Padé approximants for functions with branch points — strong asymptotics of Nuttall–Stahl polynomials

Let f be a germ of an analytic function at infinity that can be analytically continued along any path in the complex plane deprived of a finite set of points, \({f \in \mathcal{A}(\bar{\mathbb{C}} \setminus A)}\), \({\# A< \infty}\). J. Nuttall has put forward the important relation between the maximal domain of f where the function has a single-valued branch and the domain of convergence of the diagonal Padé approximants for f. The Padé approximants, which are rational functions and thus single-valued, approximate a holomorphic branch of f in the domain of their convergence. At the same time most of their poles tend to the boundary of the domain of convergence and the support of their limiting distribution models the system of cuts that makes the function f single-valued. Nuttall has conjectured (and proved for many important special cases) that this system of cuts has minimal logarithmic capacity among all other systems converting the function f to a single-valued branch. Thus the domain of convergence corresponds to the maximal (in the sense of minimal boundary) domain of single-valued holomorphy for the analytic function \({f\in\mathcal{A}(\bar{\mathbb{C}} \setminus A)}\). The complete proof of Nuttall’s conjecture (even in a more general setting where the set A has logarithmic capacity 0) was obtained by H. Stahl. In this work, we derive strong asymptotics for the denominators of the diagonal Padé approximants for this problem in a rather general setting. We assume that A is a finite set of branch points of f which have the algebro-logarithmic character and which are placed in a generic position. The last restriction means that we exclude from our consideration some degenerated “constellations” of the branch points.     

Pressure‐Induced Intersite Bi?M (M=Ru, Ir) Valence Transitions in Hexagonal Perovskites

Pressure‐induced charge transfer from Bi to Ir/Ru is observed in the hexagonal perovskites Ba_3+nBiM_2+nO_9+3n (n=0,1; M=Ir,Ru). These compounds show first‐order, circa 1 % volume contractions at room temperature above 5 GPa, which are due to the large reduction in the effective ionic radius of Bi when the 6s shell is emptied on oxidation, compared to the relatively negligible effect of reduction on the radii of Ir or Ru. They are the first such transitions involving 4d and 5d compounds, and they double the total number of cases known. Ab initio calculations suggest that magnetic interactions through very short (ca. 2.6 Å) M M bonds contribute to the finely balanced nature of their electronic states.     

Investigating Membrane-Mediated Antimicrobial Peptide Interactions with Synchrotron Radiation Far-Infrared Spectroscopy

Synchrotron radiation-based Fourier transform infrared spectroscopy enables access to vibrational information from mid over far infrared to even terahertz domains. This information may prove critical for the elucidation of fundamental bio-molecular phenomena including folding-mediated innate host defence mechanisms. Antimicrobial peptides (AMPs) represent one of such phenomena. These are major effector molecules of the innate immune system, which favour attack on microbial membranes. AMPs recognise and bind to the membranes whereupon they assemble into pores or channels destabilising the membranes leading to cell death. However, specific molecular interactions responsible for antimicrobial activities have yet to be fully understood. Herein we probe such interactions by assessing molecular specific variations in the near-THz 400–40 cm⁻¹ range for defined helical AMP templates in reconstituted phospholipid membranes. In particular, we show that a temperature-dependent spectroscopic analysis, supported by 2D correlative tools, provides direct evidence for the membrane-induced and folding-mediated activity of AMPs. The far-FTIR study offers a direct and information-rich probe of membrane-related antimicrobial interactions.     

A Regioselective Synthesis of Novel Functionalized Organochalcogen Compounds by Chalcogenocyclofunctionalization Reactions Based on Chalcogen Halides and Natural Products

The regioselective synthesis of novel functionalized condensed organochalcogen compounds by chalcogenocyclofunctionalization reactions based on chalcogen halides and the natural products thymol and carvacrol has been developed. The reactions of selenium dibromide with allyl thymol and allyl carvacrol proceeded in methylene chloride at room temperature in the presence of NaHCO₃ affording bis[(7-isopropyl-4-methyl-2,3-dihydro-1-benzofuran-2-yl)methyl] and bis[(4-isopropyl-7-methyl-2,3-dihydro-1-benzofuran-2-yl)methyl] selenides in 90–92% yield. Similar sulfides were obtained in 70–72% yields by the reaction of sulfur dichloride in chloroform under reflux. Trihalotellanes containing the same organic moieties were synthesized from allyl thymol, allyl carvacrol and tellurium tetrachloride or tetrabromide in quantitative yields. Corresponding functionalized ditellurides were prepared in 91–92% yields by the reduction of the trichlorotellanes with sodium metabisulfite in two-phase solvent system. The comparison of reactivity of sulfur, selenium and tellurium halides in chalcogenocyclofunctionalization and distinguishing features of each reaction were discussed.     

