {© 2015 Elsevier Inc. In this paper we construct numerical
             schemes to approximate linear transport equations with slab
             geometry by diffusion equations. We treat both the case of
             pure diffusive scaling and the case where kinetic and
             diffusive scalings coexist. The diffusion equations and
             their data are derived from asymptotic and layer analysis
             which allows general scattering kernels and general data. We
             apply the half-space solver in [20] to resolve the boundary
             layer equation and obtain the boundary data for the
             diffusion equation. The algorithms are validated by
             numerical experiments and also by error analysis for the
             pure diffusive scaling case.},
   Doi = {10.1016/j.jcp.2015.03.014},
   Key = {fds243732}
}

@article{fds243733,
   Author = {Lu, J and Mendl, CB},
   Title = {Numerical scheme for a spatially inhomogeneous matrix-valued
             quantum Boltzmann equation},
   Journal = {Journal of Computational Physics},
   Volume = {291},
   Pages = {303-316},
   Year = {2015},
   Month = {June},
   ISSN = {0021-9991},
   url = {http://dx.doi.org/10.1016/j.jcp.2015.03.020},
   Doi = {10.1016/j.jcp.2015.03.020},
   Key = {fds243733}
}

@article{fds243734,
   Author = {Lu, J and Liu, J-G and Margetis, D},
   Title = {Emergence of step flow from an atomistic scheme of epitaxial
             growth in 1+1 dimensions.},
   Journal = {Physical Review. E, Statistical, Nonlinear, and Soft Matter
             Physics},
   Volume = {91},
   Number = {3},
   Pages = {032403},
   Year = {2015},
   Month = {March},
   ISSN = {1539-3755},
   url = {http://dx.doi.org/10.1103/physreve.91.032403},
   Abstract = {The Burton-Cabrera-Frank (BCF) model for the flow of line
             defects (steps) on crystal surfaces has offered useful
             insights into nanostructure evolution. This model has rested
             on phenomenological grounds. Our goal is to show via scaling
             arguments the emergence of the BCF theory for noninteracting
             steps from a stochastic atomistic scheme of a kinetic
             restricted solid-on-solid model in one spatial dimension.
             Our main assumptions are: adsorbed atoms (adatoms) form a
             dilute system, and elastic effects of the crystal lattice
             are absent. The step edge is treated as a front that
             propagates via probabilistic rules for atom attachment and
             detachment at the step. We formally derive a quasistatic
             step flow description by averaging out the stochastic scheme
             when terrace diffusion, adatom desorption, and deposition
             from above are present.},
   Doi = {10.1103/physreve.91.032403},
   Key = {fds243734}
}

@article{fds243743,
   Author = {Lu, J and Nolen, J},
   Title = {Reactive trajectories and the transition path
             process},
   Journal = {Probability Theory and Related Fields},
   Volume = {161},
   Number = {1-2},
   Pages = {195-244},
   Year = {2015},
   Month = {February},
   ISSN = {0178-8051},
   url = {http://dx.doi.org/10.1007/s00440-014-0547-y},
   Doi = {10.1007/s00440-014-0547-y},
   Key = {fds243743}
}

@article{fds243736,
   Author = {Liu, J and Lu, J and Zhou, X},
   Title = {Efficient Rare Event Simulation for Failure Problems in
             Random Media},
   Journal = {Siam Journal on Scientific Computing},
   Volume = {37},
   Number = {2},
   Pages = {A609-A624},
   Year = {2015},
   Month = {January},
   ISSN = {1064-8275},
   url = {http://dx.doi.org/10.1137/140965569},
   Doi = {10.1137/140965569},
   Key = {fds243736}
}

@article{fds305050,
   Author = {Yang, H and Lu, J and Ying, L},
   Title = {Crystal Image Analysis Using 2D Synchrosqueezed
             Transforms},
   Journal = {Multiscale Modeling & Simulation},
   Volume = {13},
   Number = {4},
   Pages = {1542-1572},
   Year = {2015},
   Month = {January},
   ISSN = {1540-3459},
   url = {http://hdl.handle.net/10161/11648 Duke open
             access},
   Doi = {10.1137/140955872},
   Key = {fds305050}
}

