NDLI: Symmetry, shape, and order

Content Provider	PubMed Central
Author	Trovato, Antonio Hoang, Trinh Xuan Banavar, Jayanth R. Amos, Maritan
Copyright Year	2007
Abstract	Packing problems have been of great interest in many diverse contexts for many centuries. The optimal packing of identical objects has been often invoked to understand the nature of low-temperature phases of matter. In celebrated work, Kepler conjectured that the densest packing of spheres is realized by stacking variants of the face-centered-cubic lattice and has a packing fraction of π / ( 3 2 ) ∼ 0.7405 . Much more recently, an unusually high-density packing of ≈0.770732 was achieved for congruent ellipsoids. Such studies are relevant for understanding the structure of crystals, glasses, the storage and jamming of granular materials, ceramics, and the assembly of viral capsid structures. Here, we carry out analytical studies of the stacking of close-packed planar layers of systems made up of truncated cones possessing uniaxial symmetry. We present examples of high-density packing whose order is characterized by a broken symmetry arising from the shape of the constituent objects. We find a biaxial arrangement of solid cones with a packing fraction of π/4. For truncated cones, there are two distinct regimes, characterized by different packing arrangements, depending on the ratio c of the base radii of the truncated cones with a transition at c * = 2 − 1 .
Related Links	http://dx.doi.org/10.1073/pnas.0707523104
Starting Page	19187
File Format	PDF
ISSN	10916490
e-ISSN	10916490
Journal	Proceedings of the National Academy of Sciences of the United States of America
Issue Number	49
Volume Number	104
Language	English
Publisher	National Academy of Sciences
Publisher Date	2007-12-04
Access Restriction	Open
Rights Holder	National Academy of Sciences
Subject Keyword	Research in Higher Education
Content Type	Text
Resource Type	Article
Subject	Multidisciplinary

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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