Mcknight Presidential Professor Douglas Arnold

CSENG Mathematics, School of
College of Science & Engineering
Twin Cities
Project Title: 
Computational Study of Eigenvalue Localization and Numerical Relativity

These researchers continue to work as part of an interdisciplinary group of mathematicians and physicists on understanding Anderson localization, or, more generally, the localization of eigenfunctions of elliptic operators by disorder. This phenomenon, which is of great significance in many applications (such as quantum mechanics where it gives rise to a metal/insulator transition in disorded alloys), is famously difficult to explain, predict, and control. In the collaboration, this group handles all the computation, which is driving the collaboration. They have developed algorithms to predict both the localization regions of eigenfunctions and the values of ground states without the need to solve any eigenvalue problems!  Some of this work has been submitted and other studies and publications are underway. Certain aspects of this research require looking at very fine scale disorder in 2D, and possibly in 3D, for which the use of Mesabi and Itasca have been extremely valuable. Recent work has resulted in the development of a finite element implementation Regge calculus, a method of approximation of Einstein's equations by piecewise constant metrics, as well as extensions of it to higher degree finite elements; MSI resources will be used to study its performance.

Project Investigators

Mcknight Presidential Professor Douglas Arnold
Kaibo Hu
Tyson Loudon
Brian Shi
Kaisa Taipale
 
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