Uniform line fillings

Evangelos Marakis, Lars J. Corbijn Van Willenswaard, Ravitej Uppu, Pepijn W.H. Pinkse, Matthias Christiaan Velsink

Research output: Contribution to journalArticleAcademicpeer-review

2 Downloads (Pure)

Abstract

Deterministic fabrication of random metamaterials requires filling of a space with randomly oriented and randomly positioned chords with an on-average homogenous density and orientation, which is a nontrivial task. We describe a method to generate fillings with such chords, lines that run from edge to edge of the space, in any dimension. We prove that the method leads to random but on-average homogeneous and rotationally invariant fillings of circles, balls, and arbitrary-dimensional hyperballs from which other shapes such as rectangles and cuboids can be cut. We briefly sketch the historic context of Bertrand's paradox and Jaynes's solution by the principle of maximum ignorance. We analyze the statistical properties of the produced fillings, mapping out the density profile and the line-length distribution and comparing them to analytic expressions. We study the characteristic dimensions of the space between the chords by determining the largest enclosed circles and balls in this pore space, finding a lognormal distribution of the pore sizes. We apply the algorithm to the direct-laser-writing fabrication design of optical multiple-scattering samples as three-dimensional cubes of random but homogeneously positioned and oriented chords.

Original languageEnglish
Article number043309
Pages (from-to)043309
Number of pages16
JournalPhysical Review E
Volume99
Issue number4
DOIs
Publication statusPublished - 25 Apr 2019

Fingerprint

Chord or secant line
Line
balls
Fabrication
Circle
Ball
Cuboid
porosity
fabrication
Multiple Scattering
Log Normal Distribution
rectangles
Metamaterials
Density Profile
paradoxes
Paradox
Rectangle
Statistical property
Regular hexahedron
Laser

Keywords

  • cond-mat.soft
  • physics.comp-ph

Cite this

Marakis, E., Corbijn Van Willenswaard, L. J., Uppu, R., Pinkse, P. W. H., & Velsink, M. C. (2019). Uniform line fillings. Physical Review E, 99(4), 043309. [043309]. https://doi.org/10.1103/PhysRevE.99.043309
Marakis, Evangelos ; Corbijn Van Willenswaard, Lars J. ; Uppu, Ravitej ; Pinkse, Pepijn W.H. ; Velsink, Matthias Christiaan. / Uniform line fillings. In: Physical Review E. 2019 ; Vol. 99, No. 4. pp. 043309.
@article{f1df59b5fb954604a317f70dad43b73a,
title = "Uniform line fillings",
abstract = "Deterministic fabrication of random metamaterials requires filling of a space with randomly oriented and randomly positioned chords with an on-average homogenous density and orientation, which is a nontrivial task. We describe a method to generate fillings with such chords, lines that run from edge to edge of the space, in any dimension. We prove that the method leads to random but on-average homogeneous and rotationally invariant fillings of circles, balls, and arbitrary-dimensional hyperballs from which other shapes such as rectangles and cuboids can be cut. We briefly sketch the historic context of Bertrand's paradox and Jaynes's solution by the principle of maximum ignorance. We analyze the statistical properties of the produced fillings, mapping out the density profile and the line-length distribution and comparing them to analytic expressions. We study the characteristic dimensions of the space between the chords by determining the largest enclosed circles and balls in this pore space, finding a lognormal distribution of the pore sizes. We apply the algorithm to the direct-laser-writing fabrication design of optical multiple-scattering samples as three-dimensional cubes of random but homogeneously positioned and oriented chords.",
keywords = "cond-mat.soft, physics.comp-ph",
author = "Evangelos Marakis and {Corbijn Van Willenswaard}, {Lars J.} and Ravitej Uppu and Pinkse, {Pepijn W.H.} and Velsink, {Matthias Christiaan}",
note = "14 pages, 9 figures.",
year = "2019",
month = "4",
day = "25",
doi = "10.1103/PhysRevE.99.043309",
language = "English",
volume = "99",
pages = "043309",
journal = "Physical review E: covering statistical, nonlinear, biological, and soft matter physics",
issn = "2470-0045",
publisher = "American Physical Society",
number = "4",

