Jamming and Tiling in Aggregation of Rectangles

Ben-Naim, Daniel S; Ben-Naim, Eli; Krapivsky, Paul L

doi:10.1088/1751-8121/aae4c0

Title: Jamming and Tiling in Aggregation of Rectangles

Journal Article · 15 October 2018 · Journal of Physics. A, Mathematical and Theoretical

DOI: https://doi.org/10.1088/1751-8121/aae4c0 · OSTI ID:1492668

Ben-Naim, Daniel S ^[1];

^[2]; Krapivsky, Paul L ^[3]

Univ. of California, Santa Barbara, CA (United States). Dept. of Computer Science
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Boston Univ., MA (United States). Dept. of Physics

We study a random aggregation process involving rectangular clusters. In each aggregation event, two rectangles are chosen at random and if they have a compatible side, either vertical or horizontal, they merge along that side to form a larger rectangle. Starting with N identical squares, this elementary event is repeated until the system reaches a jammed state where each rectangle has two unique sides. The average number of frozen rectangles scales as N^α in the large-N limit. The growth exponent α = 0.229 ± 0.002 characterizes statistical properties of the jammed state and the time-dependent evolution. We also study an aggregation process where rectangles are embedded in a plane and interact only with nearest neighbors. In the jammed state, neighboring rectangles are incompatible, and these frozen rectangles form a tiling of the two-dimensional domain. Here in this case, the final number of rectangles scales linearly with system size.

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Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 1492668

Report Number(s):: LA-UR-18-26798

Journal Information:: Journal of Physics. A, Mathematical and Theoretical, Journal Name: Journal of Physics. A, Mathematical and Theoretical Journal Issue: 45 Vol. 51; ISSN 1751-8113

Publisher:: IOP PublishingCopyright Statement

Country of Publication:: United States

Language:: English

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Jamming and tiling in fragmentation of rectangles Ben-Naim, E.; Krapivsky, P. L. Physical Review E, Vol. 100, Issue 3 https://doi.org/10.1103/physreve.100.032122	journal	September 2019

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