تقرير
E2 distribution and statistical regularity in polygonal planar tessellations
| العنوان: | E2 distribution and statistical regularity in polygonal planar tessellations |
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| المؤلفون: | Li, Ran, Ibar, Consuelo, Zhou, Zhenru, Moazzeni, Seyedsajad, Irvine, Kenneth D., Liu, Liping, Lin, Hao |
| المصدر: | Phys. Rev. Research 3, 042001 (2021) |
| سنة النشر: | 2020 |
| المجموعة: | Condensed Matter Physics (Other) |
| مصطلحات موضوعية: | Condensed Matter - Statistical Mechanics, Condensed Matter - Soft Condensed Matter, Physics - Biological Physics |
| الوصف: | From solar supergranulation to salt flat in Bolivia, from veins on leaves to cells on Drosophila wing discs, polygon-based networks exhibit great complexities, yet similarities persist and statistical distributions can be remarkably consistent. Based on analysis of 99 polygonal tessellations of a wide variety of physical origins, this work demonstrates the ubiquity of an exponential distribution in the squared norm of the deformation tensor, $E^{2}$, which directly leads to the ubiquitous presence of Gamma distributions in polygon aspect ratio. The $E^{2}$ distribution in turn arises as a $\chi^{2}$-distribution, and an analytical framework is developed to compute its statistics. $E^{2}$ is closely related to many energy forms, and its Boltzmann-like feature allows the definition of a pseudo-temperature. Together with normality in other key variables such as vertex displacement, this work reveals regularities universally present in all systems alike Comment: 18 pages, 4 figures |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1103/PhysRevResearch.3.L042001 |
| URL الوصول: | http://arxiv.org/abs/2002.11166 |
| رقم الأكسشن: | edsarx.2002.11166 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1103/PhysRevResearch.3.L042001 |
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