}

Marakis, E, Corbijn Van Willenswaard, LJ, Uppu, R, Pinkse, PWH & Velsink, MC 2019, 'Uniform line fillings' Physical Review E, vol. 99, no. 4, 043309, pp. 043309. https://doi.org/10.1103/PhysRevE.99.043309

Uniform line fillings. / Marakis, Evangelos; Corbijn Van Willenswaard, Lars J.; Uppu, Ravitej; Pinkse, Pepijn W.H.; Velsink, Matthias Christiaan.

In: Physical Review E, Vol. 99, No. 4, 043309, 25.04.2019, p. 043309.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Uniform line fillings

AU - Marakis, Evangelos

AU - Corbijn Van Willenswaard, Lars J.

AU - Uppu, Ravitej

AU - Pinkse, Pepijn W.H.

AU - Velsink, Matthias Christiaan

N1 - 14 pages, 9 figures.

PY - 2019/4/25

Y1 - 2019/4/25

N2 - Deterministic fabrication of random metamaterials requires filling of a space with randomly oriented and randomly positioned chords with an on-average homogenous density and orientation, which is a nontrivial task. We describe a method to generate fillings with such chords, lines that run from edge to edge of the space, in any dimension. We prove that the method leads to random but on-average homogeneous and rotationally invariant fillings of circles, balls, and arbitrary-dimensional hyperballs from which other shapes such as rectangles and cuboids can be cut. We briefly sketch the historic context of Bertrand's paradox and Jaynes's solution by the principle of maximum ignorance. We analyze the statistical properties of the produced fillings, mapping out the density profile and the line-length distribution and comparing them to analytic expressions. We study the characteristic dimensions of the space between the chords by determining the largest enclosed circles and balls in this pore space, finding a lognormal distribution of the pore sizes. We apply the algorithm to the direct-laser-writing fabrication design of optical multiple-scattering samples as three-dimensional cubes of random but homogeneously positioned and oriented chords.

AB - Deterministic fabrication of random metamaterials requires filling of a space with randomly oriented and randomly positioned chords with an on-average homogenous density and orientation, which is a nontrivial task. We describe a method to generate fillings with such chords, lines that run from edge to edge of the space, in any dimension. We prove that the method leads to random but on-average homogeneous and rotationally invariant fillings of circles, balls, and arbitrary-dimensional hyperballs from which other shapes such as rectangles and cuboids can be cut. We briefly sketch the historic context of Bertrand's paradox and Jaynes's solution by the principle of maximum ignorance. We analyze the statistical properties of the produced fillings, mapping out the density profile and the line-length distribution and comparing them to analytic expressions. We study the characteristic dimensions of the space between the chords by determining the largest enclosed circles and balls in this pore space, finding a lognormal distribution of the pore sizes. We apply the algorithm to the direct-laser-writing fabrication design of optical multiple-scattering samples as three-dimensional cubes of random but homogeneously positioned and oriented chords.

KW - cond-mat.soft

KW - physics.comp-ph

UR - http://www.scopus.com/inward/record.url?scp=85064867242&partnerID=8YFLogxK

UR - https://arxiv.org/abs/1809.01490

U2 - 10.1103/PhysRevE.99.043309

DO - 10.1103/PhysRevE.99.043309

M3 - Article

VL - 99

SP - 043309

JO - Physical review E: covering statistical, nonlinear, biological, and soft matter physics

JF - Physical review E: covering statistical, nonlinear, biological, and soft matter physics

SN - 2470-0045

IS - 4

M1 - 043309

ER -

Marakis E, Corbijn Van Willenswaard LJ, Uppu R, Pinkse PWH, Velsink MC. Uniform line fillings. Physical Review E. 2019 Apr 25;99(4):043309. 043309. https://doi.org/10.1103/PhysRevE.99.043309