Related papers: Ordering and topological defects in social wasps' …
Active fluids, such as cytoskeletal filaments, bacterial colonies and epithelial cell layers, exhibit distinctive orientational coherence, often characterized by nematic order and topological defects. By contrast, little is known about…
Heterostructures of stacked two-dimensional lattices have shown great promise for engineering novel material properties. As an archetypal example of such a system, the hexagon-shared honeycomb-kagome lattice has been experimentally…
Topological defects with symmetry-breaking phase transitions have captured much attention. Vortex generated by topological defects exhibits exotic properties and its flow direction can be switched by altering the spin configurations.…
Filamentous cyanobacteria can show fascinating examples of nonequilibrium self-organization, which however are not well-understood from a physical perspective. We investigate the motility and collective organization of colonies of these…
This paper studies the underlying combinatorial structure of a class of object rearrangement problems, which appear frequently in applications. The problems involve multiple, similar-geometry objects placed on a flat, horizontal surface,…
We examine the fluid phase behaviour of the binary mixture of hard superellipses using the scaled particle theory The superellipse is a general two dimensional convex object which can be tuned between circular and rectangular shapes…
We classify finite posets with a particular sorting property, generalizing a result for rectangular arrays. Each poset is covered by two sets of disjoint saturated chains such that, for any original labeling, after sorting the labels along…
We demonstrate a variety of ordered patterns, including hexagonal structures and chains, formed by colloidal particles (droplets) at the free surface of a nematic liquid crystal (LC). The surface placement introduces a new type of particle…
We define a natural lattice structure on all subsets of a finite root system that extends the weak order on the elements of the corresponding Coxeter group. For crystallographic root systems, we show that the subposet of this lattice…
We introduce the concept of nested topological order in a class of exact quantum lattice Hamiltonian models with non-abelian discrete gauge symmetry. The topological order present in the models can be partially destroyed by introducing a…
Understanding the influence of an environment on the evolution of its resident population is a major challenge in evolutionary biology. Great progress has been made in homogeneous population structures while heterogeneous structures have…
Collective patterns of motion emerge across biological taxa: insects swarm, fish school, and birds flock. In particular, large migratory birds form strikingly ordered V-shaped formations, which experiments and direct numerical simulations…
There is considerable interest in understanding and controlling topological defects in nematic liquid crystals (LCs). Confinement, in the form of droplets, has been particularly effective in that regard. Here, we employ the Landau-de Gennes…
Cutting and packing problems arise in a large variety of industrial applications, where there is a need to cut pieces from a large object, or placing them inside a containers, without overlap. When the pieces or the containers have…
Defects play an important role in a number of fields dealing with ordered structures. They are often described in terms of their topology, mutual interaction and their statistical characteristics. We demonstrate theoretically and…
Many cell types spontaneously order like nematic liquid crystals, and, as such, they form topological defects. While defects with topological charge $\pm$1/2 are common in cell monolayers, the defects with charge $\pm$1, relevant in the…
Hopfions, as three-dimensional topologically nontrivial structures described by poloidal and toroidal winding numbers, hold promise as robust information carriers in spintronics, functional materials, and optical communications. Although…
This is a draft of a book submitted for publication by the AMS. Its theme is the remarkable interplay, accelerating in the last few decades, between topology and the theory of orderable groups, with applications in both directions. It…
The set of chambers of a real hyperplane arrangement may be ordered by separation from some fixed chamber. When this poset is a lattice, Bjorner, Edelman, and Ziegler proved that the chambers are in natural bijection with the biconvex sets…
When colloidal particles are vertically confined to a gap of between 1.3-1.6 particle diameters, they pack into buckled crystals of particles in either "up" or "down" states. Neighboring particles tend to occupy opposite states, analogous…