@article{fds243729,
   Author = {Lu, J and Ying, L},
   Title = {Compression of the electron repulsion integral tensor in
             tensor hypercontraction format with cubic scaling
             cost},
   Journal = {Journal of Computational Physics},
   Volume = {302},
   Pages = {329-335},
   Year = {2015},
   ISSN = {0021-9991},
   url = {http://dx.doi.org/10.1016/j.jcp.2015.09.014},
   Abstract = {© 2015 Elsevier Inc.Electron repulsion integral tensor has
             ubiquitous applications in electronic structure
             computations. In this work, we propose an algorithm which
             compresses the electron repulsion tensor into the tensor
             hypercontraction format with O(nN2logN) computational cost,
             where N is the number of orbital functions and n is the
             number of spatial grid points that the discretization of
             each orbital function has. The algorithm is based on a novel
             strategy of density fitting using a selection of a subset of
             spatial grid points to approximate the pair products of
             orbital functions on the whole domain.},
   Doi = {10.1016/j.jcp.2015.09.014},
   Key = {fds243729}
}

@article{fds243730,
   Author = {Lai, R and Lu, J and Osher, S},
   Title = {Density matrix minimization with ${\ell}_1$
             regularization},
   Journal = {Communications in Mathematical Sciences},
   Volume = {13},
   Number = {8},
   Pages = {2097-2117},
   Year = {2015},
   ISSN = {1539-6746},
   url = {http://dx.doi.org/10.4310/CMS.2015.v13.n8.a6},
   Doi = {10.4310/CMS.2015.v13.n8.a6},
   Key = {fds243730}
}

@article{fds243737,
   Author = {Lu, J and Marzuola, JL},
   Title = {Strang splitting methods for a quasilinear Schrödinger
             equation: convergence, instability, and dynamics},
   Journal = {Communications in Mathematical Sciences},
   Volume = {13},
   Number = {5},
   Pages = {1051-1074},
   Year = {2015},
   ISSN = {1539-6746},
   url = {http://dx.doi.org/10.4310/CMS.2015.v13.n5.a1},
   Doi = {10.4310/CMS.2015.v13.n5.a1},
   Key = {fds243737}
}

@article{fds243778,
   Author = {Xian, Y and Thompson, A and Qiu, Q and Nolte, L and Nowacek, D and Lu, J and Calderbank, R and IEEE},
   Title = {CLASSIFICATION OF WHALE VOCALIZATIONS USING THE WEYL
             TRANSFORM},
   Journal = {2015 Ieee International Conference on Acoustics, Speech, and
             Signal Processing (Icassp)},
   Volume = {2015-August},
   Pages = {773-777},
   Booktitle = {2015 IEEE International Conference on Acoustics, Speech and
             Signal Processing (ICASSP)},
   Year = {2015},
   ISBN = {9781467369978},
   ISSN = {1520-6149},
   url = {http://dx.doi.org/10.1109/ICASSP.2015.7178074},
   Abstract = {© 2015 IEEE.In this paper, we apply the Weyl transform to
             represent the vocalization of marine mammals. In contrast to
             other popular representation methods, such as the MFCC and
             the Chirplet transform, the Weyl transform captures the
             global information of signals. This is especially useful
             when the signal has low order polynomial phase. We can
             reconstruct the signal from the coefficients obtained from
             the Weyl transform, and perform classification based on
             these coefficients. Experimental results show that
             classification using features extracted from the Weyl
             transform outperforms the MFCC and the Chirplet transform on
             our collected whales data.},
   Doi = {10.1109/ICASSP.2015.7178074},
   Key = {fds243778}
}

@article{fds243754,
   Author = {Lu, J and Otto, F},
   Title = {Nonexistence of a Minimizer for Thomas-Fermi-Dirac-von
             Weizsäcker Model},
   Journal = {Communications on Pure and Applied Mathematics},
   Volume = {67},
   Number = {10},
   Pages = {1605-1617},
   Year = {2014},
   Month = {October},
   ISSN = {0010-3640},
   url = {http://dx.doi.org/10.1002/cpa.21477},
   Doi = {10.1002/cpa.21477},
   Key = {fds243754}
}

