https://github.com/mrp01/dissertation

My MMSC dissertation on general kernel spectral methods for equilibrium measures
https://github.com/mrp01/dissertation

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My MMSC dissertation on general kernel spectral methods for equilibrium measures

• Host: GitHub
• URL: https://github.com/mrp01/dissertation
• Owner: MrP01
• Created: 2023-03-16T23:00:13.000Z (almost 2 years ago)
• Default Branch: master
• Last Pushed: 2024-01-11T10:28:44.000Z (12 months ago)
• Last Synced: 2024-04-16T03:20:34.579Z (9 months ago)
• Language: PostScript
• Size: 83.5 MB
• Stars: 1
• Watchers: 2
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • Citation: citation.cff

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README

        
# Spectral Methods for Equilibrium Measures

[![DOI](https://zenodo.org/badge/615078885.svg)](https://zenodo.org/badge/latestdoi/615078885)

My MMSC dissertation on general kernel spectral methods for equilibrium measures.

👉 The document itself can be found [here](https://raw.githubusercontent.com/MrP01/Dissertation/master/thesis/thesis.pdf)!

Attractive-repulsive equilibrium measure problems appear in the modeling of the continuous limit of

pair-interacting particle systems, e.g. models of animal swarms or classical physical particulates.

From a computing point of view they are a combination of integral equation and minimization problem

– the aim is to find a density u(x) for a given kernel K such that the following energy is minimized.

The project would leverage kernel expansions to construct a general equilibrium measure method on

the unit interval [−1, 1]. The d-dimensional unit ball generalization is then expected to be straightforward

and can be considered as a stretch goal. Comparisons should be made with the corresponding

attractive-repulsive finite particle swarm problems.