相关论文: A Classification Scheme for Toroidal Molecules

Topology, a well-established concept in mathematics, has nowadays become essential to describe condensed matter. At its core are chiral electron states on the bulk, surfaces and edges of the condensed matter systems, in which spin and…

We consider a simple model for the assembly of chiral molecules in two dimensions driven by maximization of the contact area. We derive a macroscopic model described by a parameter taking nine possible values corresponding to the possible…

A classic result of Brooks, Smith, Stone and Tutte associates to any finite planar network with distinguished source and sink vertices, a tiling of a rectangle by smaller subrectangles whose aspect ratios are given by the conductances of…

Identifying local structural motifs and packing patterns of molecular solids is a challenging task for both simulation and experiment. We demonstrate two novel approaches to characterize local environments in different polymorphs of…

The properties of toroidal hyperheavy even-even nuclei and the role of toroidal shell structure are extensively studied within covariant density functional theory. The general trends in the evolution of toroidal shapes in the $Z\approx…

High harmonic generation in the interaction of femtosecond lasers with atoms and molecules opens the path to molecular orbital tomography and to probe the electronic dynamics with attosecond-{\AA}ngstr\"{o}m resolutions. Molecular orbital…

Molecular Mechanics describes molecules as particle configurations interacting via classical potentials. These {\it configurational energies} usually consist of the sum of different phenomenological terms which are tailored to the…

The homotopy theory of topological defects is a powerful tool for organizing and unifying many ideas across a broad range of physical systems. Recently, experimental progress has been made in controlling and measuring colloidal inclusions…

Machine learning of scalar molecular properties such as potential energy has enabled widespread applications. However, there are relatively few machine learning models targeting directional properties, including permanent and transition…

We investigate tiling properties of spectra of measures, i.e., sets $\Lambda$ in $\br$ such that $\{e^{2\pi i \lambda x}: \lambda\in\Lambda\}$ forms an orthogonal basis in $L^2(\mu)$, where $\mu$ is some finite Borel measure on $\br$. Such…

We study the tiling of a two-dimensional region of the plane by $K$-cell one-dimensional tiles, or $K$-mers. Unlike previous studies, which typically allowed for one single value of $K$ or sometimes a small assortment of fixed values, here…

Supersonic beams of polar molecules are deflected using inhomogeneous electric fields. The quantum-state selectivity of the deflection is used to spatially separate molecules according to their quantum state. A detailed analysis of the…

Attention is fixed on shells in toroidal nuclei in the intermediate mass region using a toroidal single-particle potential. We find that there are toroidal shells in the intermediate mass region with large single-particle energy gaps at…

Two-dimensional colloidal suspensions subject to laser interference patterns with decagonal symmetry can form an Archimedean-like tiling phase where rows of squares and triangles order aperiodically along one direction [J. Mikhael et al.,…

Precision calculations of the fine and hyperfine structure of muonic atoms are performed in a relativistic approach and results for muonic 205 Bi, 147 Sm, and 89 Zr are presented. The hyperfine structure due to magnetic dipole and electric…

We present a triangulation--independent area--ordering prescription which naturally generalizes the well known path ordering one. For such a prescription it is natural that the two--form ``connection'' should carry three ``color'' indices…

We construct toroidal compactifications of the moduli spaces of Drinfeld $\mathbb{F}_q[T]$-modules of rank $d$ with level $N$ structure as moduli spaces of log Drinfeld modules of rank $d$ with level $N$ structure. The toroidal…

Hierarchical granular piles composed of aggregates are key structural features in both geoscience and planetary science, from fault gouge in seismic zones to the internal structures of comets. Although experimental studies have suggested a…

We consider here square tilings of the plane. By extending the formalism introduced in [3] we build a correspondence between plane maps endowed with an harmonic vector and square tilings satisfying a condition of regularity. In the case of…

Thin films formed from small molecules rapidly gain importance in different technological fields. To explain their growth, methods developed for zero--dimensional atoms as the film forming particles are applied. However, in organic thin…