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    A convergent method for linear half-space kinetic equations 

    Li, Q; Lu, Jianfeng; Sun, W (2017-04-23)
    We give a unified proof for the well-posedness of a class of linear half-space equations with general incoming data and construct a Galerkin method to numerically resolve this type of equations in a systematic way. Our main ...
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    Asymmetry in crystal facet dynamics of homoepitaxy by a continuum model 

    Liu, J-G; Lu, Jianfeng; Margetis, D; Marzuola, Jeremy (2017-04-23)
    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 ...
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    Weak solution of a continuum model for vicinal surface in the attachment-detachment-limited regime 

    Gao, Y; Liu, J-G; Lu, Jianfeng (2017-04-23)
    We study in this work a continuum model derived from 1D attachment-detachment-limited (ADL) type step flow on vicinal surface, $ u_t=-u^2(u^3)_{hhhh}$, where $u$, considered as a function of step height $h$, is the step ...
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    Learning interacting particle systems: diffusion parameter estimation for aggregation equations 

    Huang, H; Liu, J-G; Lu, Jianfeng (2018-02-14)
    In this article, we study the parameter estimation of interacting particle systems subject to the Newtonian aggregation. Specifically, we construct an estimator $\widehat{\nu}$ with partial observed data to approximate the ...
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    Bloch dynamics with second order Berry phase correction 

    Lu, Jianfeng; Zhou, Zhennan (2017-04-23)
    We derive the semiclassical Bloch dynamics with the second order Berry phase correction, based on a two-scale WKB asymptotic analysis. For uniform external electric field, the bi-characteristics system after a positional ...
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    A Variation on the Donsker-Varadhan Inequality for the Principial Eigenvalue 

    Lu, Jianfeng; Steinerberger, S (2017-04-23)
    The purpose of this short note 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 $\Omega$ by the largest mean first ...
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    An isoperimetric problem with Coulomb repulsion and attraction to a background nucleus 

    Lu, Jianfeng; Otto, F (2017-04-23)
    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 ...
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    Convergence of Phase-Field Free Energy and Boundary Force for Molecular Solvation 

    Dai, Shibin; Li, B; Lu, Jianfeng (2017-04-23)
    We study a phase-field variational model for the solvaiton of charged molecules with an implicit solvent. The solvation free-energy functional of all phase fields consists of the surface energy, solute excluded volume and ...
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    Wavepackets in inhomogeneous periodic media: effective particle-field dynamics and Berry curvature 

    Lu, Jianfeng; Watson, AB; Weinstein, Michael I (2017-04-23)
    We consider a model of an electron in a crystal moving under the influence of an external electric field: Schr\"{o}dinger's equation with a potential which is the sum of a periodic function and a general smooth function. ...
     

     

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    Lu, Jianfeng (9)
    Liu, J-G (3)Dai, Shibin (1)Gao, Y (1)Huang, H (1)Li, B (1)Li, Q (1)Margetis, D (1)Marzuola, Jeremy (1)Otto, F (1)... View MoreDate Issued2017 (8)2018 (1)TypeJournal article (9)Subject
    math.AP (9)
    math-ph (3)math.MP (3)math.PR (2)74H05, 37N15 (1)cond-mat.mes-hall (1)cond-mat.mtrl-sci (1)cond-mat.stat-mech (1)math.NA (1)math.SP (1)... View MoreAffiliation of Duke Author(s)Chemistry (9)
    Duke (9)
    Mathematics (9)Physics (9)Trinity College of Arts & Sciences (9)