Uniform line fillings
Abstract
Deterministic fabrication of random metamaterials requires filling of a space with randomly oriented and randomly positioned chords with an onaverage 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 onaverage homogeneous and rotationally invariant fillings of circles, balls, and arbitrarydimensional 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 linelength 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 directlaserwriting fabrication design of optical multiplescattering samples as threedimensional cubes of random but homogeneously positioned and oriented chords.
 Publication:

Physical Review E
 Pub Date:
 April 2019
 DOI:
 10.1103/PhysRevE.99.043309
 arXiv:
 arXiv:1809.01490
 Bibcode:
 2019PhRvE..99d3309M
 Keywords:

 Condensed Matter  Soft Condensed Matter;
 Physics  Computational Physics
 EPrint:
 10 pages, 12 figures