Browsing by Author "Lu, J"
Now showing items 120 of 47

A convergent method for linear halfspace kinetic equations
Li, Q; Lu, J; Sun, W (20170423)We give a unified proof for the wellposedness of a class of linear halfspace equations with general incoming data and construct a Galerkin method to numerically resolve this type of equations in a systematic way. Our ... 
A Hybrid Globallocal Numerical Method for Multiscale PDEs
Huang, Y; Lu, J; Ming, P (20170423)We present a new hybrid numerical method for multiscale partial differential equations, which simultaneously captures both the global macroscopic information and resolves the local microscopic events. The convergence of ... 
A Mathematical Theory of Optimal Milestoning (with a Detour via Exact Milestoning)
Lin, L; Lu, J; VandenEijnden, E (20170423)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 ... 
A quasinonlocal coupling method for nonlocal and local diffusion models
Du, Q; Li, XH; Lu, J; Tian, X (20170423)In this paper, we extend the idea of "geometric reconstruction" to couple a nonlocal diffusion model directly with the classical local diffusion in one dimensional space. This new coupling framework removes interfacial ... 
A Surface Hopping Gaussian Beam Method for HighDimensional Transport Systems
Cai, Z; Lu, J (20170423)We propose a surface hopping Gaussian beam method to numerically solve a class of high frequency linear transport systems in high spatial dimensions, based on asymptotic analysis. The stochastic surface hopping is combined ... 
A Variation on the DonskerVaradhan Inequality for the Principial Eigenvalue
Lu, J; Steinerberger, S (20170423)The purpose of this short note is to give a variation on the classical DonskerVaradhan inequality, which bounds the first eigenvalue of a secondorder elliptic operator on a bounded domain $\Omega$ by the largest mean ... 
An isoperimetric problem with Coulomb repulsion and attraction to a background nucleus
Lu, J; Otto, F (20170423)We study an isoperimetric problem the energy of which contains the perimeter of a set, Coulomb repulsion of the set with itself, and attraction of the set to a background nucleus as a point charge with charge $Z$. For the ... 
Asymmetry in crystal facet dynamics of homoepitaxy by a continuum model
Liu, JG; Lu, J; Margetis, D; Marzuola, JL (20170423)In the absence of external material deposition, crystal surfaces usually relax to become flat by decreasing their free energy. We study an asymmetry in the relaxation of macroscopic plateaus, facets, of a periodic surface ... 
Bloch dynamics with second order Berry phase correction
Lu, J; Zhou, Z (20170423)We derive the semiclassical Bloch dynamics with the second order Berry phase correction, based on a twoscale WKB asymptotic analysis. For uniform external electric field, the bicharacteristics system after a positional ... 
Capturing and Manipulating Activated Neuronal Ensembles with CANE Delineates a Hypothalamic SocialFear Circuit
Sakurai, K; Zhao, S; Takatoh, J; Rodriguez, E; Lu, J; Leavitt, AD; Fu, M; Han, BX; Wang, F (Neuron, 20161123)© 2016 Elsevier Inc.We developed a technology (capturing activated neuronal ensembles [CANE]) to label, manipulate, and transsynaptically trace neural circuits that are transiently activated in behavioral contexts with ... 
Combining 2D synchrosqueezed wave packet transform with optimization for crystal image analysis
Lu, J; Wirth, B; Yang, H (Journal of the Mechanics and Physics of Solids, 20160401)© 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 ... 
Convergence of frozen Gaussian approximation for highfrequency wave propagation
Lu, J; Yang, X (Communications on Pure and Applied Mathematics, 20120601)The frozen Gaussian approximation provides a highly efficient computational method for highfrequency wave propagation. The derivation of the method is based on asymptotic analysis. In this paper, for general linear strictly ... 
Convergence of PhaseField Free Energy and Boundary Force for Molecular Solvation
Dai, S; Li, B; Lu, J (20170423)We study a phasefield variational model for the solvaiton of charged molecules with an implicit solvent. The solvation freeenergy functional of all phase fields consists of the surface energy, solute excluded volume and ... 
Crystal image analysis using 2D synchrosqueezed transforms
Yang, H; Lu, J; Ying, L (Multiscale Modeling and Simulation, 20150101)© 2015 Society for Industrial and Applied Mathematics.We propose efficient algorithms based on a bandlimited version of 2D synchrosqueezed transforms to extract mesoscopic and microscopic information from atomic crystal ... 
Cubic scaling algorithms for RPA correlation using interpolative separable density fitting
Lu, J; Thicke, K (20170423)We present a new cubic scaling algorithm for the calculation of the RPA correlation energy. Our scheme splits up the dependence between the occupied and virtual orbitals in $\chi^0$ by use of Cauchy's integral formula. ... 
Effective Maxwell equations from timedependent density functional theory
Weinan, E; Lu, J; Yang, X (Acta Mathematica Sinica, English Series, 20110120)The behavior of interacting electrons in a perfect crystal under macroscopic external electric and magnetic fields is studied. Effective Maxwell equations for the macroscopic electric and magnetic fields are derived starting ... 
Fast algorithm for periodic density fitting for Bloch waves
Lu, J; Ying, L (20170423)We propose an efficient algorithm for density fitting of Bloch waves for Hamiltonian operators with periodic potential. The algorithm is based on column selection and random Fourier projection of the orbital functions. The ... 
Fast construction of hierarchical matrix representation from matrixvector multiplication
Lin, L; Lu, J; Ying, L (Journal of Computational Physics, 20110510)We develop a hierarchical matrix construction algorithm using matrixvector multiplications, based on the randomized singular value decomposition of lowrank matrices. The algorithm uses O(logn) applications of the matrix ... 
Fractional stochastic differential equations satisfying fluctuationdissipation theorem
Li, L; Liu, JG; Lu, J (20170423)We consider in this work stochastic differential equation (SDE) model for particles in contact with a heat bath when the memory effects are nonnegligible. As a result of the fluctuationdissipation theorem, the differential ... 
Frozen Gaussian approximation with surface hopping for mixed quantumclassical dynamics: A mathematical justification of fewest switches surface hopping algorithms
Lu, J; Zhou, Z (20170423)We develop a surface hopping algorithm based on frozen Gaussian approximation for semiclassical matrix Schr\"odinger equations, in the spirit of Tully's fewest switches surface hopping method. The algorithm is asymptotically ...