196 citations · 1.6k across the 143 of their papers we have counts for
20 papers · 1 filter
A Regularity Theory for Static Schrödinger Equations on in Spectral Barron Spaces
Ziang Chen, Jianfeng Lu, Yulong Lu +1
Spectral Barron spaces have received considerable interest recently as it is the natural function space for approximation theory of two-layer neural networks with a dimension-free…
Optimal artificial boundary conditions based on second-order correctors for three dimensional random elliptic media
Jianfeng Lu, Felix Otto, Lihan Wang
We are interested in numerical algorithms for computing the electrical field generated by a charge distribution localized on scale in an infinite heterogeneous medium, in a…
Defect resonances of truncated crystal structures
Jianfeng Lu, Jeremy L. Marzuola, Alexander B. Watson
Defects in the atomic structure of crystalline materials may spawn electronic bound states, known as \emph{defect states}, which decay rapidly away from the defect. Simplified mode…
Analysis of a fourth order exponential PDE arising from a crystal surface jump process with Metropolis-type transition rates
Yuan Gao, Anya E. Katsevich, Jian-Guo Liu +2
We analytically and numerically study a fourth order PDE modeling rough crystal surface diffusion on the macroscopic level. We discuss existence of solutions globally in time and l…
Optimal Trapping of Brownian Motion: A Nonlinear Analogue of the Torsion Function
Jianfeng Lu, Stefan Steinerberger
We study the problem of maximizing the expected lifetime of drift diffusion in a bounded domain. More formally, we consider the PDE \[ - Δu + b(x) \cdot \nabla u = 1 \qquad \mbox{i…
On explicit -convergence rate estimate for underdamped Langevin dynamics
Yu Cao, Jianfeng Lu, Lihan Wang
We provide a refined explicit estimate of exponential decay rate of underdamped Langevin dynamics in distance, based on a framework developed in [1]. To achieve this, we firs…
Analysis of a continuum theory for broken bond crystal surface models with evaporation and deposition effects
Yuan Gao, Jian-Guo Liu, Jianfeng Lu +1
We study a th order PDE with a nd order correction that is a modification of one suggested by Peter Smereka using the tools of Krug et al (Z. Phys. B., 1994). First, we provi…
Approximating Pointwise Products of Laplacian Eigenfunctions
Jianfeng Lu, Christopher D. Sogge, Stefan Steinerberger
We consider Laplacian eigenfunctions on a dimensional bounded domain (or a dimensional compact manifold ) with Dirichlet conditions. These operators give rise to a s…
Dirac operators and domain walls
Jianfeng Lu, Alexander B. Watson, Michael I. Weinstein
We study the eigenvalue problem for a one-dimensional Dirac operator with a spatially varying ``mass'' term. It is well-known that when the mass function has the form of a kink, or…
Exponential decay of Rényi divergence under Fokker-Planck equations
Yu Cao, Jianfeng Lu, Yulong Lu
We prove the exponential convergence to the equilibrium, quantified by Rényi divergence, of the solution of the Fokker-Planck equation with drift given by the gradient of a strictl…
Scaling limit of the Stein variational gradient descent: the mean field regime
Jianfeng Lu, Yulong Lu, James Nolen
We study an interacting particle system in motivated by Stein variational gradient descent [Q. Liu and D. Wang, NIPS 2016], a deterministic algorithm for sampling fr…
Learning interacting particle systems: diffusion parameter estimation for aggregation equations
Hui Huang, Jian-Guo Liu, Jianfeng Lu
In this article, we study the parameter estimation of interacting particle systems subject to the Newtonian aggregation and Brownian diffusion. Specifically, we construct an estima…
Weak solution of a continuum model for vicinal surface in the attachment-detachment-limited regime
Yuan Gao, Jian-Guo Liu, Jianfeng Lu
We study in this work a continuum model derived from 1D attachment-detachment-limited (ADL) type step flow on vicinal surface, , where , considered as a f…
Convergence of Phase-Field Free Energy and Boundary Force for Molecular Solvation
Shibin Dai, Bo Li, Jianfeng Lu
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 s…
Continuum limit of a mesoscopic model with elasticity of step motion on vicinal surfaces
Yuan Gao, Jian-Guo Liu, Jianfeng Lu
This work considers the rigorous derivation of continuum models of step motion starting from a mesoscopic Burton-Cabrera-Frank (BCF) type model following the work [Xiang, SIAM J. A…
Validity and regularization of classical half-space equations
Qin Li, Jianfeng Lu, Weiran Sun
Recent result [Wu and Guo, Comm. Math. Phys., 2015] has shown that over the 2D unit disk, the classical half-space equation (CHS) for the neutron transport does not capture the cor…
Bloch dynamics with second order Berry phase correction
Jianfeng Lu, Zihang Zhang, Zhennan Zhou
We derive the semiclassical Bloch dynamics with the second-order Berry phase correction in the presence of the slow-varying scalar potential as perturbation. Our mathematical deriv…
An isoperimetric problem with Coulomb repulsion and attraction to a background nucleus
Jianfeng Lu, Felix Otto
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 a…
A convergent method for linear half-space kinetic equations
Qin Li, Jianfeng Lu, Weiran Sun
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…
A variational perspective on cloaking by anomalous localized resonance
Robert V. Kohn, Jianfeng Lu, Ben Schweizer +1
A body of literature has developed concerning "cloaking by anomalous localized resonance". The mathematical heart of the matter involves the behavior of a divergence-form elliptic…