@article{fds243738,
   Author = {Yang, Y and Peng, D and Lu, J and Yang, W},
   Title = {Excitation energies from particle-particle random phase
             approximation: Davidson algorithm and benchmark
             studies},
   Journal = {The Journal of Chemical Physics},
   Volume = {141},
   Number = {12},
   Pages = {124104-124104},
   Year = {2014},
   Month = {September},
   ISSN = {0021-9606},
   url = {http://dx.doi.org/10.1063/1.4895792},
   Abstract = {The particle-particle random phase approximation (pp-RPA)
             has been used to investigate excitation problems in our
             recent paper [Y. Yang, H. van Aggelen, and W. Yang, J. Chem.
             Phys. 139, 224105 (2013)]. It has been shown to be capable
             of describing double, Rydberg, and charge transfer
             excitations, which are challenging for conventional
             time-dependent density functional theory (TDDFT). However,
             its performance on larger molecules is unknown as a result
             of its expensive O(N(6)) scaling. In this article, we derive
             and implement a Davidson iterative algorithm for the pp-RPA
             to calculate the lowest few excitations for large systems.
             The formal scaling is reduced to O(N(4)), which is
             comparable with the commonly used configuration interaction
             singles (CIS) and TDDFT methods. With this iterative
             algorithm, we carried out benchmark tests on molecules that
             are significantly larger than the molecules in our previous
             paper with a reasonably large basis set. Despite some
             self-consistent field convergence problems with ground state
             calculations of (N - 2)-electron systems, we are able to
             accurately capture lowest few excitations for systems with
             converged calculations. Compared to CIS and TDDFT, there is
             no systematic bias for the pp-RPA with the mean signed error
             close to zero. The mean absolute error of pp-RPA with B3LYP
             or PBE references is similar to that of TDDFT, which
             suggests that the pp-RPA is a comparable method to TDDFT for
             large molecules. Moreover, excitations with relatively large
             non-HOMO excitation contributions are also well described in
             terms of excitation energies, as long as there is also a
             relatively large HOMO excitation contribution. These
             findings, in conjunction with the capability of pp-RPA for
             describing challenging excitations shown earlier, further
             demonstrate the potential of pp-RPA as a reliable and
             general method to describe excitations, and to be a good
             alternative to TDDFT methods.},
   Doi = {10.1063/1.4895792},
   Key = {fds243738}
}

@article{fds243739,
   Author = {Lu, J and Vanden-Eijnden, E},
   Title = {Exact dynamical coarse-graining without time-scale
             separation},
   Journal = {The Journal of Chemical Physics},
   Volume = {141},
   Number = {4},
   Pages = {044109-044109},
   Year = {2014},
   Month = {July},
   ISSN = {0021-9606},
   url = {http://dx.doi.org/10.1063/1.4890367},
   Abstract = {A family of collective variables is proposed to perform
             exact dynamical coarse-graining even in systems without time
             scale separation. More precisely, it is shown that these
             variables are not slow in general, yet satisfy an overdamped
             Langevin equation that statistically preserves the sequence
             in which any regions in collective variable space are
             visited and permits to calculate exactly the mean first
             passage times from any such region to another. The role of
             the free energy and diffusion coefficient in this overdamped
             Langevin equation is discussed, along with the way they
             transform under any change of variable in collective
             variable space. These results apply both to systems with and
             without inertia, and they can be generalized to using
             several collective variables simultaneously. The view they
             offer on what makes collective variables and reaction
             coordinates optimal breaks from the standard notion that
             good collective variable must be slow variable, and it
             suggests new ways to interpret data from molecular dynamics
             simulations and experiments.},
   Doi = {10.1063/1.4890367},
   Key = {fds243739}
}

@article{fds243740,
   Author = {E, W and Lu, J},
   Title = {Mathematical theory of solids: From quantum mechanics to
             continuum models},
   Journal = {Discrete and Continuous Dynamical Systems Series
             A},
   Volume = {34},
   Number = {12},
   Pages = {5085-5097},
   Year = {2014},
   Month = {June},
   ISSN = {1078-0947},
   url = {http://dx.doi.org/10.3934/dcds.2014.34.5085},
   Doi = {10.3934/dcds.2014.34.5085},
   Key = {fds243740}
}

@article{fds243741,
   Author = {Kohn, RV and Lu, J and Schweizer, B and Weinstein,
             MI},
   Title = {A Variational Perspective on Cloaking by Anomalous Localized
             Resonance},
   Journal = {Communications in Mathematical Physics},
   Volume = {328},
   Number = {1},
   Pages = {1-27},
   Year = {2014},
   Month = {May},
   ISSN = {0010-3616},
   url = {http://dx.doi.org/10.1007/s00220-014-1943-y},
   Doi = {10.1007/s00220-014-1943-y},
   Key = {fds243741}
}

@article{fds243742,
   Author = {Lin, L and Lu, J and Shao, S},
   Title = {Analysis of Time Reversible Born-Oppenheimer Molecular
             Dynamics},
   Journal = {Entropy},
   Volume = {16},
   Number = {1},
   Pages = {110-137},
   Editor = {G. Ciccotti and M. Ferrario and Ch. Schuette},
   Year = {2014},
   Month = {January},
   url = {http://dx.doi.org/10.3390/e16010110},
   Doi = {10.3390/e16010110},
   Key = {fds243742}
}

