‐Theory for Schrödinger systems

In this article, we study for the ‐realization of the vector‐valued Schrödinger operator . Using a noncommutative version of the Dore–Venni theorem due to Monniaux and Prüss, we prove that the ‐realization of , defined on the intersection of the natural domains of the differential and multiplication operators which form , generates a strongly continuous contraction semigroup on . We also study additional properties of the semigroup such as extension to L¹, positivity, ultracontractivity and prove that the generator has compact resolvent.     

Evolution and properties of antiphase boundaries in silicate minerals

Experimental and observational evidence is reviewed for the mechanisms and kinetics of antiphase domain coarsening in silicate minerals. The expected rate law has the form (domain size)ⁿ ≈ annealing time, but the ideal value of n=2 has been observed in only one of three cases. Values of n≈8 or 10 are interpreted as implying adsorption of impurity atoms onto the antiphase boundaries. Diffusion of these impurities can then provide the rate determining step for boundary migration. Local ordering at the boundaries can also provide some stabilising influence, though this does not appear to affect the coarsening rate law. If the stabilisation is sufficient it might result in the development of an incommensurate superstructure, either as a stable phase or as a metastable phase under non-equilibrium conditions. The effective width of these boundaries appears to be ～ 25°, or approximately two unit cells, and their maximum effective interaction length appears to be ～ 4 times this width.     

Time domain simulation of vortex-induced vibrations in stationary and oscillating flows

This paper focuses on the further development of a previously published semi-empirical method for time domain simulation of vortex-induced vibrations (VIV). A new hydrodynamic damping formulation is given, and the necessary coefficients are found from experimental data. It is shown that the new model predicts the observed hydrodynamic damping in still water and for cross-flow oscillations in stationary incoming flow with high accuracy. Next, the excitation force model, which is one component of the total hydrodynamic force model, is optimized by simulating the VIV response of an elastic cylinder in a series of experiments with stationary flow. The optimization is performed by repeating the simulations until the best possible agreement with the experiments is found. The optimized model is then applied to simulate the cross-flow VIV of an elastic cylinder in oscillating flow, without introducing any changes to the hydrodynamic force modeling. By comparison with experiment, it is shown that the model predicts the frequency content, mode and amplitude of vibration with a high level of realism, and the amplitude modulations occurring at high Keulegan–Carpenter numbers are well captured. The model is also utilized to investigate the effect of increasing the maximum reduced velocity and the mass ratio of the elastic cylinder in oscillating flow. Simulations show that complex response patterns with multiple modes and frequencies appear when the maximum reduced velocity is increased. If, however, the mass ratio is increased by a factor of 5, a single mode dominates. This illustrates that, in oscillating flows, the mass ratio is important in determining the mode participation at high maximum reduced velocities.     

Phosphoinositide-binding interface proteins involved in shaping cell membranes

The mechanism by which cell and cell membrane shapes are created has long been a subject of great interest. Among the phosphoinositide-binding proteins, a group of proteins that can change the shape of membranes, in addition to the phosphoinositide-binding ability, has been found. These proteins, which contain membrane-deforming domains such as the BAR, EFC/F-BAR, and the IMD/I-BAR domains, led to inward-invaginated tubes or outward protrusions of the membrane, resulting in a variety of membrane shapes. Furthermore, these proteins not only bind to phosphoinositide, but also to the N-WASP/WAVE complex and the actin polymerization machinery, which generates a driving force to shape the membranes.     

Rivality index neighbourhood algorithm with density and distances weighted schemes for the building of robust QSAR classification models with high reliable applicability domain

The rivality index (RI) is a normalized distance measurement between a molecule and their first nearest neighbours providing a robust prediction of the activity of a molecule based on the known activity of their nearest neighbours. Negative values of the RI describe molecules that would be correctly classified by a statistic algorithm and, vice versa, positive values of this index describe those molecules detected as outliers by the classification algorithms. In this paper, we have described a classification algorithm based on the RI and we have proposed four weighted schemes (kernels) for its calculation based on the measuring of different characteristics of the neighbourhood of molecules for each molecule of the dataset at established values of the threshold of neighbours. The results obtained have demonstrated that the proposed classification algorithm, based on the RI, generates more reliable and robust classification models than many of the more used and well-known machine learning algorithms. These results have been validated and corroborated by using 20 balanced and unbalanced benchmark datasets of different sizes and modelability. The classification models generated provide valuable information about the molecules of the dataset, the applicability domain of the models and the reliability of the predictions.     

