Dissertation Defense of CMSE Ashe Hicks

Department of Computational Mathematics, Science & Engineering

Michigan State University

Dissertation Defense Notice

August 16, 2024 at 9:00 AM

Room: BPS 1300

Zoom: https://msu.zoom.us/j/98756729855

Meeting ID: 987 5672 9855
Passcode: 772577

 

Algorithms for the Nuclear Many-Body Problem and Beyond

By: Ashe Hicks

Abstract:
The nuclear many body problem allows us to take our fundamental understanding of the most basic building blocks of the universe and from them build an understanding of larger and more complicated systems. It is the essential problem of how individual particles form atoms and larger structures. Its applications are varied, and many tools have been developed to address this problem. Despite the breakneck pace of computational development, the nuclear many-body problem still stretches our computational and numerical methods to and beyond their breaking points. In this work, we introduce two algorithms which can help in solving the nuclear many-body problem. First, we introduce trimmed sampling. This is an algorithm which can be used to treat noisy data obtained from highly sensitive calculations, particularly the generalized eigenvalue problem which emerges from a number of techniques. We solve a number of example models for which small errors such as rounding error or statistical noise are sufficient to entirely destroy any usable results, but see that trimmed sampling is able to recover good results from these methods. It does so using Bayesian inference, by applying physics-informed criteria and statistical sampling methods we are able to eliminate any solutions which are non-physical, leaving a more accurate, physically meaningful result. We show ways that this algorithm can be further expanded and enhanced, improving sampling statistics, convergence rate, and accuracy, before demonstrating its performance on the Lipkin model. In the next section, we describe the Projected Cooling algorithm. This is a method whereby we use an analogue of evaporative cooling to calculate the ground state of a system.  We show results of projected cooling for several models. Together, this work provides a description of useful algorithms which can be applied to the nuclear many-body problem.

 

 

Committee Members:

Dean Lee (chair)

Scott Bogner

Huey-Wen Lin

Alexei Bazavov

Andreas von Manteuffel