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  • Open Access

E2 and gamma distributions in polygonal networks

Ran Li1, Consuelo Ibar2, Zhenru Zhou2, Seyedsajad Moazzeni1, Andrew N. Norris1, Kenneth D. Irvine2,*, Liping Liu1,3,†, and Hao Lin1,‡

  • 1Department of Mechanical and Aerospace Engineering, Rutgers, The State University of New Jersey, New Brunswick, New Jersey 08901, USA
  • 2Waksman Institute and Department of Molecular Biology and Biochemistry, Rutgers, The State University of New Jersey, New Brunswick, New Jersey 08901, USA
  • 3Department of Mathematics, Rutgers, The State University of New Jersey, New Brunswick, New Jersey 08901, USA

  • *Corresponding author: irvine@waksman.rutgers.edu
  • †Corresponding author: liu.liping@rutgers.edu
  • ‡Corresponding author: hlin@soe.rutgers.edu
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Phys. Rev. Research 3, L042001 – Published 5 October, 2021

DOI: https://doi.org/10.1103/PhysRevResearch.3.L042001

Abstract

From solar supergranulation to salt flats in Bolivia, from veins on leaves to cells on Drosophila wing disks, polygon-based networks exhibit great complexities, yet similarities and consistent patterns emerge. Based on analysis of 99 polygonal tessellations with a wide variety of physical origins, this work demonstrates the ubiquity of an exponential distribution in the squared norm of the deformation tensor E2, which directly leads to the ubiquitous presence of gamma distributions in the polygon aspect ratio, as recently demonstrated by Atia et al. [Nat. Phys. 14, 613 (2018)]. In turn an analytical approach is developed to illustrate its origin. E2 relates to most energy forms, and its Boltzmann-like feature allows the definition of a pseudotemperature that promises utility in a thermodynamic ensemble framework.

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Phys. Rev. Research 3, L042001– Published 5 October, 2021
  • Received 12 December 2020
  • Accepted 22 July 2021
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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