Schrödinger operators on periodic discrete graphs

We consider Schrödinger operators with periodic potentials on periodic discrete graphs. The spectrum of the Schrödinger operator consists of an absolutely continuous part (a union of a finite number of non-degenerated bands) plus a finite number of flat bands, i.e., eigenvalues of infinite multiplicity. We obtain estimates of the Lebesgue measure of the spectrum in terms of geometric parameters of the graph and show that they become identities for some class of graphs. Moreover, we obtain stability estimates and show the existence and positions of large number of flat bands for specific graphs. The proof is based on the Floquet theory and the precise representation of fiber Schrödinger operators, constructed in the paper.     

Influence of inert components on the formation of conducting channels in ion-exchange membranes

In this work, the results of investigation of the influence of inert binder and reinforcing fabric on structural organization and mechanism of current transfer in homogeneous and heterogeneous ion-exchange membranes are presented by theoretical analysis of parameters of the extended three-wire conductivity model. It was established that analogy in reorganization of the current paths takes place in the course of inclusion of the reinforcing fabric in perfluorinated membranes and addition of polyethylene and nylon 6 to ion-exchange resins during preparation of heterogeneous membranes. In comparison with perfluorinated membranes, the essential difference in conducting properties of heterogeneous membranes is the opportunity for the current transfer via the channel filled with equilibrium solution. The size of this channel decreases with increase in the volume fraction of the inert component inside the membrane.     

Competitive Metal Coordination of Hexaaminotriphenylene on Cu(111) by Intrinsic Copper Versus Extrinsic Nickel Adatoms

The interplay between the self-assembly and surface chemistry of 2,3,6,7,10,11-hexaaminotriphenylene (HATP) on Cu(111) was complementarily studied by high-resolution scanning tunneling microscopy (STM) and X-ray photoelectron spectroscopy (XPS) under ultra-high vacuum conditions. To shed light on the competitive metal coordination, comparative experiments were carried out on pristine and nickel-covered Cu(111). Directly after room-temperature deposition of HATP onto pristine Cu(111), self-assembled aggregates were observed by STM, and XPS results indicated still protonated amino groups. Annealing up to 200 °C activated the progressive single deprotonation of all amino groups as indicated by chemical shifts of both the N 1s and C 1s core levels in the XP spectra. This enabled the formation of topologically diverse π–d conjugated coordination networks with intrinsic copper adatoms. The basic motif of these networks was a metal–organic trimer, in which three HATP molecules were coordinated by Cu₃ clusters, as corroborated by the accompanying density functional theory (DFT) simulations. Additional deposition of more reactive nickel atoms resulted in both chemical and structural changes with deprotonation and formation of bis(diimino)–Ni bonded networks already at room temperature. Even though fused hexagonal metal-coordinated pores were observed, extended honeycomb networks remained elusive, as tentatively explained by the restricted reversibility of these metal–organic bonds.     

Analysis of curing reaction of liquid-crystalline epoxy compositions by using temperature-modulated DSC TOPEM®

Journal of Thermal Analysis and Calorimetry - The curing behaviour of the composition of a liquid-crystalline diepoxy monomer (LCEM) with the central triaromatic mesogenic group was studied using...     

Tuning Chemical and Physical Properties of Phosphorus Corroles for Advanced Applications

Although the affinity of metallocorroles to axial ligands is quite low, this is not the case when the chelated element is phosphorus. This work is hence focused on the mechanism of ligand exchange of six-coordinate phosphorus corroles as a tool for affecting their chemical and physical properties. These fundamental investigations allowed for the development of facile methodologies for the synthesis of a large series of complexes and the establishment of several new structure/activity profiles that may be used to understand and predict spectroscopic features and for tailor-made modification of photophysical and electrochemical properties. This is exemplified by the facile access to complexes with terminal groups that are of large potential for practical applications based on click chemistry, optical imaging, and surface science.     

Fluorescent core-shell polymer particles containing luminophore dyes: synthesis and optical response to acetone

Monodisperse dye-containing crosslinked particles are promising for application in novel optical chemical sensors due to their intrinsic sensitivity. However, preparation of these particles in aqueous media still remains a challenge, since luminophores inhibit radical processes or else cannot embed into polymer chains because of difference in monomer reactivity ratios. In this work, novel dye-containing monodisperse crosslinked particles were prepared and characterized. In order to obtain dye-containing monodisperse crosslinked particles, we studied seed copolymerization of styrene in the presence of divinylbenzene. The influence of nature and concentration of the used comonomers and co-solvents on shape, size distributions and surface characteristics of the particles formed was investigated. Shapes and diameters of the particles were analyzed by DLS, TEM and SEM. The data of SEM and optical spectroscopy studies demonstrated that the synthesized particles were able to self-assemble into thin-film three-dimensional ordered structures. Finally, the structures under study are promising for development of sensor devices with optical response to acetone.     

Phase behaviour,structural properties and intermolecular interactions of systems based on substituted thiacalix[4]arene and nonionic surfactants

Supramolecular organised materials were prepared from nonionic surfactants and the following macrocyclic ionic liquids: n-tert-butylthiacalix[4]arenes containing quaternary ammonium fragments with amino acid substituents. Tetraethylene glycol monododecyl ether and decadiethylene glycol monododecyl ether were used as nonionic surfactants. They form lamellar and hexagonal mesophases in aqueous media, respectively. Liquid crystal and structural properties of these systems were studied. Intermolecular interactions of system components leading to formation of lyomesophases were estimated. Molecular structure of thiacalixarene contributes to the formation of a hydrogen bonding with surfactants. This process, in turn, initiates formation of a denser packed hexagonal structure.     

NIFTy 3 – Numerical Information Field Theory: A Python Framework for Multicomponent Signal Inference on HPC Clusters

NIFTy , “Numerical Information Field Theory,” is a software framework designed to ease the development and implementation of field inference algorithms. Field equations are formulated independently of the underlying spatial geometry allowing the user to focus on the algorithmic design. Under the hood, NIFTy ensures that the discretization of the implemented equations is consistent. This enables the user to prototype an algorithm rapidly in 1D and then apply it to high‐dimensional real‐world problems. This paper introduces NIFTy  3, a major upgrade to the original NIFTy  framework. NIFTy  3 allows the user to run inference algorithms on massively parallel high performance computing clusters without changing the implementation of the field equations. It supports n‐dimensional Cartesian spaces, spherical spaces, power spaces, and product spaces as well as transforms to their harmonic counterparts. Furthermore, NIFTy  3 is able to handle non‐scalar fields, such as vector or tensor fields. The functionality and performance of the software package is demonstrated with example code, which implements a mock inference inspired by a real‐world algorithm from the realm of information field theory. NIFTy  3 is open‐source software available under the GNU General Public License v3 (GPL‐3) at https://gitlab.mpcdf.mpg.de/ift/NIFTy/tree/NIFTy_3 .