Angular Diagrams Research Articles

Lifshitz Transitions and Angular Conductivity Diagrams in Metals with Complex Fermi Surfaces

Lifshitz Transitions and Angular Conductivity Diagrams in Metals with Complex Fermi Surfaces

Investigation of the dielectric characteristics of materials manufactured using additive technologies

Based on the existing methods of measuring the dielectric characteristics of materials, the most optimal method for performing calculations in the electrodynamic computer-aided design system is selected by the finite integration method. Based on the calculated values of the scattering matrix, the permittivity and the tangent of the dielectric loss angle of the printed polymer samples are calculated according to a given algorithm. When evaluating the accuracy of the calculation of the dielectric characteristics, validation was performed for a sample with the specified characteristics. For a sample printed using the technology of fused filament fabrication, the influence of the filling parameters on the dielectric characteristics of the printed model in the X-band of wavelengths was estimated. The description of the model implemented in the computer-aided design system is given. By processing the simulation results, approximating dependences for the permittivity and losses on the degree of filling with the dielectric are obtained. It follows from the calculated angular diagrams that the decrease in the degree of filling of the dielectric directly affects the degree of anisotropy of the polymer obtained during printing in the plane of the extruded layers. This also increases the depth of the extremes observed at angles of 0°, 90° and 180°. The presence of these extremes is directly related to the fact that the force lines of the main wave type in the waveguide are located perpendicular to the wide wall and in a situation where the volumes of air gaps between the cylinders are parallel to the force lines of tension, there is a general decrease in the dielectric constant. For a printed sample consisting of two layers of crossed cylinders, the air volumes are parallel to the lines of force with a period of ninety degrees, which is confirmed by the results obtained. An increase in the depth of the extremes with a decrease in the degree of filling is associated with a corresponding increase in the air space between the cylinders in the layer of the printed polymer.

Measurement of the refractive index of an Er3+:YAG crystal melt

A new method for measuring the refractive index of crystals and melts at high temperatures is presented. The refractive index of an Er3+:YAG crystal melt is determined during the laser-heated pedestal growth process close to the melting point. The main idea is to use the maximal difference in the intensities of two polarizations of thermal radiation passing the melt-air interface. From the Fresnel equations, it follows that this difference is almost proportional to the refractive index. Angular diagrams of the thermal radiation of the melt for two polarizations are analyzed. The obtained value of the refractive index of the Er3+:YAG melt is n = 1.84 ± 0.01 in the wavelength range of 550–620 nm.

Simulation of Reciprocal Space Maps with the Use of Spectral Angular Diagrams in the Triple Crystal X-Ray Diffraction Scheme

An approach to the simulation of reciprocal space maps corresponding to the maps obtained experimentally by the triple crystal X-ray diffractometry (TXD) is proposed. A specific feature of the approach is the use of spectral angular distribution diagrams of X-ray radiation, which allows one to visualize the two-dimensional pattern of the spectral angular “composition” of an X-ray beam after its interaction with each element of the scheme and thus to take into account the contribution of the hardware function of the experimental setup. The algorithms developed allow calculations for a wide class of radiation sources (from an X‑ray tube with any material of the anode to a synchrotron radiation source) and X-ray optical elements (slits, X-ray mirrors of monochromators, and analyzers). The results of simulation are compared with the experimental data for dispersive diffraction geometry, which confirms the adequacy of the proposed approach and its applicability to the simulation of a diffraction pattern corresponding to a real experiment in the triple crystal scheme.

The Complexity Classes of Angular Diagrams of the Metal Conductivity in Strong Magnetic Fields

We consider angular diagrams describing the dependence of the magnetic conductivity of metals on the direction of the magnetic field in rather strong fields. As it can be shown, all angular conductivity diagrams can be divided into a finite number of classes with different complexity. The greatest interest among such diagrams is represented by diagrams with the maximal complexity, which can occur for metals with rather complicated Fermi surfaces. In describing the structure of complex diagrams, in addition to the description of the conductivity itself, the description of the Hall conductivity for different directions of the magnetic field plays very important role. For the evaluation of the complexity of angular diagrams of the conductivity of metals, it is convenient also to compare such diagrams with the full mathematical diagrams that are defined (formally) for the entire dispersion relation.

