6 papers
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…
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…
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…