A thrust to trust minimum thrust

TL;DR

This paper investigates the minimum thrust required for N-particle configurations across various dimensions, providing exact results for N=5 in three dimensions and numerical estimates for larger N using optimization and statistical analysis.

Contribution

It presents the first exact minimum thrust result for N=5 in three dimensions and introduces numerical and statistical methods for larger N configurations.

Findings

Exact minimum thrust for N=5 in 3D

Numerical estimates for larger N

Application of Extreme Value Theory to analyze results

Abstract

We determine the minimum value of thrust for a number of N-particle configurations. For N=5 in three dimensions an exact result is found for the first time. For larger N we obtain numerical results through optimisation. When a definite value cannot be reliably identified, the results are analysed in the context of Extreme Value Theory, using a Maximum Likelihood Estimate and a Bayesian analysis. Results are given for three spatial dimensions, two dimensions, and selected cases in d dimensions.