The Ablowitz–Ladik hierarchy integrability analysis revisited: the vertex operator solution representation structure

A regular gradient-holonomic approach to studying the Lax type integrability of the Ablowitz–Ladik hierarchy of nonlinear Lax type integrable discrete dynamical systems in the vertex operator representation is presented. The relationship to the Lie-algebraic integrability scheme is analyzed and the connection with the τ-function representation is discussed.     

Shadow-casted ultrathin surface coatings of titanium and titanium/silicon oxide sol particles via ultrasound-assisted deposition

Ultrasound-assisted deposition (USAD) of sol nanoparticles enables the formation of uniform and inherently stable thin films. However, the technique still suffers in coating hard substrates and the use of fast-reacting sol–gel precursors still remains challenging. Here, we report on the deposition of ultrathin titanium and titanium/silicon hybrid oxide coatings using hydroxylated silicon wafers as a model hard substrate. We use acetic acid as the catalyst which also suppresses the reactivity of titanium tetraisopropoxide while increasing the reactivity of tetraethyl orthosilicate through chemical modifications. Taking the advantage of this peculiar behavior, we successfully prepared titanium and titanium/silicon hybrid oxide coatings by USAD. Varying the amount of acetic acid in the reaction media, we managed to modulate thickness and surface roughness of the coatings in nanoscale. Field-emission scanning electron microscopy and atomic force microscopy studies showed the formation of conformal coatings having nanoroughness. Quantitative chemical state maps obtained by x-ray photoelectron spectroscopy (XPS) suggested the formation of ultrathin (<10 nm) coatings and thickness measurements by rotating analyzer ellipsometry supported this observation. For the first time, XPS chemical maps revealed the transport effect of ultrasonic waves since coatings were directly cast on rectangular substrates as circular shadows of the horn with clear thickness gradient from the center to the edges. In addition to the progress made in coating hard substrates, employing fast-reacting precursors and achieving hybrid coatings; this report provides the first visual evidence on previously suggested “acceleration and smashing” mechanism as the main driving force of USAD.     

Quantitative measurement of hard X-ray spectra from laser-driven fast ignition plasma

Absolute Kα line spectroscopy is proposed for studying laser–plasma interactions taking place in the Au cone-guided fast ignition targets. X-ray spectra ranging from 20 to 100 keV were quantitatively measured with a Laue spectrometer composed of a cylindrically curved crystal and a filter-absorption method for Bremsstrahlung continuum emission. The absolute sensitivities of the Laue spectrometer systems were calibrated using pre-characterized laser-produced X-ray sources and radioisotopes. The integrated reflectivity for the crystal is in good agreement with predictions by an X-ray diffraction code. The energy transfer efficiency from incident laser beams to hot electrons, as the energy transfer mechanism, is derived from this work. The absolute yield of Au and Ta Kα lines were measured in the fast ignition experimental campaign performed at Institute of Laser Engineering, Osaka University. Applying the hot electron spectrum information from electron spectrometer and scaling laws, the energy transfer efficiency from the incident LFEX, a kJ-class PW laser, to hot electrons was derived for the first time.     

Dislocation driven chromium precipitation in Fe-9Cr binary alloy: a positron lifetime study

The influence of initial heat treatment on anomalous Cr precipitation within high temperature solubility region of the Fe–9Cr alloy has been investigated using positron lifetime studies. Air-quenched samples with pre-existing dislocations exhibited a distinct annealing stage in positron lifetime between 800 and 1100?K corresponding to Cr-precipitation. During this stage, Transmission Electron Microscopy showed fine precipitates of average size 4 nm, dispersed throughout the sample and from Energy-dispersive X-ray spectroscopy (EDS) analysis they are found to be Cr-enriched. The presence of dislocations is found to be responsible for Cr precipitation.     

A preliminary approach of dynamic identification of slender buildings by neuronal networks

The study of the dynamic behavior of slender masonry structures is usually related to the preservation of the historic heritage. This study, for bell towers and industrial masonry chimneys, is particularly relevant in areas with an important seismic hazard. The analysis of the dynamic behavior of masonry structures is particularly complex due to the multiple effects that can affect the variation of its main frequencies along the seasons of the year: temperature and humidity. Moreover, these dynamic properties also vary considerably in structures built in areas where land subsidence due to the variation of the phreatic level along the year is particularly evident: the stiffness of the soil–structure interaction also varies. This paper presents a study to evaluate the possibility of detecting the variation of groundwater level based on the readings obtained using accelerometers in different positions on the structure. To do this a general case study was considered: a 3D numerical model of a bellower. The variation of the phreatic level was evaluated between 0 and −20 m, and 81 cases studies were developed modifying the rigidity of the soil–structure interaction associated to a position of the phreatic level. To simulate the dispositions of accelerometers on a real construction, 16 points of the numerical model were selected along the structure to obtain modal displacements in two orthogonal directions. Through an adjustment by using neural networks, a good correlation has been observed between the predicted position of the water table and acceleration readings obtained from the numerical model. It is possible to conclude that with a discrete register of accelerations on the tower it is possible to predict the water table depth.     

