Solitons supported by singular spatial modulation of the Kerr nonlinearity

We introduce a setting based on the one-dimensional (1D) nonlinear Schroedinger equation (NLSE) with the self-focusing (SF) cubic term modulated by a singular function of the coordinate, |x|^{-a}. It may be additionally combined with the uniform self-defocusing (SDF) nonlinear background, and with a similar singular repulsive linear potential. The setting, which can be implemented in optics and BEC, aims to extend the general analysis of the existence and stability of solitons in NLSEs. Results for fundamental solitons are obtained analytically and verified numerically. The solitons feature a quasi-cuspon shape, with the second derivative diverging at the center, and are stable in the entire existence range, which is 0 < a < 1. Dipole (odd) solitons are found too. They are unstable in the infinite domain, but stable in the semi-infinite one. In the presence of the SDF background, there are two subfamilies of fundamental solitons, one stable and one unstable, which exist together above a threshold value of the norm (total power of the soliton). The system which additionally includes the singular repulsive linear potential emulates solitons in a uniform space of the fractional dimension, 0 < D < 1. A two-dimensional extension of the system, based on the quadratic nonlinearity, is formulated too.Comment: Physical Review A, in pres

Extragalactic Relativistic Jets and Nuclear Regions in Galaxies

Past years have brought an increasingly wider recognition of the ubiquity of relativistic outflows (jets) in galactic nuclei, which has turned jets into an effective tool for investigating the physics of nuclear regions in galaxies. A brief summary is given here of recent results from studies of jets and nuclear regions in several active galaxies with prominent outflows.Comment: 5 pages; contribution to ESO Astrophysical Symposia, "Relativistic Astrophysics and Cosmology", eds. B. Aschenbach, V. Burwitz, G. Hasinger, B. Leibundgut (Springer: Heidelberg 2006

Effect of Structure and Texture on Failure of Pipe Steel Sheets produced by TMCP

The method of orientation microscopy (EBSD) is used to study the structure and texture of low-carbon, low-alloy pipe steel sheets processed by controlled thermomechanical processing (TMCP). The temperatures of isothermal hot rolling varied. Samples cut from sheets showed a different fracture tendency during mechanical testing. The formation of cleavages (secondary cracks) during failure of steel is related to the presence of ferrite grains with orientation {001} &lt;110&gt; extended in the hot rolling direction. The formation of grains is a consequence of the isothermal hot rolling below the temperature

The features of steel surface hardening with high energy heating by high frequency currents and shower cooling

The paper examines the process of surface hardening of steel 45 with the help of high energy heating by high frequency currents with simultaneous shower water cooling. We theoretically justified and experimentally proved a possibility of liquid phase forming in the course of heating not on the surface, but in the depth of the surface layer

Practical analytical solutions for benchmarking of 2-D and 3-D geodynamic Stokes problems with variable viscosity

Geodynamic modeling is often related with challenging computations involving solution of the Stokes and continuity equations under the condition of highly variable viscosity. Based on a new analytical approach we have developed particular analytical solutions for 2-D and 3-D incompressible Stokes flows with both linearly and exponentially variable viscosity. We demonstrate how these particular solutions can be converted into 2-D and 3-D test problems suitable for benchmarking numerical codes aimed at modeling various mantle convection and lithospheric dynamics problems. The Main advantage of this new generalized approach is that a large variety of benchmark solutions can be generated, including relatively complex cases with open model boundaries, non-vertical gravity and variable gradients of the viscosity and density fields, which are not parallel to the Cartesian axes. Examples of respective 2-D and 3-D MatLab codes are provided with this paper

