Related papers: Ordering and topological defects in social wasps' …
For each composition $\vec{c}$ we show that the order complex of the poset of pointed set partitions $\Pi^{\bullet}_{\vec{c}}$ is a wedge of spheres of the same dimension with the multiplicity given by the number of permutations with…
Network topologies can be non-trivial, due to the complex underlying behaviors that form them. While past research has shown that some processes on networks may be characterized by low-order statistics describing nodes and their neighbors,…
During colony growth, complex interactions regulate the bacterial orientation, leading to the formation of large-scale ordered structures, including topological defects and microdomains. These structures may benefit bacterial strains,…
Questions that seek to determine whether a hyperplane arrangement property, be it geometric, arithmetic or topological, is of a combinatorial nature (that is determined by the intersection lattice) are abundant in the literature. To tackle…
We describe those complete linearly ordered topological spaces $X$ which are homogeneous (=CHLOTS). That is, $X$ is order isomorphic with any nonempty open interval in $X$. Using countable tail-like ordinals as indices, we build towers of…
Community structure in networks is often a consequence of homophily, or assortative mixing, based on some attribute of the vertices. For example, researchers may be grouped into communities corresponding to their research topic. This is…
We investigate the impact of crystal alignment on excitonic behavior in WSe$_{2}$/MoS$_{2}$ van der Waals heterostructures by comparing eclipsed (AA) and staggered (AB) stacking configurations. Our first-principles and symmetry-based…
Motivation coming from the study of affine Weyl groups, a structure of ranked poset is defined on the set of circular permutations in $S_n$ (that is, $n$-cycles). It is isomorphic to the poset of so-called admitted vectors, and to an…
The most energetically favourable arrangement of low-density electrons in an infinite two-dimensional plane is the ordered triangular Wigner lattice. However, in most instances of contemporary interest one deals instead with finite clusters…
We investigate the orientational ordering and close-packing behavior of hard Gaussian overlap (HGO) particles, which are confined into a quasi-one-dimensional (q1D) channel. In the channel, particles are allowed to move along the channel…
Many soft matter systems exhibit ordered, polycontinuous network morphologies, such as the cubic (double) gyroid or diamond, as well as disordered network morphologies known generically as ``random sponges". While presumed to share similar…
We exploit the long-ranged elastic fields inherent to confined nematic liquid crystals to assemble colloidal particles trapped at the liquid crystal interface into reconfigurable structures with complex symmetries and packings. Spherical…
A panoptic view of architectured planar lattices based on star-polygon tilings was developed. Four star-polygon-based lattice sub-families, formed of systematically arranged triangles, squares, or hexagons, were investigated numerically and…
The W-set of an element of a weak order poset is useful in the cohomological study of the closures of spherical subgroups in generalized flag varieties. We explicitly describe in a purely combinatorial manner the W-sets of the weak order…
Besides magnetic and charge order, regular arrangements of orbital occupation constitute a fundamental order parameter of condensed matter physics. Even though orbital order is difficult to identify directly in experiments, its presence was…
The moduli space $\Delta_{g,w}$ of tropical $w$-weighted stable curves of volume $1$ is naturally identified with the dual complex of the divisor of singular curves in Hassett's spaces of $w$-weighted stable curves. If at least two of the…
We investigate the ordering properties of vertically-vibrated monolayers of granular cylinders in a circular container at high packing fraction. In line with previous works by other groups, we identify liquid-crystalline ordering behaviour…
All intelligence is collective intelligence, in the sense that it is made of parts which must align with respect to system-level goals. Understanding the dynamics which facilitate or limit navigation of problem spaces by aligned parts thus…
We report an experimental study of the development of orientational order in a crumpled sheet, with a particular focus on the role played by the geometry of confinement. Our experiments are performed on elastomeric sheets immersed in a…
Topological defects play a central role in the formation and organization of various biological systems. Historically, such nonequilibrium defects have been mainly studied in the context of homogeneous active nematics. Phase-separated…