Dimensional analysis using toric ideals
Data Analysis, Statistics and Probability
2013-04-25 v1 Commutative Algebra
Abstract
Classical dimensional analysis is one of the cornerstones of qualitative physics and is also used in the analysis of engineering systems, for example in engineering design. The basic power product relationship in dimensional analysis is identical to one way of defining toric ideals in algebraic geometry, a large and growing field. This paper exploits the toric representation to provide a method for automatic dimensional analysis for engineering systems. In particular all "primitive", invariants for a particular problem, in a well defined sense, can be found using such methods.
Cite
@article{arxiv.1304.6659,
title = {Dimensional analysis using toric ideals},
author = {M. A. Atherton and R. A. Bates and H. P. Wynn},
journal= {arXiv preprint arXiv:1304.6659},
year = {2013}
}
Comments
13 pages. Article under review: Journal of the Franklin Institute