25 citations · 71 across the 13 of their papers we have counts for
14 papers
Analysis of a dislocation model for earthquakes
Jing Liu, Xin Yang Lu, Noel J Walkington
Approximation of problems in linear elasticity having small shear modulus in a thin region is considered. Problems of this type arise when modeling ground motion due to earthquakes…
Stability and Convergence of HDG Schemes under Minimal Regularity
Jiannan Jiang, Noel J. Walkington, Yukun Yue
Convergence and compactness properties of approximate solutions to elliptic partial differential computed with the hybridized discontinuous Galerkin (HDG) are established. While it…
Spectral Clustering on Large Datasets: When Does it Work? Theory from Continuous Clustering and Density Cheeger-Buser
Timothy Chu, Gary Miller, Noel Walkington
Spectral clustering is one of the most popular clustering algorithms that has stood the test of time. It is simple to describe, can be implemented using standard linear algebra, an…
A new reduced order model of linear parabolic PDEs
Noel Walkington, Franziska Weber, Yangwen Zhang
How to build an accurate reduced order model (ROM) for multidimensional time dependent partial differential equations (PDEs) is quite open. In this paper, we propose a new ROM for…
Energetic Formulation of Large-Deformation Poroelasticity
Mina Karimi, Mehrdad Massoudi, Noel Walkington +2
The modeling of coupled fluid transport and deformation in a porous medium is essential to predict the various geomechanical process such as CO2 sequestration, hydraulic fracturing…
Surface Growth in Deformable Solids using an Eulerian Formulation
S. Kiana Naghibzadeh, Noel Walkington, Kaushik Dayal
Accretion and ablation, i.e. the addition and removal of mass at the surface, is important in a wide range of physical processes including solidification, growth of biological tiss…
Weighted Cheeger and Buser Inequalities, with Applications to Clustering and Cutting Probability Densities
Timothy Chu, Gary L. Miller, Noel J. Walkington +1
In this paper, we show how sparse or isoperimetric cuts of a probability density function relate to Cheeger cuts of its principal eigenfunction, for appropriate definitions of `spa…
Numerical Approximation of Nonlinear SPDE's
Martin Ondrejat, Andreas Prohl, Noel Walkington
The numerical analysis of stochastic parabolic partial differential equations of the form is surveyed, where is a partial operator and a…
Hardy-Muckenhoupt Bounds for Laplacian Eigenvalues
Gary L. Miller, Noel J. Walkington, Alex L. Wang
We present two graph quantities Psi(G,S) and Psi_2(G) which give constant factor estimates to the Dirichlet and Neumann eigenvalues, lambda(G,S) and lambda_2(G), respectively. Our…
Computational modeling of tactoid dynamics in chromonic liquid crystals
Chiqun Zhang, Amit Acharya, Noel J. Walkington +1
Motivated by recent experiments, the isotropic-nematic phase transition in chromonic liquid crystals is studied. As temperature decreases, nematic nuclei nucleate, grow, and coales…
Q-tensor model for electrokinetics in nematic liquid crystals
Oleh M. Tovkach, Christopher Conklin, M. Carme Calderer +4
We use a variational principle to derive a mathematical model for a nematic electrolyte in which the liquid crystalline component is described in terms of a second-rank order tenso…
Electro-osmosis in nematic liquid crystals
O. M. Tovkach, M. Carme Calderer, Dmitry Golovaty +2
We derive a mathematical model of a nematic electrolyte based on a variational formulation of nematodynamics. Extending our previous work, we consider a general setup which incorpo…
A non-traditional view on the modeling of nematic disclination dynamics
Chiqun Zhang, Xiaohan Zhang, Amit Acharya +2
Nonsingular disclination dynamics in a uniaxial nematic liquid crystal is modeled within a mathematical framework where the kinematics is a direct extension of the classical way of…
Modeling of nematic electrolyte and nonlinear electroosmosis
M. Carme Calderer, Dmitry Golovaty, Oleg Lavrentovich +1
We derive a mathematical model of a nematic electrolyte based on the Leslie-Ericksen theory of liquid crystal flow. Our goal is to investigate the nonlinear electrokinetic effects…