An Approach to Structural and Functional Modeling of the Surface Morphology of Materials Based on Fluorinated Polymers

Russian Journal of General Chemistry - Dynamic modeling of the polymodal morphological structure of the polymer surface, with modified polyethylene terephthalate as an example, was performed. In...     

Dislocation nonlinearity and nonlinear wave processes in polycrystals with dislocations

Based on the modification of the linear part of the Granato–Lücke dislocation theory of absorption, the equation of state of polycrystalline solids with dissipative and reactive nonlinearity has been derived. The nonlinear effects of the interaction and self-action of longitudinal elastic waves in such media have been theoretically studied.     

Topological transition in coated wire medium

Employing nonlocal homogenization approach, we investigate the properties of a metamaterial consisting of parallel metallic wires with dielectric coating. We demonstrate that manipulation of dielectric contrast between wire dielectric shell and host material at fixed frequency results in dynamic switching of metamaterial dispersion regime from elliptic to the hyperbolic one, i.e. the topological transition takes place. It is proved that such transition can be induced by the variation of the metamaterial temperature. Our findings thus pave a way to the implementation of a tunable ‘elliptic‐hyperbolic’ metamaterial.     

Low-temperature plasticity in nanocrystalline titanium and copper

The stress-strain compressive curves, temperature dependences of the yield stress, and small-inelastic-strain rate spectra of coarse-grained and ultrafine-grained (produced by equal-channel angular pressing) titanium and copper are compared in the temperature range 4.2–300 K. As the temperature decreases, copper undergoes mainly strain hardening and titanium undergoes thermal hardening. The temperature dependences of the yield stress of titanium and copper have specific features which correlate with the behavior of their small-inelastic-strain rate spectra. Under the same loading conditions, the rate of microplastic deformation of ultrafine-grained titanium is lower than that of coarse-grained titanium and the rate peaks shift toward high temperatures. The deformation activation volumes of titanium samples differing in terms of their grain size are (10–35)b ³, where b is the Burgers vector magnitude. The dependences of the yield stress on the grain size at various temperatures are satisfactorily described by the Hall-Petch relation.     

Shocks and cold fronts in galaxy clusters

The currently operating X-ray imaging observatories provide us with an exquisitely detailed view of the Megaparsec-scale plasma atmospheres in nearby galaxy clusters. At z<0.05$z<0.05$, the Chandra  's 1^″$1^{″}$ angular resolution corresponds to linear resolution of less than a kiloparsec, which is smaller than some interesting linear scales in the intracluster plasma. This enables us to study the previously unseen hydrodynamic phenomena in clusters: classic bow shocks driven by the infalling subclusters, and the unanticipated “cold fronts,” or sharp contact discontinuities between regions of gas with different entropies. The ubiquitous cold fronts are found in mergers as well as around the central density peaks in “relaxed” clusters. They are caused by motion of cool, dense gas clouds in the ambient higher-entropy gas. These clouds are either remnants of the infalling subclusters, or the displaced gas from the cluster's own cool cores.     

Effects produced by metal-coated near-field probes on the performance of silicon waveguides and resonators

We study the effects of metal-coated fiber near-field probes on the performance of nanophotonic devices. Employing a heterodyne near-field scanning optical microscope and analyzing transmission characteristics, we find that a metal-coated probe can typically introduce a 3 dB intensity loss and a 0.2 rad phase shift during characterization of a straight waveguide made in a silicon-on-insulator system. In resonant nanophotonic structures such as a 5 mum radius microring resonator, we demonstrate that the probe induces a 1 nm shift in resonant wavelength and decreases the resonator quality factor, Q, from 1100 to 480.