Browsing by Author "0598771"
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A convergent method for linear halfspace kinetic equations
Li, Q; Lu, Jianfeng; 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 main ... 
A Diabatic Surface Hopping Algorithm based on Time Dependent Perturbation Theory and Semiclassical Analysis
Fang, D; Lu, Jianfeng (20171130)Surface hopping algorithms are popular tools to study dynamics of the quantumclassical mixed systems. In this paper, we propose a surface hopping algorithm in diabatic representations, based on time dependent perturbation ... 
A Hybrid Globallocal Numerical Method for Multiscale PDEs
Huang, Y; Lu, Jianfeng; 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, Jianfeng; 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 Quantum Kinetic Monte Carlo Method for Quantum Manybody Spin Dynamics
Cai, Zhenning; Lu, Jianfeng (20171130)We propose a general framework of quantum kinetic Monte Carlo algorithm, based on a stochastic representation of a series expansion of the quantum evolution. Two approaches have been developed in the context of quantum manybody ... 
A quasinonlocal coupling method for nonlocal and local diffusion models
Du, Q; Li, XH; Lu, Jianfeng; 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, Zhenning; Lu, Jianfeng (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, Jianfeng; 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 first ... 
A variational perspective on cloaking by anomalous localized resonance
Kohn, RV; Lu, Jianfeng; Schweizer, B; Weinstein, Michael I (Communications in Mathematical Physics, 20140314)© SpringerVerlag Berlin Heidelberg 2014.A body of literature has developed concerning “cloaking by anomalous localized resonance.” The mathematical heart of the matter involves the behavior of a divergenceform elliptic ... 
Accelerated sampling by infinite swapping of path integral molecular dynamics with surface hopping
Lu, Jianfeng; Zhou, Zhennan (20171130)To accelerate the thermal equilibrium sampling of multilevel quantum systems, the infinite swapping limit of a recently proposed multilevel ring polymer representation is investigated. In the infinite swapping limiting, ... 
Adaptive local basis set for KohnSham density functional theory in a discontinuous Galerkin framework I: Total energy calculation
Lin, L; Lu, Jianfeng; Ying, L; Weinan, E (Journal of Computational Physics, 20120220)KohnSham density functional theory is one of the most widely used electronic structure theories. In the pseudopotential framework, uniform discretization of the KohnSham Hamiltonian generally results in a large number ... 
An asymptotic preserving method for transport equations with oscillatory scattering coefficients
Li, Q; Lu, Jianfeng (20170426)We design a numerical scheme for transport equations with oscillatory periodic scattering coefficients. The scheme is asymptotic preserving in the diffusion limit as Knudsen number goes to zero. It also captures ... 
An isoperimetric problem with Coulomb repulsion and attraction to a background nucleus
Lu, Jianfeng; 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 ... 
Analysis of the divideandconquer method for electronic structure calculations
Chen, J; Lu, Jianfeng (20170426)We study the accuracy of the divideandconquer method for electronic structure calculations. The analysis is conducted for a prototypical subdomain problem in the method. We prove that the pointwise difference between electron ... 
Analysis of time reversible bornoppenheimer molecular dynamics
Lin, L; Lu, Jianfeng; Shao, S (Entropy, 20140101)We analyze the time reversible BornOppenheimer molecular dynamics (TRBOMD) scheme, which preserves the time reversibility of the BornOppenheimer molecular dynamics even with nonconvergent selfconsistent field iteration. ... 
Asymmetry in crystal facet dynamics of homoepitaxy by a continuum model
Liu, JG; Lu, Jianfeng; Margetis, D; Marzuola, Jeremy (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, Jianfeng; Zhou, Zhennan (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 ... 
Bold Diagrammatic Monte Carlo in the Lens of Stochastic Iterative Methods
Li, Yingzhou; Lu, Jianfeng (20171130)This work aims at understanding of bold diagrammatic Monte Carlo (BDMC) methods for stochastic summation of Feynman diagrams from the angle of stochastic iterative methods. The convergence enhancement trick of the BDMC is ... 
ButterflyNet: Optimal Function Representation Based on Convolutional Neural Networks
Li, Yingzhou; Lu, Jianfeng; Cheng, XiuyuanDeep networks, especially Convolutional Neural Networks (CNNs), have been successfully applied in various areas of machine learning as well as to challenging problems in other scientific and engineering fields. ... 
Capturing and Manipulating Activated Neuronal Ensembles with CANE Delineates a Hypothalamic SocialFear Circuit
Fu, M; Han, BX; Leavitt, AD; Lu, Jianfeng; Rodriguez, E; Sakurai, K; Takatoh, J; ... (9 authors) (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 high ...