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Liquid water, besides being fundamental for life on Earth, has long fascinated scientists due to several anomalies. Different hypotheses have been put forward to explain these peculiarities. The most accredited one foresees the presence in…
We probe gravitational clustering in N-body simulations using geometrical descriptors sensitive to `connectedness': the genus curve, percolation and shape statistics. We find that both genus and percolation curves provide complementary…
Many systems in nature and the synthetic world involve ordered arrangements of units on two-dimensional surfaces. We review here the fundamental role payed by both the topology of the underlying surface and its detailed curvature. Topology…
We consider problem of constructing purely Voronoi mesh where the union of uncut Voronoi cells approximates the planar computational domain with piecewise-smooth boundary. Smooth boundary fragments are approximated by the Voronoi edges and…
Following work by Hochman and Meyerovitch on multidimensional SFT, we give computability-theoretic characterizations of the real numbers that can appear as the topological entropies of one-dimensional and two-dimensional cellular automata.
Topological properties of crystalline ice structures are studied by considering ring statistics, coordination sequences, and topological density of different ice phases. The coordination sequences (number of sites at topological distance k…
Self-assembly of chiral particles with an L-shape is explored by Monte-Carlo computer simulations in two spatial dimensions. For sufficiently high packing densities in confinement, a carpet-like texture emerges due to the interlocking of…
Using computer simulations we investigate the microscopic structure of the singular director field within a nematic droplet. As a theoretical model for nematic liquid crystals we take hard spherocylinders. To induce an overall topological…
Hierarchical networks are attracting a renewal interest for modelling the organization of a number of biological systems and for tackling the complexity of statistical mechanical models beyond mean-field limitations. Here we consider the…
We study the deformation of a fluctuating crystalline sheet confined between two flat rigid walls as a simple model for layered solids where bonds among atoms {\it within} the same layer are much stronger than those {\it between} layers.…
Band-topology is traditionally analyzed in terms of gauge-invariant observables associated with crystalline Bloch wavefunctions. Recent work has demonstrated that many of the free fermion topological characteristics survive even in an…
The large-scale matter distribution represents a complex network of structure elements such as voids, clusters, filaments, and sheets. This network is spanned by a point distribution. The global properties of the point process can be…
Quantifying the size of cell populations is crucial for understanding biological processes such as growth, injury repair, and disease progression. Often, experimental data offer information in the form of relative frequencies of distinct…
Recently a novel type of epithelial cell has been discovered and dubbed the "scutoid". It is induced by curvature of the bounding surfaces. We show by simulations and experiments that such cells are to be found in a dry foam subjected to…
We map out the phase diagram of strongly interacting fermions in a potential trap with mass and population imbalance between the two spin components. As a unique feature distinctively different from the equal-mass case, we show that the…
How much structural information is needed to distinguish living from non-living systems? Here, we show that the statistical properties of Delaunay tessellations suffice to differentiate prokaryotic and eukaroytic cell packings from a wide…
Cellular structures manifest their outstanding mechanical properties in many biological systems. One key challenge for designing and optimizing these geometrically complicated structures lies in devising an effective geometric…
The Partition function of two Hard Spheres in a Hard Wall Pore is studied appealing to a graph representation. The exact evaluation of the canonical partition function, and the one-body distribution function, in three different shaped pores…
The aim of this study is to develop a semi-analytical method to investigate fluid-structure coupling of concentric double shells with different lengths and elastic behaviours. Co-axial shells constitute a cylindrical circular container and…
In topological data analysis, we want to discern topological and geometric structure of data, and to understand whether or not certain features of data are significant as opposed to simply random noise. While progress has been made on…