@article{fds243744,
   Author = {Lu, J and Ming, P},
   Title = {Stability Of A Force-Based Hybrid Method With Planar Sharp
             Interface},
   Journal = {Siam Journal on Numerical Analysis},
   Volume = {52},
   Number = {4},
   Pages = {2005-2026},
   Year = {2014},
   Month = {January},
   ISSN = {0036-1429},
   url = {http://dx.doi.org/10.1137/130904843},
   Doi = {10.1137/130904843},
   Key = {fds243744}
}

@article{fds318298,
   Author = {Lu, J and Otto, F},
   Title = {Nonexistence of a minimizer for Thomas-Fermi-Dirac-von
             Weizsäcker model},
   Journal = {Communications on Pure and Applied Mathematics},
   Volume = {67},
   Number = {10},
   Pages = {1605-1617},
   Year = {2014},
   url = {http://dx.doi.org/10.1002/cpa.21477},
   Doi = {10.1002/cpa.21477},
   Key = {fds318298}
}

@article{fds243745,
   Author = {Lu, J and Vanden-Eijnden, E},
   Title = {Infinite swapping replica exchange molecular dynamics leads
             to a simple simulation patch using mixture
             potentials.},
   Journal = {The Journal of Chemical Physics},
   Volume = {138},
   Number = {8},
   Pages = {084105},
   Year = {2013},
   Month = {February},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/23464138},
   Abstract = {Replica exchange molecular dynamics (REMD) becomes more
             efficient as the frequency of swap between the temperatures
             is increased. Recently Plattner et al. [J. Chem. Phys. 135,
             134111 (2011)] proposed a method to implement infinite
             swapping REMD in practice. Here we introduce a natural
             modification of this method that involves molecular dynamics
             simulations over a mixture potential. This modification is
             both simple to implement in practice and provides a better,
             energy based understanding of how to choose the temperatures
             in REMD to optimize efficiency. It also has implications for
             generalizations of REMD in which the swaps involve other
             parameters than the temperature.},
   Doi = {10.1063/1.4790706},
   Key = {fds243745}
}

@article{fds243747,
   Author = {Lu, J and Ming, P},
   Title = {Convergence of a Force-Based Hybrid Method in Three
             Dimensions},
   Journal = {Communications on Pure and Applied Mathematics},
   Volume = {66},
   Number = {1},
   Pages = {83-108},
   Year = {2013},
   Month = {January},
   ISSN = {0010-3640},
   url = {http://dx.doi.org/10.1002/cpa.21429},
   Doi = {10.1002/cpa.21429},
   Key = {fds243747}
}

@article{fds243746,
   Author = {E, W and Lu, JF and Yang, X},
   Title = {Asymptotic analysis of quantum dynamics in crystals: The
             Bloch-Wigner transform, Bloch dynamics and Berry
             phase},
   Journal = {Acta Mathematicae Applicatae Sinica, English
             Series},
   Volume = {29},
   Number = {3},
   Pages = {465-476},
   Year = {2013},
   ISSN = {0168-9673},
   url = {http://dx.doi.org/10.1007/s10255-011-0095-5},
   Abstract = {We study the semi-classical limit of the Schrödinger
             equation in a crystal in the presence of an external
             potential and magnetic field. We first introduce the
             Bloch-Wigner transform and derive the asymptotic equations
             governing this transform in the semi-classical setting. For
             the second part, we focus on the appearance of the Berry
             curvature terms in the asymptotic equations. These terms
             play a crucial role in many important physical phenomena
             such as the quantum Hall effect. We give a simple derivation
             of these terms in different settings using asymptotic
             analysis. © 2013 Institute of Applied Mathematics, Academy
             of Mathematics and System Sciences, Chinese Academy of
             Sciences and Springer-Verlag Berlin Heidelberg.},
   Doi = {10.1007/s10255-011-0095-5},
   Key = {fds243746}
}

@article{fds243750,
   Author = {E, W and Lu, J and Yao, Y},
   Title = {The landscape of complex networks: Critical nodes and a
             hierarchical decomposition},
   Journal = {Methods and Applications of Analysis},
   Volume = {20},
   Number = {4},
   Pages = {383-404},
   Year = {2013},
   ISSN = {1073-2772},
   url = {http://dx.doi.org/10.4310/MAA.2013.v20.n4.a5},
   Doi = {10.4310/MAA.2013.v20.n4.a5},
   Key = {fds243750}
}