Efficient removal of crystal violet and methylene blue from wastewater by ultrasound nanoparticles Cu-MOF in comparison with mechanosynthesis method

The present investigation reports the synthesis of CuBTC (BTC = 1,3,5-benzenetricarboxylate) metal–organic frameworks (MOFs) under solid-state conditions and ultrasound irradiation. Herein, we study uptake and release properties of crystal violet (CV) and methylene blue (MB) from ultrasound nano-CuBTC MOF in comparison with mechanosynthesis method (bulk structure). The ultrasound-assisted methods give a decrease in the surface area as calculated from the reduced nitrogen adsorption capability. In comparison, the uptake of guest molecules on ultrasound nano-CuBTC is remarkable and clearly exceeds that of bulk structure in the aqueous solution of guests. In bulk compound the channel length is increased so that the amount of adsorption is decreased a little. The small guest enters and leaves the cavity rapidly, whereas larger guests enter slowly due to their size relative to the size of the gaps in the capsule. As a result, the uptake and release of MB from CuBTC is faster than that of CV.     

Numerical study on combustion of H2—O2 in a supersonic reactive expansion in a nozzle

A study on expansion flow inside a nozzle considering full mechanism chemistry of hydrogen and oxygen was carried out. In this study, a full implicit scheme for turbulent reactive flow was obtained by combining the second order TVD scheme of Yee and Harten (1987, Implicit TVD schemes for hyperbolic conservation laws in curvilinear coordinates. American Institute of Aeronautics and Astronautics Journal, 25(2), 266–274) with the efficient implicit lower-upper scheme of Shuen and Yoon (1989, Numerical study of chemically reacting flows using a lower-upper symmetric successive overrelaxation scheme. American Institute of Aeronautics and Astronautics Journal, 27(12), 1752–1756). The species equations, Navier–Stokes equations and turbulence model were implemented in the numerical scheme and solved in conjunction with full detailed finite rate chemistry. The numerical scheme is verified by comparison with experimental results of a converging–diverging nozzle. Effects of inlet pressure, temperature and fuel-oxidant mass ratio on nozzle flow field were studied. Variation of chemical species under different conditions was investigated by considering a chemical mechanism. Results show that increasing inlet pressure increases the rate of reactions due to increasing the concentration of reactants. For lower inlet pressure the radical H increases slightly in the diverging part of the nozzle, while for higher pressures it decreases along the nozzle. Inlet fuel–oxidant mass ratio affects the variation of all species with a greater effect for a near stoichiometric ratio. It was also shown that a higher inlet temperature provides a more enhanced reaction zone in the diverging part of the nozzle.     

ХроматограФкчеекое разделеиие изотоиов җелеза

Es werden Aufbau, Arbeitsweise und Eigenschaften einer Apparatur beschrieben, mit der natiürliche Tritium-Aktivitäten in Oberflächen- und Grundwässern gemessen werden können. Diese Messungen erfolgen in 4 Arbitsschritten: elektrolytische Anreicherung der natiärlichen Tritium-Konzentrationen, Messung des Anreicherungsfaktors mit einem Flüssigkeitsszintillationszähler, Synthese von Äthan aus dem angereicherten Probenwasser und tritiumfreiem Acetylen, Messung des Probentritiums in Äthan mit einem Proportionalzähler. Die untcre Nachweisgrenze (Meβzeit 48 Studnden, statistischer Fehler 50%) beträgt 1 T.E.     

On the domain of fractional Laplacians and related generators of Feller processes

In this paper we study the domain of the generator of stable processes, stable-like processes and more general pseudo- and integro-differential operators which naturally arise both in analysis and as infinitesimal generators of Lévy- and Lévy-type (Feller) processes. In particular we obtain conditions on the symbol of the operator ensuring that certain (variable order) Hölder and Hölder–Zygmund spaces are in the domain. We use tools from probability theory to investigate the small-time asymptotics of the generalized moments of a Lévy or Lévy-type process ${(X_t)}_{t\ge 0}$,

$\underset{t\to 0}{\lim }?\frac{1}{t}({\mathbb{E}}^{x}f(X_t)?f(x)),x\in {\mathbb{R}}^d,$

for functions f which are not necessarily bounded or differentiable. The pointwise limit exists for fixed $x\in {\mathbb{R}}^d$ if f satisfies a Hölder condition at x. Moreover, we give sufficient conditions which ensure that the limit exists uniformly in the space of continuous functions vanishing at infinity. As an application we prove that the domain of the generator of ${(X_t)}_{t\ge 0}$ contains certain Hölder spaces of variable order. Our results apply, in particular, to stable-like processes, relativistic stable-like processes, solutions of Lévy-driven SDEs and Lévy processes.