3,753 research outputs found
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
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} <110> extended in the hot rolling direction. The formation of grains is a consequence of the isothermal hot rolling below the temperature
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
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
ΠΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠ΅ ΡΠ°Π²Π½ΠΎΠ²Π΅ΡΠ½ΠΎΠΉ ΡΡΡΡΠΊΡΡΡΡ ΠΌΠΎΠ»Π΅ΠΊΡΠ»Ρ 3,4-Π΄ΠΈΡΠΈΠ°Π½ΠΎΡΡΡΠΎΠΊΡΠ°Π½Π°
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.Π¦Π΅Π»ΠΈ. ΠΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΠ΅ ΡΠ°Π²Π½ΠΎΠ²Π΅ΡΠ½ΡΡ
ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΎΠ² ΠΌΠΎΠ»Π΅ΠΊΡΠ»Ρ 3,4-Π΄ΠΈΡΠΈΠ°Π½ΠΎΡΡΡΠΎΠΊΡΠ°Π½Π° ΠΏΠΎΡΡΠ΅Π΄ΡΡΠ²ΠΎΠΌ ΠΎΠΏΡΠΈΠΌΠΈΠ·Π°ΡΠΈΠΈ Π³Π΅ΠΎΠΌΠ΅ΡΡΠΈΠΈ ΠΌΠΎΠ»Π΅ΠΊΡΠ»Ρ ΠΌΠ΅ΡΠΎΠ΄Π°ΠΌΠΈ ΠΊΠ²Π°Π½ΡΠΎΠ²ΠΎΠΉ Ρ
ΠΈΠΌΠΈΠΈ, ΠΏΡΠΎΠ²Π΅ΡΠΊΠ° Π°Π΄Π΅ΠΊΠ²Π°ΡΠ½ΠΎΡΡΠΈ ΠΈΡΠΏΠΎΠ»ΡΠ·ΡΠ΅ΠΌΡΡ
ΠΌΠ΅ΡΠΎΠ΄ΠΎΠ², Π° ΡΠ°ΠΊΠΆΠ΅ ΡΠΎΠΏΠΎΡΡΠ°Π²Π»Π΅Π½ΠΈΠ΅ ΠΏΠΎΠ»ΡΡΠ΅Π½Π½ΡΡ
ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠΎΠ² Ρ Π΄Π°Π½Π½ΡΠΌΠΈ ΡΠ΅Π½ΡΠ³Π΅Π½ΠΎΠ΄ΠΈΡΡΠ°ΠΊΡΠΈΠΎΠ½Π½ΠΎΠ³ΠΎ Π°Π½Π°Π»ΠΈΠ·Π° (Π Π‘Π) ΠΈ Π³Π°Π·ΠΎΠ²ΠΎΠΉ ΡΠ»Π΅ΠΊΡΡΠΎΠ½ΠΎΠ³ΡΠ°ΡΠΈΠΈ (ΠΠ) ΡΠΎΠ΄ΡΡΠ²Π΅Π½Π½ΡΡ
ΡΠΎΠ΅Π΄ΠΈΠ½Π΅Π½ΠΈΠΉ.ΠΠ΅ΡΠΎΠ΄Ρ. ΠΠ²Π°Π½ΡΠΎΠ²ΠΎΡ
ΠΈΠΌΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΡΠ°ΡΡΠ΅ΡΡ ΠΌΠ΅ΡΠΎΠ΄Π°ΠΌΠΈ B3LYP, MP2 ΠΈ CCSD(T) c Π±Π°Π·ΠΈΡΠ½ΡΠΌΠΈ Π½Π°Π±ΠΎΡΠ°ΠΌΠΈ 6-31G(d,p), cc-pVTZ ΠΈ aug-cc-pVTZ.Π Π΅Π·ΡΠ»ΡΡΠ°ΡΡ. Π£ΡΠΎΡΠ½Π΅Π½Π° ΡΠ°Π²Π½ΠΎΠ²Π΅ΡΠ½Π°Ρ ΠΌΠΎΠ»Π΅ΠΊΡΠ»ΡΡΠ½Π°Ρ ΡΡΡΡΠΊΡΡΡΠ° 3,4-Π΄ΠΈΡΠΈΠ°Π½ΠΎ- ΡΡΡΠΎΠΊΡΠ°Π½Π° Ρ ΠΏΠΎΠΌΠΎΡΡΡ ΠΊΠ²Π°Π½ΡΠΎΠ²ΠΎ-Ρ
ΠΈΠΌΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΠ°ΡΡΠ΅ΡΠΎΠ² Π² ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌΠ΅ Gaussian09. ΠΡΠΎΠ²Π΅Π΄Π΅Π½ΠΎ ΡΡΠ°Π²Π½Π΅Π½ΠΈΠ΅ Π³Π΅ΠΎΠΌΠ΅ΡΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΎΠ² ΡΠΎ ΡΡΡΡΠΊΡΡΡΠΎΠΉ Π΄Π°Π½Π½ΠΎΠ³ΠΎ ΡΠΎΠ΅Π΄ΠΈΠ½Π΅Π½ΠΈΡ Π² ΡΠ²Π΅ΡΠ΄ΠΎΠΉ ΡΠ°Π·Π΅ ΠΈ Ρ ΡΡΠ΄ΠΎΠΌ ΡΠΎΠ΄ΡΡΠ²Π΅Π½Π½ΡΡ
ΡΠΎΠ΅Π΄ΠΈΠ½Π΅Π½ΠΈΠΉ Π² Π³Π°Π·ΠΎΠ²ΠΎΠΉ ΠΈ ΡΠ²Π΅ΡΠ΄ΠΎΠΉ ΡΠ°Π·Π΅. Π’Π΅ΠΎΡΠ΅ΡΠΈΡΠ΅ΡΠΊΠΈ ΡΡΡΠ°Π½ΠΎΠ²Π»Π΅Π½ΠΎ, ΡΡΠΎ ΡΠ°Π²Π½ΠΎΠ²Π΅ΡΠ½Π°Ρ ΡΡΡΡΠΊΡΡΡΠ° ΠΌΠΎΠ»Π΅ΠΊΡΠ»Ρ Π΄ΠΈΡΠΈΠ°Π½ΠΎΡΡΡΠΎΠΊΡΠ°Π½Π° ΡΠ²Π»ΡΠ΅ΡΡΡ ΠΏΠ»ΠΎΡΠΊΠΎΠΉ ΠΈ ΠΈΠΌΠ΅Π΅Ρ ΡΠΈΠΌΠΌΠ΅ΡΡΠΈΡ CS. Π£ΡΡΠ°Π½ΠΎΠ²Π»Π΅Π½ΠΎ, ΡΡΠΎ ΡΡΡΡΠΊΡΡΡΠ° ΡΠ²ΠΎΠ±ΠΎΠ΄Π½ΠΎΠΉ ΠΌΠΎΠ»Π΅ΠΊΡΠ»Ρ Π΄ΠΈΡΠΈΠ°Π½ΠΎΡΡΡΠΎΠΊΡΠ°Π½Π° Π² Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΠΈ ΠΎΡ ΡΠ°Π·Ρ ΡΠ°Π·Π»ΠΈΡΠ°Π΅ΡΡΡ. ΠΠ΅ΡΠΎΠ΄Ρ CCSD(T) ΠΈ B3LYP ΡΠΎΡΠ½Π΅Π΅ ΠΎΠΏΠΈΡΡΠ²Π°Π΅Ρ ΠΌΠΎΠ»Π΅ΠΊΡΠ»ΡΡΠ½ΡΡ ΡΡΡΡΠΊΡΡΡΡ Π΄ΠΈΡΠΈΠ°Π½ΠΎΡΡΡΠΎΠΊΡΠ°Π½Π° ΠΏΠΎ ΡΡΠ°Π²Π½Π΅Π½ΠΈΡ Ρ ΠΌΠ΅ΡΠΎΠ΄ΠΎΠΌ MP2. ΠΡΡΠ²Π»Π΅Π½Π° Π·Π°ΠΊΠΎΠ½ΠΎΠΌΠ΅ΡΠ½ΠΎΡΡΡ, ΡΠΎΠ³Π»Π°ΡΠ½ΠΎ ΠΊΠΎΡΠΎΡΠΎΠΉ ΡΠ²Π΅Π»ΠΈΡΠ΅Π½ΠΈΠ΅ Π±Π°Π·ΠΈΡΠ°, ΠΊΠ°ΠΊ ΠΏΡΠ°Π²ΠΈΠ»ΠΎ, ΠΏΡΠΈΠ²ΠΎΠ΄ΠΈΡ ΠΊ Π»ΡΡΡΠ΅ΠΌΡ ΡΠΎΠ³Π»Π°ΡΠΎΠ²Π°Π½ΠΈΡ Π³Π΅ΠΎΠΌΠ΅ΡΡΠΈΠΈ Π½Π΅Π·Π°Π²ΠΈΡΠΈΠΌΠΎ ΠΎΡ ΡΡΠ½ΠΊΡΠΈΠΎΠ½Π°Π»Π°.ΠΡΠ²ΠΎΠ΄Ρ. ΠΡΠΎΠ²Π΅Π΄Π΅Π½Π½ΡΠ΅ ΡΠ°ΡΡΠ΅ΡΡ Ρ