@article{fds243756,
   Author = {E, W and Lu, J},
   Title = {Stability and the continuum limit of the spin-polarized
             Thomas-Fermi-Dirac-von Weizsäcker model},
   Journal = {Journal of Mathematical Physics},
   Volume = {53},
   Number = {11},
   Pages = {115615-115615},
   Year = {2012},
   Month = {November},
   ISSN = {0022-2488},
   url = {http://dx.doi.org/10.1063/1.4755952},
   Doi = {10.1063/1.4755952},
   Key = {fds243756}
}

@article{fds243755,
   Author = {Lin, L and Lu, J and Ying, L and E, W},
   Title = {Optimized local basis set for Kohn–Sham density functional
             theory},
   Journal = {Journal of Computational Physics},
   Volume = {231},
   Number = {13},
   Pages = {4515-4529},
   Year = {2012},
   Month = {May},
   ISSN = {0021-9991},
   url = {http://dx.doi.org/10.1016/j.jcp.2012.03.009},
   Doi = {10.1016/j.jcp.2012.03.009},
   Key = {fds243755}
}

@article{fds243751,
   Author = {Lin, L and Lu, J and Ying, L and E, W},
   Title = {Adaptive local basis set for Kohn–Sham density functional
             theory in a discontinuous Galerkin framework I: Total energy
             calculation},
   Journal = {Journal of Computational Physics},
   Volume = {231},
   Number = {4},
   Pages = {2140-2154},
   Year = {2012},
   Month = {February},
   ISSN = {0021-9991},
   url = {http://dx.doi.org/10.1016/j.jcp.2011.11.032},
   Doi = {10.1016/j.jcp.2011.11.032},
   Key = {fds243751}
}

@article{fds243749,
   Author = {E, W and Lu, J},
   Title = {The Kohn-Sham equation for deformed crystals},
   Journal = {Memoirs of the American Mathematical Society},
   Volume = {221},
   Number = {1040},
   Pages = {1-1},
   Year = {2012},
   ISSN = {0065-9266},
   url = {http://dx.doi.org/10.1090/S0065-9266-2012-00659-9},
   Doi = {10.1090/S0065-9266-2012-00659-9},
   Key = {fds243749}
}

@article{fds243752,
   Author = {Lu, J and Yang, X},
   Title = {Convergence of frozen Gaussian approximation for
             high-frequency wave propagation},
   Journal = {Communications on Pure and Applied Mathematics},
   Volume = {65},
   Number = {6},
   Pages = {759-789},
   Year = {2012},
   ISSN = {0010-3640},
   url = {http://dx.doi.org/10.1002/cpa.21384},
   Abstract = {The frozen Gaussian approximation provides a highly
             efficient computational method for high-frequency wave
             propagation. The derivation of the method is based on
             asymptotic analysis. In this paper, for general linear
             strictly hyperbolic systems, we establish the rigorous
             convergence result for frozen Gaussian approximation. As a
             byproduct, higher-order frozen Gaussian approximation is
             developed. © 2011 Wiley Periodicals, Inc.},
   Doi = {10.1002/cpa.21384},
   Key = {fds243752}
}

@article{fds243753,
   Author = {Lu, J and Yang, X},
   Title = {Frozen gaussian approximation for general linear strictly
             hyperbolic systems: Formulation and eulerian
             methods},
   Journal = {Multiscale Modeling & Simulation},
   Volume = {10},
   Number = {2},
   Pages = {451-472},
   Year = {2012},
   ISSN = {1540-3459},
   url = {http://dx.doi.org/10.1137/10081068X},
   Abstract = {The frozen Gaussian approximation, proposed in [J. Lu and X.
             Yang, Commun. Math. Sci., 9 (2011), pp. 663-683], is an
             efficient computational tool for high frequency wave
             propagation. We continue in this paper the development of
             frozen Gaussian approximation. The frozen Gaussian
             approximation is extended to general linear strictly
             hyperbolic systems. Eulerian methods based on frozen
             Gaussian approximation are developed to overcome the
             divergence problem of Lagrangian methods. The proposed
             Eulerian methods can also be used for the Herman-Kluk
             propagator in quantum mechanics. Numerical examples verify
             the performance of the proposed methods. © 2012 Society for
             Industrial and Applied Mathematics.},
   Doi = {10.1137/10081068X},
   Key = {fds243753}
}

