Laplacian networks: Growth, local symmetry, and shape optimization
Name
PhysRevE.95.033113.pdf
Size
1.04 MB
Format
Adobe PDF
Checksum (MD5)
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Author(s)
Devauchelle, O.
Szymczak, P.
Pecelerowicz, M.
Seybold, H. J.
Cohen, Yosef
Rothman, Daniel H.
Date Issued
March 2017
Journal
Physical Review E
Publisher
American Physical Society
Citation
Devauchelle, O. et al. “Laplacian Networks: Growth, Local Symmetry, and Shape Optimization.” Physical Review E 95.3 (2017): n. pag. © 2017 American Physical Society
Version
Final published version
Abstract
Inspired by river networks and other structures formed by Laplacian growth, we use the Loewner equation to investigate the growth of a network of thin fingers in a diffusion field. We first review previous contributions to illustrate how this formalism reduces the network's expansion to three rules, which respectively govern the velocity, the direction, and the nucleation of its growing branches. This framework allows us to establish the mathematical equivalence between three formulations of the direction rule, namely geodesic growth, growth that maintains local symmetry, and growth that maximizes flux into tips for a given amount of growth. Surprisingly, we find that this growth rule may result in a network different from the static configuration that optimizes flux into tips.
MIT Department
Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences
Lorenz Center (Massachusetts Institute of Technology)
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DOI of Published Version
https://doi.org/10.1103/PhysRevE.95.033113
