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Higher Dimensional Lattices

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Coherent Structures in Granular Crystals

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Abstract

Two-dimensional granular crystals have been investigated far less than 1D configurations. In two spatial dimensions, the nodes can be arranged in a number of ways. While the role of disorder is of particular interest for engineering applications (Behringer RP (2015) Jamming in granular materials. C R Phys 16:10 [1], Liu A, Nagel SR (2010) The jamming transition and the marginally jammed solid. Annu Rev Cond Matter Phys 1:347 [2]) we will focus on ordered configurations, such as hexagonal (see Figs.7.1 a,b) or square packings.

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Notes

  1. 1.

    Notice, however, that the potential presence of intruders would enable this “cross-communication” between adjacent chains, a feature that has been utilized to showcase phenomena such as energy redistribution and equipartition [3,4,5].

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Authors and Affiliations

  1. Bowdoin College, Brunswick, ME, USA

    Christopher Chong

  2. University of Massachusetts, Amherst, MA, USA

    Panayotis G. Kevrekidis

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  1. Christopher Chong
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  2. Panayotis G. Kevrekidis
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Correspondence to Christopher Chong .

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Chong, C., Kevrekidis, P.G. (2018). Higher Dimensional Lattices. In: Coherent Structures in Granular Crystals. SpringerBriefs in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-77884-6_7

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