@article{fds243761,
   Author = {Schütte, C and Noé, F and Lu, J and Sarich, M and Vanden-Eijnden,
             E},
   Title = {Markov state models based on milestoning},
   Journal = {The Journal of Chemical Physics},
   Volume = {134},
   Number = {20},
   Pages = {204105-204105},
   Year = {2011},
   Month = {May},
   ISSN = {0021-9606},
   url = {http://dx.doi.org/10.1063/1.3590108},
   Doi = {10.1063/1.3590108},
   Key = {fds243761}
}

@article{fds243759,
   Author = {Lin, L and Lu, J and Ying, L},
   Title = {Fast construction of hierarchical matrix representation from
             matrix–vector multiplication},
   Journal = {Journal of Computational Physics},
   Volume = {230},
   Number = {10},
   Pages = {4071-4087},
   Year = {2011},
   Month = {May},
   ISSN = {0021-9991},
   url = {http://dx.doi.org/10.1016/j.jcp.2011.02.033},
   Abstract = {We develop a hierarchical matrix construction algorithm
             using matrix-vector multiplications, based on the randomized
             singular value decomposition of low-rank matrices. The
             algorithm uses O(logn) applications of the matrix on
             structured random test vectors and O(nlogn) extra
             computational cost, where n is the dimension of the unknown
             matrix. Numerical examples on constructing Green's functions
             for elliptic operators in two dimensions show efficiency and
             accuracy of the proposed algorithm. © 2011 Elsevier
             Inc.},
   Doi = {10.1016/j.jcp.2011.02.033},
   Key = {fds243759}
}

@article{fds243764,
   Author = {Daubechies, I and Lu, J and Wu, H-T},
   Title = {Synchrosqueezed wavelet transforms: An empirical mode
             decomposition-like tool},
   Journal = {Applied and Computational Harmonic Analysis},
   Volume = {30},
   Number = {2},
   Pages = {243-261},
   Year = {2011},
   Month = {March},
   ISSN = {1063-5203},
   url = {http://dx.doi.org/10.1016/j.acha.2010.08.002},
   Abstract = {The EMD algorithm, first proposed in [11], made more robust
             as well as more versatile in [12], is a technique that aims
             to decompose into their building blocks functions that are
             the superposition of a (reasonably) small number of
             components, well separated in the time-frequency plane, each
             of which can be viewed as approximately harmonic locally,
             with slowly varying amplitudes and frequencies. The EMD has
             already shown its usefulness in a wide range of applications
             including meteorology, structural stability analysis,
             medical studies -- see, e.g. [13]. On the other hand, the
             EMD algorithm contains heuristic and ad-hoc elements that
             make it hard to analyze mathematically. In this paper we
             describe a method that captures the flavor and philosophy of
             the EMD approach, albeit using a different approach in
             constructing the components. We introduce a precise
             mathematical definition for a class of functions that can be
             viewed as a superposition of a reasonably small number of
             approximately harmonic components, and we prove that our
             method does indeed succeed in decomposing arbitrary
             functions in this class. We provide several examples, for
             simulated as well as real data.},
   Doi = {10.1016/j.acha.2010.08.002},
   Key = {fds243764}
}

@article{fds243763,
   Author = {Lin, L and Yang, C and Meza, JC and Lu, J and Ying, L and E,
             W},
   Title = {SelInv---An Algorithm for Selected Inversion of a Sparse
             Symmetric Matrix},
   Journal = {Acm Transactions on Mathematical Software},
   Volume = {37},
   Number = {4},
   Pages = {1-19},
   Year = {2011},
   Month = {February},
   ISSN = {0098-3500},
   url = {http://dx.doi.org/10.1145/1916461.1916464},
   Doi = {10.1145/1916461.1916464},
   Key = {fds243763}
}

@article{fds243765,
   Author = {E, W and Lu, J},
   Title = {The Electronic Structure of Smoothly Deformed Crystals:
             Wannier Functions and the Cauchy–Born Rule},
   Journal = {Archive for Rational Mechanics and Analysis},
   Volume = {199},
   Number = {2},
   Pages = {407-433},
   Year = {2011},
   Month = {February},
   ISSN = {0003-9527},
   url = {http://dx.doi.org/10.1007/s00205-010-0339-1},
   Doi = {10.1007/s00205-010-0339-1},
   Key = {fds243765}
}

@article{fds243757,
   Author = {Lin, L and Yang, C and Lu, J and Ying, L and E, W},
   Title = {A Fast Parallel Algorithm for Selected Inversion of
             Structured Sparse Matrices with Application to 2D Electronic
             Structure Calculations},
   Journal = {Siam Journal on Scientific Computing},
   Volume = {33},
   Number = {3},
   Pages = {1329-1351},
   Year = {2011},
   Month = {January},
   ISSN = {1064-8275},
   url = {http://dx.doi.org/10.1137/09077432X},
   Doi = {10.1137/09077432X},
   Key = {fds243757}
}

