Related papers: Methodology to Construct Large Realizations of Per…

We report the discovery of a mixed orientational structure in the quasi-one-dimensional fluid of hard non-spherical bodies with the exact calculation of the thermodynamic and structural quantities using the transfer operator method. The…

Disordered systems like liquids, gels, glasses, or granular materials are not only ubiquitous in daily life and in industrial applications but they are also crucial for the mechanical stability of cells or the transport of chemical and…

We analyze the large scale structure and fluctuations of jammed packings of size disperse spheres, produced in a granular experiment as well as numerically. While the structure factor of the packings reveals no unusual behavior for small…

Materials with nanoscale phase separation are considered. These materials are formed by a mixture of several phases, so that inside one phase there exist nanosize inclusions of other phases, with random shapes and random spatial locations.…

There are deep, but hidden, geometric structures within jammed systems, associated with hidden symmetries. These can be revealed by repeated transformations under which these structures lead to fixed points. These geometric structures can…

We perform extensive computational studies of two-dimensional static bidisperse disk packings using two distinct packing-generation protocols. The first involves thermally quenching equilibrated liquid configurations to zero temperature…

While topological phases have been extensively studied in amorphous systems in recent years, it remains unclear whether the random nature of amorphous materials can give rise to higher-order topological phases that have no crystalline…

In the present work, the overall nonlinear elastic behavior of a 1D multi-modular structure incorporating possible imperfections at the discrete (micro-scale) level, is derived with respect to both tensile and compressive applied loads. The…

We introduce a new class of functional correlated disordered materials, termed Gyromorphs, which uniquely combine liquid-like translational disorder with quasi-long-range rotational order, induced by a ring of $G$ delta peaks in their…

We give theorems that can be used to upper bound the densities of packings of different spherical caps in the unit sphere and of translates of different convex bodies in Euclidean space. These theorems extend the linear programming bounds…

Packing problems, which ask how to arrange a collection of objects in space to meet certain criteria, are important in a great many physical and biological systems, where geometrical arrangements at small scales control behaviour at larger…

We systematically explore the self-assembly of semi-flexible polymers in deformable spherical confinement across a wide regime of chain stiffness, contour lengths and packing fractions by means of coarse-grained molecular dynamics…

Topological defects play a key role in nonequilibrium phase transitions, ranging from birth of the early universe to quantum critical behavior of ultracold atoms. In solids, transient defects are known to generate a variety of hidden orders…

The famous Kepler conjecture has a less spectacular, two-dimensional equivalent: The theorem of Thue states that the densest circle packing in the Euclidean plane has a hexagonal structure. A common proof uses Voronoi cells and analyzes…

The spatial cosmic matter distribution on scales of a few up to more than a hundred Megaparsec displays a salient and pervasive foamlike pattern. Voronoi tessellations are a versatile and flexible mathematical model for such weblike spatial…

This review describes the diversity of jammed configurations attainable by frictionless convex nonoverlapping (hard) particles in Euclidean spaces and for that purpose it stresses individual-packing geometric analysis. A fundamental feature…

The concept of hyperuniformity has been introduced by Torquato and Stillinger in 2003 as a notion to detect structural behaviour intermediate between amorphous disorder and crystalline order. The present paper studies a generalisation of…

Understanding and controlling self-assembly processes at multiple length scales is vital if we are to design and create advanced materials. In particular, our ability to organise matter on the nanoscale has advanced considerably, but still…

Optimal spatial sampling of light rigorously requires that identical photoreceptors be arranged in perfectly regular arrays in two dimensions. Examples of such perfect arrays in nature include the compound eyes of insects and the nearly…

A decoration of a hyperbolic surface of finite type is a choice of circle, horocycle or hypercycle about each cone-point, cusp or flare of the surface, respectively. In this article we show that a decoration induces a unique canonical…