%% Papers Published @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{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}, Year = {2017}, Month = {September}, url = {http://dx.doi.org/10.1016/j.cpc.2017.09.007}, Doi = {10.1016/j.cpc.2017.09.007}, Key = {fds329344} } @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}, Year = {2017}, Month = {September}, url = {http://dx.doi.org/10.1016/j.jcp.2017.09.012}, Doi = {10.1016/j.jcp.2017.09.012}, Key = {fds329343} } @article{fds328895, Author = {Lu, J and Steinerberger, S}, Title = {A variation on the Donsker-Varadhan inequality for the principal eigenvalue.}, Journal = {Proceedings of the Royal Society of London: 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 = {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 = {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{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{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{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}, 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 USA}, 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 = {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 = {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{fds243754, Author = {Lu, J and Otto, F}, Title = {Nonexistence of a Minimizer for Thomas-Fermi-Dirac-von Weizsäcker Model}, Journal = {Communications on Pure & 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 = {Journal of Chemical Physics}, Volume = {141}, Number = {12}, Pages = {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 = {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}, 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}, 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 (Basel, Switzerland)}, 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 & 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 = {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 & 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 & 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 = {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{fds243764, Author = {Daubechies, I and Lu, J and Wu, H-T}, Title = {Synchrosqueezed Wavelet Transforms: a Tool for Empirical Mode Decomposition}, 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{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}, 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{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 & 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 USA}, Volume = {107}, Number = {4}, Pages = {1273-1278}, Year = {2010}, Month = {January}, ISSN = {0027-8424}, url = {http://dx.doi.org/10.1073/pnas.0913345107}, 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 - Condensed Matter and Materials Physics}, 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 - Condensed Matter and Materials Physics}, 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 = {Lin, L and Lu, J and Ying, L and Car, R and E, W}, Title = {Fast algorithm for extracting the diagonal of the inverse matrix with application to the electronic structure analysis of metallic systems}, Journal = {Commun. Math. Sci.}, Volume = {7}, Pages = {755-777}, Year = {2009}, 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 - Condensed Matter and Materials Physics}, 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} }