## 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}
}