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We use Topological Data Analysis tools for studying the inner organization of cells in segmented images of epithelial tissues. More specifically, for each segmented image, we compute different persistence barcodes, which codify lifetime of…
A 2D foam can be characterised by its distribution of bubble areas, and of number of sides. Both distributions have an average and a width (standard deviation). There are therefore at least two very different ways to characterise the…
A review on the properties and dynamical origin and nature of the cosmic foam, the tenuous space-filling frothy network permeating the interior of the Universe. We discuss the properties of this striking and intriguing pattern, describing…
We use molecular dynamics to study the ordering of a nematic liquid crystal around a spherical particle or droplet. Homeotropic boundary conditions and strong anchoring create a hedgehog director configuration on the particle surface and in…
Building on the striking similarity between the structure of the spindle during mitosis in living cells and nematic textures in confined liquid crystals, we use a continuum model of two-dimensional nematic liquid crystal droplets, to…
Multicellular rosettes are observed in different situations such as morphogenesis, wound healing, and cancer progression. While some molecular insights have been gained to explain the presence of these assemblies of five or more cells…
Fundamental theories and models of many-body physics can be probed in experiments on ultracold atoms held in place by electromagnetic fields. In particular, of considerable interest are systems under curved confinement, since they can yield…
Topological defects, which are singular points in a director field, play a major role in shaping active systems. Here, we experimentally study topological defects and the flow patterns around them, that are formed during the highly rapid…
Voronoi tessellations have been used to model the geometric arrangement of cells in morphogenetic or cancerous tissues, however so far only with flat hypersurfaces as cell-cell contact borders. In order to reproduce the experimentally…
Colloidal particles that are confined to an interface such as the air-water interface are an example of a two-dimensional fluid. Such dispersions have been observed to spontaneously form cluster and stripe morphologies in certain systems…
Physical systems are frequently modeled as sets of points in space, each representing the position of an atom, molecule, or mesoscale particle. As many properties of such systems depend on the underlying ordering of their constituent…
We describe the extension of a "viscous froth" model to the dynamics of a wet foam in a Hele-Shaw cell. The two-dimensional model includes the friction experienced by the soap films as they are dragged along the cell walls, while retaining…
In random cellular systems, both observation and maximum entropy inference give a specific form to the topological pair correlation: it is bi-affine in the cells number of edges with coefficients depending on the distance between the two…
Voronoi tessellations of scale-invariant fractal sets are characterized by topological and metrical properties that are significantly different from those of natural cellular structures. As an example we analyze Voronoi diagrams of…
We introduce a general, efficient method to completely describe the topology of individual grains, bubbles, and cells in three-dimensional polycrystals, foams, and other multicellular microstructures. This approach is applied to a pair of…
The Materials Project crystal structure database has been searched for materials possessing layered motifs in their crystal structures using a topology-scaling algorithm. The algorithm identifies and measures the sizes of bonded atomic…
Cells of Voronoi diagrams in two dimensions are usually considered as having edges of zero width. However, this is not the case in several experimental situations in which the thickness of the edges of the cells is relatively large. In this…
We study the properties of 2D fibre clusters and networks formed by deposition processes. We first examine the growth and scaling properties of single clusters. We then consider a network of such clusters, whose spatial distribution obeys…
An important open question in the modeling of biological tissues is how to identify the right scale for coarse-graining, or equivalently, the right number of degrees of freedom. For confluent biological tissues, both vertex and Voronoi…
Cell deformability is an essential determinant for tissue-scale mechanical nature, such as fluidity and rigidity, and is thus crucial for understanding tissue homeostasis and stable developmental processes. However, numerical simulations…