ΠΎΡΠΎΡΠΎ ΡΠΎΠ³Π»Π°ΡΡΡΡΡΡ Ρ Π»ΠΈΡΠ΅ΡΠ°ΡΡΡΠ½ΡΠΌΠΈ Π΄Π°Π½Π½ΡΠΌΠΈ, Π° ΡΠ°ΠΊΠΆΠ΅ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠ°ΠΌΠΈ ΡΠΎΠ²ΠΌΠ΅ΡΡΠ½ΠΎΠ³ΠΎ Π°Π½Π°Π»ΠΈΠ·Π° ΠΌΠ΅ΡΠΎΠ΄Π°ΠΌΠΈ ΠΠ ΠΈ Π Π‘Π. ΠΠ»ΠΈΡΠ½ΠΈΠ΅ ΡΠΈΠ°Π½ΠΎ-Π·Π°ΠΌΠ΅ΡΡΠΈΡΠ΅Π»Π΅ΠΉ Π½Π° Π³Π΅ΠΎΠΌΠ΅ΡΡΠΈΡ ΠΊΠΎΠ»ΡΡΠ° Π½Π°Π±Π»ΡΠ΄Π°Π΅ΡΡΡ Π² ΡΡΠ°Π²Π½Π΅Π½ΠΈΠΈ Ρ Π»ΠΈΡΠ΅ΡΠ°ΡΡΡΠ½ΡΠΌΠΈ Π΄Π°Π½Π½ΡΠΌΠΈ Π΄Π»Ρ ΠΌΠΎΠ»Π΅ΠΊΡΠ»Ρ Π΄ΠΈΡΠΈΠ°Π½ΠΎΡΡΡΠΎΠΊΡΠ°Π½Π°. ΠΠ»Ρ ΡΠ°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°Π΅ΠΌΠΎΠΉ ΠΌΠΎΠ»Π΅ΠΊΡΠ»Ρ Π»ΡΡΡΠ΅ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°ΡΡ ΠΌΠ΅ΡΠΎΠ΄ B3LYP/aug-cc-pVTZ. ΠΠ½Π°ΡΠ΅Π½ΠΈΡ Π³Π΅ΠΎΠΌΠ΅ΡΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΎΠ², ΠΏΠΎΠ»ΡΡΠ΅Π½Π½ΡΠ΅ ΡΡΠΈΠΌ ΠΌΠ΅ΡΠΎΠ΄ΠΎΠΌ, Π»ΡΡΡΠ΅ ΡΠΎΠ³Π»Π°ΡΡΡΡΡΡ ΡΠΎ ΡΡΡΡΠΊΡΡΡΠΎΠΉ Π² Π³Π°Π·ΠΎΠ²ΠΎΠΉ ΡΠ°Π·Π΅. Π Π°ΡΡ
ΠΎΠΆΠ΄Π΅Π½ΠΈΡ Ρ ΡΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ°Π»ΡΠ½ΡΠΌΠΈ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠ°ΠΌΠΈ Π Π‘Π ΠΌΠΎΠ³ΡΡ Π±ΡΡΡ ΠΎΠ±ΡΡΠ»ΠΎΠ²Π»Π΅Π½Ρ Π²Π·Π°ΠΈΠΌΠΎΠ΄Π΅ΠΉΡΡΠ²ΠΈΡΠΌΠΈ Π² ΠΊΡΠΈΡΡΠ°Π»Π»ΠΈΡΠ΅ΡΠΊΠΎΠΉ ΡΡΡΡΠΊΡΡΡΠ΅. Π Π°Π·Π»ΠΈΡΠΈΡ Π² Π³Π΅ΠΎΠΌΠ΅ΡΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠ°Ρ
, ΠΏΠΎΠ»ΡΡΠ΅Π½Π½ΡΡ
Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ ΡΠ°Π·Π½ΡΡ
