Geometric effects in random assemblies of ellipses

Abstract

Assemblies of anisotropic particles commonly appear in studies of active many-body systems. However, in two dimensions, the geometric ramifications of the finite density of such objects are not entirely understood. To fully characterize these effects, we perform an in-depth study of random assemblies generated by a slow compression of frictionless elliptical particles. The obtained configurations are then analysed using the Set Voronoi tessellation which takes the particle shape into the account. Not only that we analyse most scalar and vectorial morphological measures, which are commonly discussed in the literature or which have been recently addressed in experiments, but also systematically explore the correlations between them. While in a limited range of parameters similarities with findings in 3D assemblies could be identified, important differences are found when a broad range of aspect ratios and packing fractions are considered. The data discussed in this study should thus provide a unique reference set such that geometric effects and differences from random assemblies could be clearly identified in more complex systems, including ones with soft and active particles that are typically found in biological systems.

On the mechanical regulation of epithelial tissue homeostasis

“…Indeed, these linear relationships are also conrmed in MDCK-II tissues (see Fig. 10), suggesting again that geometrical elements, as emphasized by random packings [40] remain important even in tissues, even though the cell and nuclei shape distributions are strongly regulated in the homeostatic state.…”

“…Actually the fractions of cells with ve and seven neighbors are signicant, with a larger pentagon component (30% pentagon compared to 20% heptagon). This asymmetry exists already in the random packings of ellipses at densities and elongations comparable to the nuclei density and shapes [40], albeit, in tissues, the disparity in the fractions of pentagons and heptagons is signicantly larger.…”

“…n is the second central moment of the distribution of n, and γ is a constant that may decrease as σ 2 n increases [44,45], or may be independent of σ 2 n [46]. This relation has been commonly used to explore the topology of tessellations and arrangements in cellular assemblies [40,47,48]. In the case of homeostatic MDCK-II tissues, irrespective of the conditions in which they were grown, all tissues show the same linear dependence (Fig.…”

“…On 11 kPa PA gels we have 5244 cells from 27 regions (28000 and 128000 µm 2 ). All morphological measures were obtained using a previously described procedure [34,40], from the Set-based Voronoi Tessellation (SVT).…”

Hard superellipse phases: particle shape anisotropy & curvature

“…38 For anisotropic particles with different aspect ratios and curvatures, accurate identification of neighbors in concentrated conditions requires tessellation based on surfaces (rather than particle centers). 39,40 In our work, the tessellated space is calculated along the continuous path connecting the locus of centers of circles tangent to the surface of different shaped particles (red lines Fig. S2a and c, ESI,† tessellated space for many particles Fig.…”