Copper-containing dendromesogens: the influence of the metal on the mesomorphism

The synthesis and liquid crystalline behaviour of the first and second generations of a dendrimeric structure based on poly(propyleneimine)(DAB-dendr(NH₂)_x) are reported. 4-(4-n-Alkoxybenzoyloxy)salicylaldehydes are used as mesogenic moieties attached at the peripheral amino groups of the dendrimers giving rise to dendromesogens with four and eight mesogenic branches. From these dendromesogens, considered as organic ligands, were prepared six metal-containing dendrimers which incorporate two or four copper atoms in their structures. All the dendrimeric ligands and three of the metal-containing dendrimers exhibit liquid crystalline properties which were studied by optical microscopy, DSC, X-ray diffraction and EPR spectroscopy.     

Borylated Arylisoquinolines: Photophysical Properties and Switching Behavior of Promising Tunable Fluorophores

A series of nine borylated arylisoquinolines has been prepared with systematic variation in their electronic properties and their photophysical properties were investigated. The color of their fluorescence can be finely tuned by changing the properties of the aryl moiety, which is involved in internal‐charge‐transfer processes. For example, methoxy‐substituted compound 5 showed an intense green emission, whereas dimethylamino‐substituted compound 6 showed an orange‐red emission. These new fluorophores were tested for their potential as molecular switches with external ionic stimuli, such as protons and fluoride ions. On the one hand, protonation of the isoquinoline moiety led to fluorescence enhancement for compounds that showed weak charge transfer and fluorescence quenching for compounds that showed strong charge transfer. On the other hand, the formation of ate complexes with fluoride led to strong fluorescence quenching in all of the investigated cases.     

Theoretical Modelling of Photoswitching of Hyperpolarisabilities in Ruthenium Complexes

Static excited‐state polarisabilities and hyperpolarisabilities of three Ru^II ammine complexes are computed at the density functional theory (DFT) and several correlated ab initio levels. Most accurate modelling of the low energy electronic absorption spectrum is obtained with the hybrid functionals B3LYP, B3P86 or M06 for the complex [Ru^II(NH₃)₅(MeQ⁺)]³⁺ (MeQ⁺=N‐methyl‐4,4′‐bipyridinium, 3 ) in acetonitrile. The match with experimental data is less good for [Ru^II(NH₃)₅L]³⁺ (L=N‐methylpyrazinium, 2 ; N‐methyl‐4‐{E,E‐4‐(4‐pyridyl)buta‐1,3‐dienyl}pyridinium, 4 ). These calculations confirm that the first dipole‐ allowed excited state (FDAES) has metal‐to‐ligand charge‐transfer (MLCT) character. Both the solution and gas‐phase results obtained for 3 by using B3LYP, B3P86 or M06 are very similar to those from restricted active‐space SCF second‐order perturbation theory (RASPT2) with a very large basis set and large active space. However, the time‐dependent DFT λ_max predictions from the long‐range corrected functionals CAM‐B3LYP, LC‐ωPBE and wB97XB and also the fully ab initio resolution of identity approximate coupled‐cluster method (gas‐phase only) are less accurate for all three complexes. The ground state (GS) two‐state approximation first hyperpolarisability β_2SA for 3 from RASPT2 is very close to that derived experimentally via hyper‐Rayleigh scattering, whereas the corresponding DFT‐based values are considerably larger. The β responses calculated by using B3LYP, B3P86 or M06 increase markedly as the π‐conjugation extends on moving along the series 2 → 4 , for both the GS and FDAES species. All three functionals predict substantial FDAES β enhancements for each complex, increasing with the π‐conjugation, up to about sevenfold for 4 . Also, the computed second hyperpolarisabilities γ generally increase in the FDAES, but the results vary between the different functionals.