Discrete rearranging disordered patterns, part I: Robust statistical tools in two or three dimensions

Abstract

Discrete rearranging patterns include cellular patterns, for instance liquid foams, biological tissues, grains in polycrystals; assemblies of particles such as beads, granular materials, colloids, molecules, atoms; and interconnected networks. Such a pattern can be described as a list of links between neighbouring sites. Performing statistics on the links between neighbouring sites yields average quantities (hereafter "tools") as the result of direct measurements on images. These descriptive tools are flexible and suitable for various problems where quantitative measurements are required, whether in two or in three dimensions. Here, we present a coherent set of robust tools, in three steps. First, we revisit the definitions of three existing tools based on the texture matrix. Second, thanks to their more general definition, we embed these three tools in a self-consistent formalism, which includes three additional ones. Third, we show that the six tools together provide a direct correspondence between a small scale, where they quantify the discrete pattern's local distortion and rearrangements, and a large scale, where they help describe a material as a continuous medium. This enables to formulate elastic, plastic, fluid behaviours in a common, self-consistent modelling using continuous mechanics. Experiments, simulations and models can be expressed in the same language and directly compared. As an example, a companion paper (Marmottant, Raufaste and Graner, joint paper) provides an application to foam plasticity.

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Cited by in corpus (23)

• Local elasticity map and plasticity in a model Lennard-Jones glass
• Minkowski Tensors of Anisotropic Spatial Structure
• Triangles bridge the scales: Quantifying cellular contributions to tissue deformation
• Relating cell shape and mechanical stress in a spatially disordered epithelium using a vertex-based model
• From cells to tissue: A continuum model of epithelial mechanics
• Active dynamics of tissue shear flow
• On the study of local stress rearrangements during quasistatic plastic shear of a model glass: do local stress components contain enough information?
• A migrating epithelial monolayer flows like a Maxwell viscoelastic liquid
• Shear-driven solidification and nonlinear elasticity in epithelial tissues
• Bubbly vertex dynamics: a dynamical and geometrical model for epithelial tissues with curved cell shapes
• Local description of the two-dimensional flow of foam through a contraction
• Topological rearrangements and stress fluctuations in quasi-two-dimensional hopper flow of emulsions
• Discrete rearranging disordered patterns: Prediction of elastic and plastic behaviour, and application to two-dimensional foams
• Three-dimensional foam flow resolved by fast X-ray tomographic microscopy
• Classical Nucleation Theory for the Crystallization Kinetics in Sheared Liquids
• Fast determination of coarse grained cell anisotropy and size in epithelial tissue images using Fourier transform
• Poisson-bracket formulation of the dynamics of fluids of deformable particles
• Models, measurement and inference in epithelial tissue dynamics
• Depletion attraction favors the elastic response of emulsions flowing in a constriction
• Fluctuations of cell geometry and their non-equilibrium thermodynamics in living epithelial tissue
• Random walk models for the propagation of signalling molecules in one-dimensional spatial networks and their continuum limit
• Mechanical state, material properties and continuous description of an epithelial tissue
• Collective epithelial migration mediated by the unbinding of hexatic defects