@article{fds243758,
   Author = {E, W and Lu, J and Yang, X},
   Title = {Effective Maxwell equations from time-dependent density
             functional theory},
   Journal = {Acta Math. Sin.},
   Volume = {32},
   Pages = {339-339},
   Year = {2011},
   Key = {fds243758}
}

@article{fds243760,
   Author = {Lu, J and Yang, X},
   Title = {Frozen Gaussian approximation for high frequency wave
             propagation},
   Journal = {Communications in Mathematical Sciences},
   Volume = {9},
   Number = {3},
   Pages = {663-683},
   Year = {2011},
   ISSN = {1539-6746},
   url = {http://dx.doi.org/10.4310/CMS.2011.v9.n3.a2},
   Abstract = {We propose the frozen Gaussian approximation for computation
             of high frequency wave propagation. This method approximates
             the solution to the wave equation by an integral
             representation. It provides a highly efficient computational
             tool based on the asymptotic analysis on the phase plane.
             Compared to geometric optics, it provides a valid solution
             around caustics. Compared to the Gaussian beam method, it
             overcomes the drawback of beam spreading. We give several
             numerical examples to verify that the frozen Gaussian
             approximation performs well in the presence of caustics and
             when the Gaussian beam spreads. Moreover, it is observed
             numerically that the frozen Gaussian approximation exhibits
             better accuracy than the Gaussian beam method. © 2011
             International Press.},
   Doi = {10.4310/CMS.2011.v9.n3.a2},
   Key = {fds243760}
}

@article{fds243762,
   Author = {E, W and Lu, J},
   Title = {Multiscale modeling},
   Journal = {Scholarpedia},
   Volume = {6},
   Pages = {11527},
   Year = {2011},
   url = {http://www.scholarpedia.org/article/Multiscale_modeling},
   Key = {fds243762}
}

@article{fds243766,
   Author = {E, W and Lu, J},
   Title = {Electronic structure of smoothly deformed crystals:
             Cauchy-born rule for the nonlinear tight-binding
             model},
   Journal = {Communications on Pure and Applied Mathematics},
   Volume = {63},
   Number = {11},
   Pages = {1432-1468},
   Year = {2010},
   Month = {November},
   ISSN = {0010-3640},
   url = {http://dx.doi.org/10.1002/cpa.20330},
   Doi = {10.1002/cpa.20330},
   Key = {fds243766}
}

@article{fds243767,
   Author = {E, W and Li, T and Lu, J},
   Title = {Localized bases of eigensubspaces and operator
             compression.},
   Journal = {Proceedings of the National Academy of Sciences of the
             United States of America},
   Volume = {107},
   Number = {4},
   Pages = {1273-1278},
   Year = {2010},
   Month = {January},
   ISSN = {0027-8424},
   url = {http://dx.doi.org/10.1073/pnas.0913345107},
   Abstract = {Given a complex local operator, such as the generator of a
             Markov chain on a large network, a differential operator, or
             a large sparse matrix that comes from the discretization of
             a differential operator, we would like to find its best
             finite dimensional approximation with a given dimension. The
             answer to this question is often given simply by the
             projection of the original operator to its eigensubspace of
             the given dimension that corresponds to the smallest or
             largest eigenvalues, depending on the setting. The
             representation of such subspaces, however, is far from being
             unique and our interest is to find the most localized bases
             for these subspaces. The reduced operator using these bases
             would have sparsity features similar to that of the original
             operator. We will discuss different ways of obtaining
             localized bases, and we will give an explicit
             characterization of the decay rate of these basis functions.
             We will also discuss efficient numerical algorithms for
             finding such basis functions and the reduced (or compressed)
             operator.},
   Doi = {10.1073/pnas.0913345107},
   Key = {fds243767}
}

@article{fds243769,
   Author = {García-Cervera, CJ and Lu, J and Xuan, Y and E, W},
   Title = {Linear-scaling subspace-iteration algorithm with optimally
             localized nonorthogonal wave functions for Kohn-Sham density
             functional theory},
   Journal = {Physical Review B},
   Volume = {79},
   Number = {11},
   Pages = {115110},
   Year = {2009},
   Month = {March},
   ISSN = {1098-0121},
   url = {http://dx.doi.org/10.1103/PhysRevB.79.115110},
   Doi = {10.1103/PhysRevB.79.115110},
   Key = {fds243769}
}

