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We suggest a geometrical mechanism for the ordering of slender filaments inside non-isotropic containers, using cortical microtubules in plant cells and packing of viral genetic material inside capsids as concrete examples. We show…
The local nuclear and magnetic structure of wustite, Fe1-xO, and the coupling between them, has been examined using reverse Monte Carlo refinements of variable-temperature neutron total scattering data. The results from this analysis…
We investigate the spatial structure of cohesive granular matter with spheres floating at an air-liquid interface that form disordered close packings with pores in between. The interface is slowly lowered in a conical container to uniformly…
We study large uniform random quadrangulations whose genus grow linearly with the number of faces, whose local convergence was recently established by Budzinski and the author arXiv:1902.00492,arXiv:2012.05813. Here we study several…
The selection of stacking order in a broad range of close-packed polymorphic materials remains a challenging enigma. Using in situ cryogenic transmission electron microscopy, we uncover the atomistic mechanisms governing the vapour…
Topological states of matter are, generally, quantum liquids of conserved topological defects. We establish this by constructing and analyzing topological field theories which describe the dynamics of field singularities using gauge fields.…
Emergence of regular spatial patterns is a hallmark in living matter ranging from subcellular organelles to developing embryos and to ecosystems. Mechanisms for the formation of ordered spatial patterns in biology often require chemical…
Using topological band theory analysis we show that the nonsymmorphic symmetry operations in hexagonal lattices enforce Weyl points at the screw-invariant high-symmetry lines of the band structure. The corepresentation theory and…
Elucidating long-range interaction guided organization of matter is a fundamental question in physical systems covering multiple length scales. Here, based on the hexagonal disk model, we analyze the characteristic inhomogeneity created by…
We investigate resolutions of letterplace ideals of posets. We develop topological results to compute their multigraded Betti numbers, and to give structural results on these Betti numbers. If the poset is a union of no more than $c$…
Systems of randomly packed, macroscopic elements, from jammed spherical grains to tangled long filaments, represent a broad class of disordered meta-materials with a wide range of applications and manifestations in nature. A `bird nest'…
We define a new lattice structure on the elements of a finite Coxeter group W. This lattice, called the shard intersection order, is weaker than the weak order and has the noncrossing partition lattice NC(W) as a sublattice. The new…
Topological defects in nematically aligned cell populations play a critical role in modulating collective motion, from microbial colonies to epithelial tissues. Despite the potential of manipulating such topological defects to control…
Using first-principles density functional theory calculations, we investigate a family of stable two-dimensional crystals with chemical formula $A_2B_2$, where $A$ and $B$ belong to groups IV and V, respectively ($A$ = C, Si, Ge, Sn, Pb;…
Poisson structures vanishing linearly on a set of smooth closed disjoint curves are generic in the set of all Poisson structures on a compact connected oriented surface. We construct a complete set of invariants classifying these structures…
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…
Disclinations, first observed in mesomorphic phases, are relevant to a number of ill-ordered condensed matter media, with continuous symmetries or frustrated order. They also appear in polycrystals at the edges of grain boundaries. They are…
The paper is devoted to study the structure of Hawaiian groups of some topological spaces. We present some behaviors of Hawaiian groups with respect to product spaces, weak join spaces, cone spaces, covering spaces and locally trivial…
In contrast to dyadic interactions, higher-order interactions may contain one another, with subgroups naturally embedded within larger groups. These containment patterns arise empirically in ecology, sociology, computer science and the…
We study pattern formation in a reaction-diffusion system for a benthic bacteria-nutrient model in a marine sediment, which originally contains some spatially varying coefficients and with these shows some layering of patterns. Using the…