On the Galois coverings of a cluster-tilted algebra

We study the module category of a certain Galois covering of a cluster-tilted algebra which we call the cluster repetitive algebra. Our main result compares the module categories of the cluster repetitive algebra of a tilted algebra C and the repetitive algebra of C, in the sense of Hughes and Waschbüsch.     

1,1′ Ferrocenylenediol as chelating ligand for cobalt in fivefold and sixfold coordination geometry: Synthesis,Electrochemistry and X-ray crystal structure of [{((1,1′ O2(η5-C5H5)2Fe)2}Co(OEt2){(η5-Me5C5)Co}2] and [{((1,1′ O2(η5-C5H5)2Fe)3}Co((η5-EtMe4C5)Co)2]

The title compounds 3 and 4 were synthesized by reaction of 1,1′ ferrocenylenediol with the Co triple decker compounds [{(η⁵-Me₅C₅)Co}₂(η⁶:η⁶-toluene)] and [{(η⁵-EtMe₄C₅)Co}₂(η⁶:η⁶-toluene)], respectively. The central Co atom of 3 is coordinated by five O atoms in a square-pyramidal manner. The remaining two Co atoms of 3 are coordinated to a Me₅C₅ ligand in a η⁵-fashion and by the two O atoms of two 1,1′ ferrocenylenediolato ligands which serve as chelating ligands. In 4, the central Co atom is coordinated to all six O atoms of three ferrocenylenediolato ligands in a trigonal-prismatic manner, whereas the two other Co atoms are coordinated by an EtMe₄C₅ ligand in a η⁵-fashion and by three O atoms of three ferrocenylenediolato ligands resulting in an overall tripoidal structure for 4.     

Supercoiling induces denaturation bubbles in circular DNA

We present a theoretical framework for the thermodynamic properties of supercoiling-induced denaturation bubbles in circular double-stranded DNA molecules. We explore how DNA supercoiling, ambient salt concentration, and sequence heterogeneity impact on the bubble occurrence. An analytical derivation of the probability distribution to find multiple bubbles is derived and the relevance for supercoiled DNA discussed. We show that in?vivo sustained DNA bubbles are likely to occur due to partial twist release in regions rich in weaker AT base pairs. Single DNA plasmid imaging experiments clearly demonstrate the existence of bubbles in free solution.     

Signatures of the Unruh effect from electrons accelerated by ultrastrong laser fields

We calculate the radiation resulting from the Unruh effect for strongly accelerated electrons and show that the photons are created in pairs whose polarizations are perfectly correlated. Apart from the photon statistics, this quantum radiation can further be discriminated from the classical (Larmor) radiation via the different spectral and angular distributions. The signatures of the Unruh effect become significant if the external electromagnetic field accelerating the electrons is not too far below the Schwinger limit and might be observable with future facilities. Finally, the corrections due to the birefringent nature of the QED vacuum at such ultrahigh fields are discussed.     

Thermal emission properties of 2D and 3D silicon photonic crystals

We present measurements of the thermal emission properties of 2D and 3D silicon photonic crystals with and without substrate heated resistively as well as passively with an aluminium hotplate. The out-of-plane and in-plane emission properties were recorded and compared to numerical simulation. It turned out that for the in-plane 2D photonic crystal and out-of-plane 3D photonic crystal emission a photonic stop gap effect is visible. For the out-of-plane 2D photonic crystal emission, no photonic bandgap effect is observable but instead strong silicon oxide emission from native oxide inside the pores of silicon are observable. A model for the modified thermal emission is presented.     

Formation of Glyoxylic Acid in Interstellar Ices: A Key Entry Point for Prebiotic Chemistry

With nearly 200 molecules detected in interstellar and circumstellar environments, the identification of the biologically relevant α‐keto carboxylic acid, glyoxylic acid (HCOCOOH), is still elusive. Herein, the formation of glyoxylic acid via cosmic‐ray driven, non‐equilibrium chemistry in polar interstellar ices of carbon monoxide (CO) and water (H₂O) at 5 K via barrierless recombination of formyl (HCO) and hydroxycarbonyl radicals (HOCO) is reported. In temperature‐programmed desorption experiments, the subliming neutral molecules were selectively photoionized and identified based on the ionization energy and distinct mass‐to‐charge ratios in combination with isotopically labeled experiments exploiting reflectron time‐of‐flight mass spectrometry. These studies unravel a key reaction path to glyoxylic acid, an organic molecule formed in interstellar ices before subliming in star‐forming regions like SgrB2(N), thus providing a critical entry point to prebiotic organic synthesis.     

Local Multigrid in H（curl）

We consider H（curl, Ω）-elliptic variational problems on bounded Lipschitz polyhedra and their finite element Galerkin discretization by means of lowest order edge elements. We assume that the underlying tetrahedral mesh has been created by successive local mesh refinement, either by local uniform refinement with hanging nodes or bisection refinement. In this setting we develop a convergence theory for the the so-called local multigrid correction scheme with hybrid smoothing. We establish that its convergence rate is uniform with respect to the number of refinement steps. The proof relies on corresponding results for local multigrid in a H^1 （Ω）-context along with local discrete Helmholtz-type decompositions of the edge element space.