Исследование равновесной структуры молекулы 3,4-дицианофуроксана

Objectives. The study set out to determine the equilibrium parameters of the 3,4-dicyanofuroxan molecule by means of molecule geometry optimization by quantum chemistry methods, verify the adequacy of the methods used, and compare the obtained results with X-ray diffraction analysis (XRD) and gas electron diffraction (GED) data.Methods. Quantum chemical calculations were carried out using B3LYP, MP2, and CCSD(T) methods with 6-31G(d,p), cc-pVTZ, and aug-cc-pVTZ basis sets.Results. The equilibrium molecular structure of 3,4-dicyanofuroxan was refined by means of quantum chemical calculations using the Gaussian09 program. The geometrical parameters were compared with the structure of this compound in the solid phase and a number of related compounds in gas and solid phases. It was theoretically established that the planar equilibrium structure of the dicyanofuroxan molecule has CS symmetry. The structure of the free dicyanofuroxan molecule was found to differ depending on the phase. The B3LYP and CCSD(T) methods describe the molecular structure of dicyanofuroxan more accurately than the MP2 method. A regularity was revealed, according to which an increase in the basis, as a rule, leads to a better agreement of the geometry, regardless of the functional.Conclusions. The calculations performed are in good agreement with the literature data and results of joint analysis by GED and XRD. The effect of cyano substituents on the ring geometry is observed in comparison with the literature data for the dicyanofuroxan molecule. For the molecule in question, it is better to use the B3LYP/aug-cc-pVTZ method. The values of geometric parameters obtained by this method are in better agreement with the structure in the gas phase. The discrepancies with the experimental XRD results may be due to interactions in the crystal structure. Differences in the geometric parameters obtained on the basis of different functionals and bases make this molecule interesting for experimental structural studies using GED or microwave spectroscopy, which will permit the identification of optimal methods and bases for obtaining the geometric parameters of furoxan class molecules.Цели. Определение равновесных параметров молекулы 3,4-дицианофуроксана посредством оптимизации геометрии молекулы методами квантовой химии, проверка адекватности используемых методов, а также сопоставление полученных результатов с данными рентгенодифракционного анализа (РСА) и газовой электронографии (ГЭ) родственных соединений.Методы. Квантовохимические расчеты методами B3LYP, MP2 и CCSD(T) c базисными наборами 6-31G(d,p), cc-pVTZ и aug-cc-pVTZ.Результаты. Уточнена равновесная молекулярная структура 3,4-дициано- фуроксана с помощью квантово-химических расчетов в программе Gaussian09. Проведено сравнение геометрических параметров со структурой данного соединения в твердой фазе и с рядом родственных соединений в газовой и твердой фазе. Теоретически установлено, что равновесная структура молекулы дицианофуроксана является плоской и имеет симметрию CS. Установлено, что структура свободной молекулы дицианофуроксана в зависимости от фазы различается. Методы CCSD(T) и B3LYP точнее описывает молекулярную структуру дицианофуроксана по сравнению с методом MP2. Выявлена закономерность, согласно которой увеличение базиса, как правило, приводит к лучшему согласованию геометрии независимо от функционала.Выводы. Проведенные расчеты хорошо согласуются с литературными данными, а также результатами совместного анализа методами ГЭ и РСА. Влияние циано-заместителей на геометрию кольца наблюдается в сравнении с литературными данными для молекулы дицианофуроксана. Для рассматриваемой молекулы лучше использовать метод B3LYP/aug-cc-pVTZ. Значения геометрических параметров, полученные этим методом, лучше согласуются со структурой в газовой фазе. Расхождения с экспериментальными результатами РСА могут быть обусловлены взаимодействиями в кристаллической структуре. Различия в геометрических параметрах, полученных на основе разных функционалов и базисов, делают эту молекулу интересной для проведения экспериментального структурного исследования методами ГЭ или микроволновой спектроскопии, что позволит в будущем найти оптимальные методы и базисы для получения геометрических параметров молекул класса фуроксанов

Controlling circular polarization of light emitted by quantum dots using chiral photonic crystal slab

We study the polarization properties of light emitted by quantum dots that are embedded in chiral photonic crystal structures made of achiral planar GaAs waveguides. A modification of the electromagnetic mode structure due to the chiral grating fabricated by partial etching of the wave\-guide layer has been shown to result in a high circular polarization degree $\rho_c$ of the quantum dot emission in the absence of external magnetic field. The physical nature of the phenomenon can be understood in terms of the reciprocity principle taking into account the structural symmetry. At the resonance wavelength, the magnitude of $|\rho_c|$ is predicted to exceed 98%. The experimentally achieved value of $|\rho_c|=81$% is smaller, which is due to the contribution of unpolarized light scattered by grating defects, thus breaking its periodicity. The achieved polarization degree estimated removing the unpolarized nonresonant background from the emission spectra can be estimated to be as high as 96%, close to the theoretical prediction

The effect of accelerated cooling on the structure of pipe steels for thermomechanical controlled processing

Scanning electron microscopy with orientation analysis by the electron backscatter diffraction (EBSD) method is used to study microstructures and textures formed in low-carbon low-alloy pipe steel after thermomechanical controlled processing (TMCP) and subsequent quenching with cooling rates of 50 to 700 °/s. It has been established that, in the range of industrial rates of cooling between 50 and 350 °/s from austenitic regions, the γ→α transformation starts at temperatures of 700-670 °C and proceeds by the shear mechanism. As a result, a bainite structure of different dispersity with martensitic inclusions is predominantly formed. © 2018 Author(s)