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The effect of strong confinement on the positional and orientational ordering is examined in a system of hard rectangular rods with length L and diameter D (L>D) using the Parsons-Lee modification of the second virial density functional…

Using ground-state and relative-entropy based inverse design strategies, isotropic interactions with an attractive well are determined to stabilize and promote as- sembly of particles into two-dimensional square, honeycomb, and kagome…

Most types of retinal neurons are spatially positioned in non-random patterns, termed retinal mosaics. Several developmental mechanisms are thought to be important in the formation of these mosaics. Most evidence to date suggests that…

This work focuses on the formation of mating aggregates in zooplankton. In particular, sexual encounters are behaviourally supported by males actively swimming in search for females, and approaching them for mating once they are found.…

We show that the order dimension of the weak order on a Coxeter group of type A, B or D is equal to the rank of the Coxeter group, and give bounds on the order dimensions for the other finite types. This result arises from a unified…

The structure of topological spaces is analysed here through the lenses of fibrous preorders. Each topological space has an associated fibrous preorder and those fibrous preorders which return a topological space are called spacial. A…

We investigate the problem of assembling general shapes and patterns in a model in which particles move based on uniform external forces until they encounter an obstacle. While previous work within this model of assembly has focused on…

Dynamical systems containing heteroclinic cycles and networks can be invoked as models of intransitive competition between three or more species. When populations are assumed to be well-mixed, a system of ordinary differential equations…

Excitons in van der Waals heterostructures come in many different forms. In bilayer structures, the electron and hole may be localized on the same layer or they may be separated forming an interlayer exciton with a finite out-of-plane…

It is shown that the rotational band structure of the cluster states in 12C and 16O can be understood in terms of the underlying discrete symmetry that characterizes the geometrical configuration of the alpha-particles, i.e. an equilateral…

Square-root topological insulators are recently-proposed intriguing topological insulators, where the topologically nontrivial nature of Bloch wave functions is inherited from the square of the Hamiltonian. In this paper, we propose that…

Birds, bats and many insects can tuck their wings against their bodies at rest and deploy them to power flight. Whereas birds and bats use well-developed pectoral and wing muscles and tendons, how insects control these movements remains…

High order networks are weighted hypergraphs col- lecting relationships between elements of tuples, not necessarily pairs. Valid metric distances between high order networks have been defined but they are difficult to compute when the…

Topological materials occupy the central stage in the modern condensed matter physics because of their robust metallic edge or surface states protected by the topological invariant, characterizing the electronic band structure in the bulk.…

We discover two distinct topological pathways through which the pentagonal Cairo tiling (P5), a structural model for single-layer $AB_2$ pyrite materials, respectively transforms into a crystalline rhombus-hexagon (C46) tiling and random…

Physical properties of composite materials can be pre-engineered by controlling their structure and composition at the mesoscale. Yet, approaches for achieving this are limited and rarely scalable. We introduce a new breed of self-assembled…

Topologically nontrivial adiabatic loops of the orientation of a homogeneous external magnetic field drive the walking of paramagnetic colloidal bipeds above a deformed quasi-periodic magnetic square pattern. Depending on the topological…

Let $X$ be 2n-dimensional compact manifold with a locally standard action of a compact torus. The orbit space $X/T$ is a manifold with corners. Suppose that all proper faces of $X/T$ are acyclic. In the paper we study the homological…

We study computationally the local structure of aggregated systems of patchy particles. By calculating the probability distribution functions of various rotational invariants we can identify the precursors of orientation order in amorphous…

Topological dislocations in otherwise periodic lattices represent global structural defects that, nevertheless, typically leave the lattice periodicity intact far from the dislocation. Such dislocations arise in diverse physical systems…