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Jamming and Tiling in Aggregation of Rectangles

Journal Article · · Journal of Physics. A, Mathematical and Theoretical
 [1];  [2];  [3]
  1. Univ. of California, Santa Barbara, CA (United States). Dept. of Computer Science
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  3. Boston Univ., MA (United States). Dept. of Physics
+ Show Author Affiliations
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 Nα 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.
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
Alternate ID(s):
OSTI ID: 22986081
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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Cited By (1)

Jamming and tiling in fragmentation of rectangles journal September 2019

Figures / Tables (17)

FIG. 1(p. 2)figure FIG. 1
FIG. 2(p. 3)figure FIG. 2
TABLE I(p. 3)table TABLE I
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FIG. 12(p. 9)figure FIG. 12
FIG. 13(p. 9)figure FIG. 13
TABLE III(p. 9)table TABLE III
TABLE IV(p. 9)table TABLE IV

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Related Subjects

97 MATHEMATICS AND COMPUTING
aggregation
random processes
tiling