ΡΡΠ½ΠΊΡΠΈΠΎΠ½Π°Π»ΠΎΠ² ΠΈ Π±Π°Π·ΠΈΡΠΎΠ², Π΄Π΅Π»Π°ΡΡ ΡΡΡ ΠΌΠΎΠ»Π΅ΠΊΡΠ»Ρ ΠΈΠ½ΡΠ΅ΡΠ΅ΡΠ½ΠΎΠΉ Π΄Π»Ρ ΠΏΡΠΎΠ²Π΅Π΄Π΅Π½ΠΈΡ ΡΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ°Π»ΡΠ½ΠΎΠ³ΠΎ ΡΡΡΡΠΊΡΡΡΠ½ΠΎΠ³ΠΎ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ ΠΌΠ΅ΡΠΎΠ΄Π°ΠΌΠΈ ΠΠ ΠΈΠ»ΠΈ ΠΌΠΈΠΊΡΠΎΠ²ΠΎΠ»Π½ΠΎΠ²ΠΎΠΉ ΡΠΏΠ΅ΠΊΡΡΠΎΡΠΊΠΎΠΏΠΈΠΈ, ΡΡΠΎ ΠΏΠΎΠ·Π²ΠΎΠ»ΠΈΡ Π² Π±ΡΠ΄ΡΡΠ΅ΠΌ Π½Π°ΠΉΡΠΈ ΠΎΠΏΡΠΈΠΌΠ°Π»ΡΠ½ΡΠ΅ ΠΌΠ΅ΡΠΎΠ΄Ρ ΠΈ Π±Π°Π·ΠΈΡΡ Π΄Π»Ρ ΠΏΠΎΠ»ΡΡΠ΅Π½ΠΈΡ Π³Π΅ΠΎΠΌΠ΅ΡΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΎΠ² ΠΌΠΎΠ»Π΅ΠΊΡΠ» ΠΊΠ»Π°ΡΡΠ° ΡΡΡΠΎΠΊΡΠ°Π½ΠΎΠ²
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
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 Β°/s. It has been established that, in the range of industrial rates of cooling between 50 and 350 Β°/s from austenitic regions, the Ξ³βΞ± transformation starts at temperatures of 700-670 Β°C and proceeds by the shear mechanism. As a result, a bainite structure of different dispersity with martensitic inclusions is predominantly formed. Β© 2018 Author(s)
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 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 is predicted to exceed 98%. The experimentally achieved
value of % 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
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