36 citations · 79 across the 14 of their papers we have counts for
16 papers
Numerical stability revisited: A family of benchmark problems for the analysis of explicit stochastic differential equation integrators
Thomas Hudson, Sarah Helfert, Xingjie Helen Li
We revisit the numerical stability of four well-established explicit stochastic integration schemes through a new generic benchmark stochastic differential equation designed to ass…
A Comprehensive Study of Covid 19 in Florida
Julian Bennett, Lauren Eriksen, Xingjie Helen Li
Within the likes of any highly contagious and unpredictable disease, lies a predictable and attainable growth rate that researchers can find in order to make logistical conclusions…
Automated construction of effective potential via algorithmic implicit bias
Xingjie Helen Li, Molei Tao
We introduce a novel approach for decomposing and learning every scale of a given multiscale objective function in , where . This approach leverages a recentl…
A One-Dimensional Symmetric Force-Based Blending Method for Atomistic-to-Continuum Coupling
Elaine Gorom-Alexander, Xingjie Helen Li
Inspired by the blending method developed by [P. Seleson, S. Beneddine, and S. Prudhome, \emph{A Force-Based Coupling Scheme for Peridynamics and Classical Elasticity}, (2013)] for…
Dynamical properties of coarse-grained linear SDEs
Thomas Hudson, Xingjie Helen Li
Coarse-graining or model reduction is a term describing a range of approaches used to extend the time-scale of molecular simulations by reducing the number of degrees of freedom. I…
Coarse-graining of overdamped Langevin dynamics via the Mori-Zwanzig formalism
Thomas Hudson, Xingjie Helen Li
The Mori-Zwanzig formalism is applied to derive an equation for the evolution of linear observables of the overdamped Langevin equation. To illustrate the resulting equation and it…
A quasinonlocal coupling method for nonlocal and local diffusion models
Qiang Du, Xingjie Helen Li, Jianfeng Lu +1
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…
Quasinonlocal coupling of nonlocal diffusions
Xingjie Helen Li, Jianfeng Lu
We developed a new self-adjoint, consistent, and stable coupling strategy for nonlocal diffusion models, inspired by the quasinonlocal atomistic-to-continuum method for crystalline…
Analysis of Blended Atomistic/Continuum Hybrid Methods
Xingjie Helen Li, Christoph Ortner, Alexander V. Shapeev +1
We present a comprehensive error analysis of two prototypical atomistic-to-continuum coupling methods of blending type: the energy-based and the force-based quasicontinuum methods.…
Numerical solution of Dyson Brownian motion and a sampling scheme for invariant matrix ensembles
Xingjie Helen Li, Govind Menon
The Dyson Brownian Motion (DBM) describes the stochastic evolution of points on the line driven by an applied potential, a Coulombic repulsion and identical, independent Browni…
Theory-based Benchmarking of the Blended Force-Based Quasicontinuum Method
Xingjie Helen Li, Mitchell Luskin, Christoph Ortner +1
We formulate an atomistic-to-continuum coupling method based on blending atomistic and continuum forces. Our precise choice of blending mechanism is informed by theoretical predict…
Positive-Definiteness of the Blended Force-Based Quasicontinuum Method
Xingjie Helen Li, Mitchell Luskin, Christoph Ortner
The development of consistent and stable quasicontinuum models for multi-dimensional crystalline solids remains a challenge. For example, proving stability of the force-based quasi…
Lattice Stability for Atomistic Chains Modeled by Local Approximations of the Embedded Atom Method
Xingjie Helen Li, Mitchell Luskin
The accurate approximation of critical strains for lattice instability is a key criterion for predictive computational modeling of materials. In this paper, we present a comparison…
A Computational and Theoretical Investigation of the Accuracy of Quasicontinuum Methods
Brian Van Koten, Xingjie Helen Li, Mitchell Luskin +1
We give computational results to study the accuracy of several quasicontinuum methods for two benchmark problems - the stability of a Lomer dislocation pair under shear and the sta…
An Analysis of the Quasi-Nonlocal Quasicontinuum Approximation of the Embedded Atom Model
Xingjie Helen Li, Mitchell Luskin
The quasi-nonlocal quasicontinuum method (QNL) is a consistent hybrid coupling method for atomistic and continuum models. Embedded atom models are empirical many-body potentials th…
A Generalized Quasi-Nonlocal Atomistic-to-Continuum Coupling Method with Finite Range Interaction
Xingjie Helen Li, Mitchell Luskin
The accurate and efficient computation of the deformation of crystalline solids requires the coupling of atomistic models near lattice defects such as cracks and dislocations with…