Related papers: Viruses and Fullerenes - Symmetry as a Common Thre…
In this paper, we explore the interplay between symmetry and fracton order, motivated by the analogous close relationship for topologically ordered systems. Specifically, we consider models with 3D planar subsystem symmetry, and show that…
We develop a coarse notion of bundle and use it to understand the coarse geometry of group extensions and, more generally, groups acting on proper metric spaces. The results are particularly sharp for groups acting on (locally finite) trees…
The infrared bar-spectrum of a single ammonia molecule encapsulated in nano-cage C$_{60}$ fullerene molecule is modelled using the site inclusion model successfully applied to analyze spectra of CO$_2$ isotopologues isolated in rare gas…
We introduce and study kernel algebras, i.e., algebras in the category of sheaves on a square of a scheme, where the latter category is equipped with a monoidal structure via a natural convolution operation. We show that many interesting…
The supercritical state is currently viewed as uniform and homogeneous on the pressure-temperature phase diagram in terms of physical properties. Here, we study structural properties of the supercritical carbon dioxide, and discover the…
Convex geometry has recently attracted great attention as a framework to formulate general probabilistic theories. In this framework, convex sets and affine maps represent the state spaces of physical systems and the possible dynamics,…
We establish that QED3 can possess a critical number of flavours, N_f^c, associated with dynamical chiral symmetry breaking if, and only if, the fermion wave function renormalisation and photon vacuum polarisation are homogeneous functions…
Given a quantum system consisting of many parts, we show that symmetry of the system's state, i.e., invariance under swappings of the subsystems, implies that almost all of its parts are virtually identical and independent of each other.…
The uniform asymptotic approximation of Green's kernel for the transmission problem of antiplane shear is obtained for domains with small inclusions. The remainder estimates are provided. Numerical simulations are presented to illustrate…
Working over imperfect fields, we give a comprehensive classification of genus-one curves that are regular but not geometrically regular, extending the known case of geometrically reduced curves. The description is given intrinsically, in…
Molecular-like carbon-nitrogen complexes in GaAs are investigated both experimentally and theoretically. Two characteristic high-frequency stretching modes at \num{1973} and \SI{2060}{cm^{-1}}, detected by Fourier transform infrared…
Complex organic molecules are ubiquitous companions of young low-mass protostars. Recent observations suggest that their emission stems, not only from the traditional hot corino, but also from offset positions. In this work, 2D…
Real physical systems with reflective and rotational symmetries such as viruses, fullerenes and quasicrystals have recently been modeled successfully in terms of three-dimensional (affine) Coxeter groups. Motivated by this progress, we…
We develop criteria for affine varieties to admit uniruled subvarieties of certain dimensions. The measurements are from long exact sequences of versions of symplectic cohomology, which is a Hamiltonian Floer theory for some open symplectic…
In this paper we look at the notion of cohomological triviality of fibrations of homogeneous spaces of affine algebraic groups defined over $\mathbb{C}$ and use topological methods, primarily the theory of covering spaces. This is made…
The projections of the lattices, may be used as models of quasicrystals, and the particular affine extension of the $H_2$ symmetry as a subgroup of $A_4$, discussed in the work, presents a different perspective to 5-fold symmetric…
We generalize finite-sample bounds for convex clustering to the setting where affinity weights appearing in the objective correspond to a general connected graph. These bounds and their analysis lead to a better understanding of clustering…
It is well known that all torsors under an affine algebraic group over an algebraically closed field are trivial. We note that under suitable conditions this also holds if the the group is not necessarily of finite type. This has an…
Besides graphite and diamond, the solid allotropes of carbon in sp2 and sp3 hybridization, the possible existence of a third allotrope based on the sp-carbon linear chain, the Carbyne, has stimulated researchers for a long time. The advent…
We present several models where the QCD axion arises accidentally. Confining gauge theories can generate axion candidates whose properties are uniquely determined by the quantum numbers of the new fermions under the Standard Model. The…