A Connectedness Theorem for Products of Weighted Projective Spaces

We prove a connectedness result for products of weighted projective spaces.     

Structure Results for Multiple Tilings in 3D

We study multiple tilings of 3-dimensional Euclidean space by a convex body. In a multiple tiling, a convex body $P$ is translated with a discrete multiset $\Lambda $ in such a way that each point of ${\mathbb {R}}^d$ gets covered exactly $k$ times, except perhaps the translated copies of the boundary of $P$ . It is known that all possible multiple tilers in ${\mathbb {R}}^3$ are zonotopes. In ${\mathbb {R}}^2$ it was known by the work of Kolountzakis (Discrete Comput Geom 23(4):537–553, 2000) that, unless $P$ is a parallelogram, the multiset of translation vectors $\Lambda $ must be a finite union of translated lattices (also known as quasi periodic sets). In that work (Kolountzakis, Discrete Comput Geom 23(4):537–553, 2000) the author asked whether the same quasi-periodic structure on the translation vectors would be true in ${\mathbb {R}}^3$ . Here we prove that this conclusion is indeed true for ${\mathbb {R}}^3$ . Namely, we show that if $P$ is a convex multiple tiler in ${\mathbb {R}}^3$ , with a discrete multiset $\Lambda $ of translation vectors, then $\Lambda $ has to be a finite union of translated lattices, unless $P$ belongs to a special class of zonotopes. This exceptional class consists of two-flat zonotopes $P$ , defined by the Minkowski sum of two 2-dimensional symmetric polygons in ${\mathbb {R}}^3$ , one of which may degenerate into a single line segment. It turns out that rational two-flat zonotopes admit a multiple tiling with an aperiodic (nonquasi-periodic) set of translation vectors $\Lambda $ . We note that it may be quite difficult to offer a visualization of these 3-dimensional non-quasi-periodic tilings, and that we discovered them by using Fourier methods.     

Survival of the Dirac points in rippled graphene

We study the effects of the rippling of a graphene sheet on quasiparticle dispersion. This is achieved using a generalization to the honeycomb lattice of the momentum average approximation, which is accurate for all coupling strengths and at all energies. We show that even though the position of the Dirac points may move and the Fermi speed can be renormalized significantly, quasiparticles with very long lifetimes survive near the Dirac points even for very strong couplings.     

Electron-vibrational interaction in 4f-5d optical transitions in Ba, Ca, Sr thiogallates doped with Eu ions

This study is devoted to the problem of the electron-vibrational interaction in 4f-5d optical transitions. We analyze the room temperature experimental data on the vibronically assisted broad bands arising from the 4f-5d transitions in Ba, Ca, and Sr thiogallates doped with Eu²⁺ ions. An approximate simple expression is given for the shape function of the broad vibronic bands with allowance for the terms corresponding to the emission (absorption) from both ground and first excited vibrational levels. We estimate the vibronic coupling parameters and the Stokes shifts for these systems. The theoretical results are in a good agreement with the experimental data.     

Collapse of the electron gas to two dimensions in density functional theory

Local and semilocal density functional approximations for the exchange-correlation energy fail badly in the zero-thickness limit of a quasi-two-dimensional electron gas, where the density variation is rapid almost everywhere. Here we show that a fully nonlocal fifth-rung functional, the inhomogeneous Singwi-Tosi-Land-Sj?lander (STLS) approach, which employs both occupied and unoccupied Kohn-Sham orbitals, recovers the true two-dimensional STLS limit and appears to be remarkably accurate for any thickness of the slab (and thus for the dimensional crossover). We also show that this good behavior is only partly due to the use of the full exact exchange energy.     

High-level correlated approach to the jellium surface energy, without uniform-gas input

We resolve the long-standing controversy over the metal surface energy: Density-functional methods that require uniform-electron-gas input agree with each other, but not with high-level correlated calculations such as Fermi hypernetted chain and diffusion Monte Carlo calculations that predict the uniform-gas correlation energy. Here we apply the inhomogeneous Singwi-Tosi-Land-Sj?lander method, and find that the density functionals are indeed reliable (because the surface energy is bulklike). Our work also vindicates the use of uniform-gas-based nonlocal kernels in time-dependent density-functional theory.     

An Approach to Paracyclophane-Based Tetrathiafulvalenes: Synthesis and Characterization of a Pseudo-Geminal [2.2]Paracyclophane 1,3-Dithia-2-Thione

The synthesis of paracyclophane-based tetrathiafulvalene precursors is described in the context of the importance of these compounds in the field of material chemistry. Pseudo-geminal bis(1,3-dithia-2-thione) was synthesized via the corresponding 1,3-dithiol-2-ylium salt. The latter was obtained by a synthetic procedure that involves 4,15-bis(acetyl)[2.2]paracyclophane, a new compound of interest for many researchers.     

Biomimetic Approach for Highly Selective Artificial Water Channels Based on Tubular Pillar[5]arene Dimers

Artificial water channels mimicking natural aquaporins (AQPs) can be used for selective and fast transport of water. Here, we quantify the transport performances of peralkyl-carboxylate-pillar[5]arenes dimers in bilayer membranes. They can transport ≈10⁷ water molecules/channel/second, within one order of magnitude of the transport rates of AQPs, rejecting Na⁺ and K⁺ cations. The dimers have a tubular structure, superposing pillar[5]arene pores of 5 Å diameter with twisted carboxy-phenyl pores of 2.8 Å diameter. This biomimetic platform, with variable pore dimensions within the same structure, offers size restriction reminiscent of natural proteins. It allows water molecules to selectively transit and prevents bigger hydrated cations from passing through the 2.8 Å pore. Molecular simulations prove that dimeric or multimeric honeycomb aggregates are stable in the membrane and form water pathways through the bilayer. Over time, a significant shift of the upper vs. lower layer occurs initiating new unexpected water permeation events through toroidal pores.