Laplacian networks: Growth, local symmetry, and shape optimization
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 r...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2017
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| Online Access: | http://hdl.handle.net/1721.1/107752 https://orcid.org/0000-0002-7997-0119 https://orcid.org/0000-0003-4006-7771 |
| _version_ | 1826212023484022784 |
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| author | Devauchelle, O. Szymczak, P. Pecelerowicz, M. Seybold, H. J. Cohen, Yosef Rothman, Daniel H. |
| author2 | Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences |
| author_facet | Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences Devauchelle, O. Szymczak, P. Pecelerowicz, M. Seybold, H. J. Cohen, Yosef Rothman, Daniel H. |
| author_sort | Devauchelle, O. |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T15:14:56Z |
| format | Article |
| id | mit-1721.1/107752 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T15:14:56Z |
| publishDate | 2017 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/1077522022-09-29T13:39:52Z Laplacian networks: Growth, local symmetry, and shape optimization Devauchelle, O. Szymczak, P. Pecelerowicz, M. Seybold, H. J. Cohen, Yosef Rothman, Daniel H. Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences Lorenz Center (Massachusetts Institute of Technology) Cohen, Yosef Rothman, Daniel H 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. Poland. National Science Centre (Grant 2012/07/E/ST3/01734) Paris (France). Mairie. Emergence(s) Program United States. Dept. of Energy. Office of Basic Energy Sciences. Chemical Sciences, Geosciences, & Biosciences Division (Award FG02-99ER15004) 2017-03-28T15:34:05Z 2017-03-28T15:34:05Z 2017-03 2017-01 2017-03-24T22:00:07Z Article http://purl.org/eprint/type/JournalArticle 2470-0045 2470-0053 http://hdl.handle.net/1721.1/107752 Devauchelle, O. et al. “Laplacian Networks: Growth, Local Symmetry, and Shape Optimization.” Physical Review E 95.3 (2017): n. pag. © 2017 American Physical Society https://orcid.org/0000-0002-7997-0119 https://orcid.org/0000-0003-4006-7771 en http://dx.doi.org/10.1103/PhysRevE.95.033113 Physical Review E Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. American Physical Society application/pdf American Physical Society American Physical Society |
| spellingShingle | Devauchelle, O. Szymczak, P. Pecelerowicz, M. Seybold, H. J. Cohen, Yosef Rothman, Daniel H. Laplacian networks: Growth, local symmetry, and shape optimization |
| title | Laplacian networks: Growth, local symmetry, and shape optimization |
| title_full | Laplacian networks: Growth, local symmetry, and shape optimization |
| title_fullStr | Laplacian networks: Growth, local symmetry, and shape optimization |
| title_full_unstemmed | Laplacian networks: Growth, local symmetry, and shape optimization |
| title_short | Laplacian networks: Growth, local symmetry, and shape optimization |
| title_sort | laplacian networks growth local symmetry and shape optimization |
| url | http://hdl.handle.net/1721.1/107752 https://orcid.org/0000-0002-7997-0119 https://orcid.org/0000-0003-4006-7771 |
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