Non-Euclidean geometry in nature
Soft Condensed Matter
2017-05-30 v2
Abstract
I describe the manifestation of the non-Euclidean geometry in the behavior of collective observables of some complex physical systems. Specifically, I consider the formation of equilibrium shapes of plants and statistics of sparse random graphs. For these systems I discuss the following interlinked questions: (i) the optimal embedding of plants leaves in the three-dimensional space, (ii) the spectral statistics of sparse random matrix ensembles.
Keywords
Cite
@article{arxiv.1705.08013,
title = {Non-Euclidean geometry in nature},
author = {Sergei Nechaev},
journal= {arXiv preprint arXiv:1705.08013},
year = {2017}
}
Comments
52 pages, 21 figures, last section is rewritten, a reference to chaotic Hamiltonian systems is added