Related papers: Cell shape analysis of random tessellations based …
We present a new method for embedding a causal set into an interval of Minkowski spacetime. The method uses spacetime volumes for causally related elements to define causal set analogs of Minkowski inner products. These are used to…
This study investigates the relationship between cell shape and cell-generated stresses in confluent cell layers. Using simultaneous measurements of cell shape orientation and cell-generated contractile forces in MDCK and LP-9 colonies, we…
The intent of this paper is to describe the large scale asymptotic geometry of iteration stable (STIT) tessellations in $\mathbb{R}^d$, which form a rather new, rich and flexible class of random tessellations considered in stochastic…
Given a network, the statistical ensemble of its graph-Voronoi diagrams with randomly chosen cell centers exhibits properties convertible into information on the network's large scale structures. We define a node-pair level measure called…
Porous media, while ubiquitous across many engineering disciplines, is inherently difficult to characterize due to their innate stochasticity and heterogeneity. The key for predicting porous material behavior comes down to the structuring…
Disordered hyperuniform packings are unusual amorphous states of two-phase materials that are endowed with exotic physical properties. Such hyperuniform systems are characterized by an anomalous suppression of volume-fraction fluctuations…
Different cell types aggregate and sort into hierarchical architectures during the formation of animal tissues. The resulting spatial organization depends (in part) on the strength of adhesion of one cell type to itself relative to other…
Twisted ribbons subjected to a tension exhibit a remarkably rich morphology, from smooth and wrinkled helicoids, to cylindrical or faceted patterns. These shapes are intimately related to the instability of the natural, helicoidal symmetry…
As hydrodynamic simulations increase in scale and resolution, identifying structures with non-trivial geometries or regions of general interest becomes increasingly challenging. There is a growing need for algorithms that identify a variety…
In particulate systems with short-range interactions, such as granular matter or simple fluids, local structure plays a pivotal role in determining the macroscopic physical properties. Here, we analyse local structure metrics derived from…
We investigate the morphological properties of large-scale structure in the Universe and the physical processes that modify the excursion-set morphology of the three-dimensional matter density field. Using the Quijote N-body simulation…
Processes of random tessellations of the Euclidean space $\mathbb{R}^d$, $d\geq 1$, are considered which are generated by subsequent division of their cells. Such processes are characterized by the laws of the life times of the cells until…
Tessellations are an important tool to model the microstructure of cellular and polycrystalline materials. Classical tessellation models include the Voronoi diagram and Laguerre tessellation whose cells are polyhedra. Due to the convexity…
We use the Millennium and Millennium-II simulations to illustrate the Tessellation-Level-Tree (TLT), a hierarchical tree structure linking density peaks in a field constructed by voronoi tessellation of the particles in a cosmological…
Biological cells are able to generate intricate structures and respond to external stimuli, sculpting their membrane from within. Simplified biomimetic systems can aid in understanding the principles which govern these shape changes and…
We consider the Voronoi diagram generated by $n$ i.i.d. $\mathbb{R}^{d}$-valued random variables with an arbitrary underlying probability density function $f$ on $\mathbb{R}^{d}$, and analyse the asymptotic behaviours of certain geometric…
Capturing and predicting the effective mechanical properties of highly porous cellular media still represents a significant challenge for the research community, due to their complex structural interdependencies and known size effects.…
Context. Convective regions in stellar models are always associated with uncertainties, for example due to extra-mixing or the possible inaccurate position of the transition from convective to radiative transport of energy. These have a…
Thin solids often develop elastic instabilities and subsequently complex, multiscale deformation patterns. Revealing the organizing principles of this spatial complexity has ramifications for our understanding of morphogenetic processes in…
Evaporative lithography in cells of arbitrary configuration allows for the creation of diverse particle deposition patterns due to the formation of a specific flow structure in the liquid caused by non-uniform evaporation. The latter in…