Related papers: Self-shrinking Platonic solids
We report experimental and simulation studies of the structure of a monolayer of indented ("lock and key") colloids, on a planar surface. On adding a non-absorbing polymer with prescribed radius and volume fraction, depletion interactions…
Shellings of simplicial complexes have long been a useful tool in topological and algebraic combinatorics. Shellings of a complex expose a large amount of information in a helpful way, but are not easy to construct, often requiring deep…
We consider the primitive quaternionic reflection groups of type P for H^2 that are obtained from Blichfeldt's collineation groups for C^4.These are seen to be intimately related to the maximal set of five quaternionic mutually unbiased…
Self-polar polytopes are convex polytopes that are equal to an orthogonal transformation of their polar sets. These polytopes were first studied by Lov\'{a}sz as a means of establishing the chromatic number of distance graphs on spheres,…
We introduce a type $A$ crystal structure on decreasing factorizations of fully-commutative elements in the 0-Hecke monoid which we call $\star$-crystal. This crystal is a $K$-theoretic generalization of the crystal on decreasing…
In this paper, we study complete self-shrinkers in Euclidean space and prove that an $n$-dimensional complete self-shrinker in Euclidean space $\mathbb{R}^{n+1}$ is isometric to either $\mathbb{R}^{n}$, $S^{n}(\sqrt{n})$, or $S^k…
In this paper we bring into attention variable coefficient cubic-quintic nonlinear Schr\"odinger equations which admit Lie symmetry algebras of dimension four. Within this family, we obtain the reductions of canonical equations of…
A new kind of composite were manufactured by densification of co-crumpled aluminium and tantalum thin foils using close die compression. It was shown by optical micrography that its microstructure is highly interlocked. The morphology was…
When considered as a Deligne-Lusztig variety, the Drinfeld half space $\Omega_V$ over a finite field $k$ has a compactification whose boundary divisor is normal crossing and which can be obtained by successively blowing-up projective space…
Using the orthogonal connectedness, we introduce the notion of orthogonal decomposability of convex polytopes and study it in the case of Platonic and Archimedean solids. While doing so, we also encounter polytopes which are not…
We consider the automorphism groups of various Lorentzian lattices over the Eisenstein, Gaussian, and Hurwitz integers, and in some of them we find reflection groups of finite index. These provide new finite-covolume reflection groups…
A silicene-like polymorph of the Si111 7x7 surface is proposed that resolves numerous experimental paradoxes and inconsistencies arising over the past 34 years. An analysis of the three established surface state charge densities from atom…
We establish the analog for real spherical varieties of the Scattering Theorem of Sakellaridis and Venkatesh (\cite{SV}, Theorem 7.3.1) for p-adic spherical varieties. We use properties of the Harish-Chandra homomorphism of Knop for…
Self-assembling peptides (SAPs) have the ability to spontaneously assemble into ordered nanostructures enabling the manufacture of "designer" nanomaterials. The reversible molecular association of SAPs has been shown to offer great promise…
We introduce the notion of confinement of decompositions for forms or vector of forms. The confinement, when it holds, lowers the number of parameters that one needs to consider, in order to find all the possible decompositions of a given…
We report small-angle x-ray scattering (SAXS) experiments on aqueous dispersions of colloidal silica with a broad monomodal size distribution (polydispersity 18%, size 8 nm). Over a range of volume fractions the silica particles segregate…
Some physics models have 10 dimensions that are usually decomposed into: 4 spacetime dimensions with local Lorentz Spin(1,3) symmetry plus a 6-dimensional compact space related to internal symmetries. A possibly useful alternative…
Entangled embedded periodic nets and crystal frameworks are defined, along with their dimension type, homogeneity type, adjacency depth and periodic isotopy type. We obtain periodic isotopy classifications for various families of embedded…
Tying knots and linking microscopic loops of polymers, macromolecules, or defect lines in complex materials is a challenging task for material scientists. We demonstrate the knotting of microscopic topological defect lines in chiral nematic…
Shear bands are narrow zones of intense shear observed during plastic deformations of metals at high strain rates. Because they often precede rupture, their study attracted attention as a mechanism of material failure. Here, we aim to…