Calculations of the minimal perimeter for N deformable cells of equal area confined in a circle

Simon Cox

doi:10.1080/09500830600929083

Calculations of the minimal perimeter for N deformable cells of equal area confined in a circle

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Calculations of the minimal perimeter for N deformable cells of equal area confined in a circle. / Cox, Simon.

In: Philosophical Magazine Letters, Vol. 86, No. 9, 09.2006, p. 569-578.

Research output: Contribution to journal › Article › peer-review

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@article{6fe19b2a61704413bab7cd52a9a34b9e,

title = "Calculations of the minimal perimeter for N deformable cells of equal area confined in a circle",

abstract = "Candidates to the least perimeter partition of a disk into N planar connected regions are calculated for N ≤43. A Voronoi construction is used to randomly create the candidates and then the perimeter of each is found with the Surface Evolver. Formulae for the perimeter and number of peripheral regions are given, and the candidates classified according to their topology. The simulation technique also provides improved candidates to the unconstrained problem of finding the least perimeter arrangement of N planar regions.",

author = "Simon Cox",

note = "Cox, S.J. (2006) Calculations of the minimal perimeter for N deformable cells of equal area confined in a circle. Philosophical Magazine Letters. 86:569-578.",

year = "2006",

month = sep,

doi = "10.1080/09500830600929083",

language = "English",

volume = "86",

pages = "569--578",

journal = "Philosophical Magazine Letters",

issn = "0950-0839",

publisher = "Taylor & Francis",

number = "9",

}

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TY - JOUR

T1 - Calculations of the minimal perimeter for N deformable cells of equal area confined in a circle

AU - Cox, Simon

N1 - Cox, S.J. (2006) Calculations of the minimal perimeter for N deformable cells of equal area confined in a circle. Philosophical Magazine Letters. 86:569-578.

PY - 2006/9

Y1 - 2006/9

N2 - Candidates to the least perimeter partition of a disk into N planar connected regions are calculated for N ≤43. A Voronoi construction is used to randomly create the candidates and then the perimeter of each is found with the Surface Evolver. Formulae for the perimeter and number of peripheral regions are given, and the candidates classified according to their topology. The simulation technique also provides improved candidates to the unconstrained problem of finding the least perimeter arrangement of N planar regions.

AB - Candidates to the least perimeter partition of a disk into N planar connected regions are calculated for N ≤43. A Voronoi construction is used to randomly create the candidates and then the perimeter of each is found with the Surface Evolver. Formulae for the perimeter and number of peripheral regions are given, and the candidates classified according to their topology. The simulation technique also provides improved candidates to the unconstrained problem of finding the least perimeter arrangement of N planar regions.

U2 - 10.1080/09500830600929083

DO - 10.1080/09500830600929083

M3 - Article

VL - 86

SP - 569

EP - 578

JO - Philosophical Magazine Letters

JF - Philosophical Magazine Letters

SN - 0950-0839

IS - 9

ER -

IRUS-UK