@article{fds243770,
   Author = {Lin, L and Lu, J and Car, R and E, W},
   Title = {Multipole representation of the Fermi operator with
             application to the electronic structure analysis of metallic
             systems},
   Journal = {Physical Review B},
   Volume = {79},
   Number = {11},
   Pages = {115133},
   Year = {2009},
   Month = {March},
   ISSN = {1098-0121},
   url = {http://dx.doi.org/10.1103/PhysRevB.79.115133},
   Doi = {10.1103/PhysRevB.79.115133},
   Key = {fds243770}
}

@article{fds243768,
   Author = {Car, R and E, W and Lin, L and Lu, J and Ying, L},
   Title = {Fast algorithm for extracting the diagonal of the inverse
             matrix with application to the electronic structure analysis
             of metallic systems},
   Journal = {Communications in Mathematical Sciences},
   Volume = {7},
   Number = {3},
   Pages = {755-777},
   Year = {2009},
   url = {http://dx.doi.org/10.4310/CMS.2009.v7.n3.a12},
   Doi = {10.4310/CMS.2009.v7.n3.a12},
   Key = {fds243768}
}

@article{fds243771,
   Author = {Lin, L and Lu, J and Ying, L and E, W},
   Title = {Pole-based approximation of the Fermi-Dirac
             function},
   Journal = {Chin. Ann. Math. Ser. B},
   Volume = {30},
   Pages = {729-742},
   Year = {2009},
   Key = {fds243771}
}

@article{fds243772,
   Author = {Garcia-Cervera, CJ and Ren, W and Lu, J and E, W},
   Title = {Sequential multiscale modelling using sparse
             representation},
   Journal = {Commun. Comput. Phys.},
   Volume = {4},
   Pages = {1025-1033},
   Year = {2008},
   Key = {fds243772}
}

@article{fds243776,
   Author = {E, W and Lu, J},
   Title = {The Elastic Continuum Limit of the Tight Binding
             Model*},
   Journal = {Chinese Annals of Mathematics, Series B},
   Volume = {28},
   Number = {6},
   Pages = {665-676},
   Year = {2007},
   Month = {December},
   ISSN = {0252-9599},
   url = {http://dx.doi.org/10.1007/s11401-006-0447-2},
   Doi = {10.1007/s11401-006-0447-2},
   Key = {fds243776}
}

@article{fds243773,
   Author = {E, W and García-Cervera, CJ and Lu, J},
   Title = {A sub-linear scaling algorithm for computing the electronic
             structure of materials},
   Journal = {Communications in Mathematical Sciences},
   Volume = {5},
   Number = {4},
   Pages = {999-1026},
   Year = {2007},
   ISSN = {1539-6746},
   url = {http://dx.doi.org/10.4310/CMS.2007.v5.n4.a14},
   Doi = {10.4310/CMS.2007.v5.n4.a14},
   Key = {fds243773}
}

@article{fds243774,
   Author = {E, W and Lu, J},
   Title = {Seamless multiscale modeling via dynamics on fiber
             bundles},
   Journal = {Communications in Mathematical Sciences},
   Volume = {5},
   Number = {3},
   Pages = {649-663},
   Year = {2007},
   ISSN = {1539-6746},
   url = {http://dx.doi.org/10.4310/CMS.2007.v5.n3.a7},
   Doi = {10.4310/CMS.2007.v5.n3.a7},
   Key = {fds243774}
}

@article{fds243775,
   Author = {E, W and Lu, J},
   Title = {The continuum limit and QM-continuum approximation of
             quantum mechanical models of solids},
   Journal = {Communications in Mathematical Sciences},
   Volume = {5},
   Number = {3},
   Pages = {679-696},
   Year = {2007},
   ISSN = {1539-6746},
   url = {http://dx.doi.org/10.4310/CMS.2007.v5.n3.a9},
   Doi = {10.4310/CMS.2007.v5.n3.a9},
   Key = {fds243775}
}

@article{fds243777,
   Author = {E, W and Lu, J and Yang, JZ},
   Title = {Uniform accuracy of the quasicontinuum method},
   Journal = {Physical Review B},
   Volume = {74},
   Number = {21},
   Pages = {214115},
   Year = {2006},
   Month = {December},
   ISSN = {1098-0121},
   url = {http://dx.doi.org/10.1103/PhysRevB.74.214115},
   Doi = {10.1103/PhysRevB.74.214115},
   Key = {fds243777}
}