The Second Boundaries of Stability Zones and the Angular Diagrams of Conductivity for Metals Having Complicated Fermi Surfaces

We consider some general aspects of dependence of magneto-conductivity on a magnetic field in metals having complicated Fermi surfaces. As it is well known, a nontrivial behavior of conductivity in metals in strong magnetic fields is connected usually with appearance of non-closed quasiclassical electron trajectories on the Fermi surface in a magnetic field. The structure of the electron trajectories depends strongly on the direction of the magnetic field and usually the greatest interest is caused by open trajectories that are stable to small rotations of the direction of $\, {\bf B} $. The geometry of the corresponding Stability Zones on the angular diagram in the space of directions of $\, {\bf B} \, $ represents a very important characteristic of the electron spectrum in a metal linking the parameters of the spectrum to the experimental data. Here we will consider some very general features inherent in the angular diagrams of metals with Fermi surfaces of the most arbitrary form. In particular, we will show here that any Stability Zone actually has a second boundary, restricting a larger region with a certain behavior of conductivity. Besides that, we shall discuss here general questions of complexity of the angular diagrams for the conductivity and propose a theoretical scheme for dividing the angular diagrams into "simple" and "complex" diagrams. The proposed scheme will in fact also be closely related to behavior of the Hall conductivity in a metal in strong magnetic fields. In conclusion, we will also discuss the relationship of the questions under consideration to the general features of an (abstract) angular diagram describing the behavior of quasiclassical electron trajectories at all energy levels in the conduction band.

Comparative analysis of designing wall panels with hole based on one-dimensional and two-dimensional computer models

The operation of reinforced concrete wall panels with holes used in civil engineering has been studied. Under conditions of plane stress wall panels operate in vertical (qy) and horizontal (qx) evenly distributed loads conditioned by the own weight of the panels and pressure of the overlying overlap and covering structures. The effect of wind load on the building develops the flexural state of wall panels, i.e. loading the structures with the transverse evenly distributed load takes place. To study the stress-strain state of the above-mentioned structures, the work proposes a rod approximation in the form of a rod of a step-variable cross section, taking into account the presence of a hole in the body of the wall panel. Using the numerical finite-difference method there one solved the initial fourth-order differential equation for the compressed-bent state of the deformed rod. The results are presented in the form of the diagrams of transverse, axial and angular displacements, bending moments, longitudinal and shear forces diagrams. The results of the studies are of scientific and practical importance.

Diagrammatic MonteCarlo Approach to Angular Momentum in Quantum Many-Particle Systems.

We introduce a diagrammatic MonteCarlo approach to angular momentum properties of quantum many-particle systems possessing a macroscopic number of degrees of freedom. The treatment is based on a diagrammatic expansion that merges the usual Feynman diagrams with the angular momentum diagrams known from atomic and nuclear structure theory, thereby incorporating the non-Abelian algebra inherent to quantum rotations. Our approach is applicable at arbitrary coupling, is free of systematic errors and of finite-size effects, and naturally provides access to the impurity Green function. We exemplify the technique by obtaining an all-coupling solution of the angulon model; however, the method is quite general and can be applied to a broad variety of systems in which particles exchange quantum angular momentum with their many-body environment.

Double-Crystal Rocking Curve Simulation Using 2D Spectral Angular Diagrams of X-Ray Radiation

A new approach to numerical simulation of double-crystal rocking curves is proposed. This approach is based on the use of experimental spectral angular diagrams of X-ray intensity distribution. Special calculation algorithms, which take into account the instrumental function of X-ray diffractometer and possible effects of dispersion and Bragg reflection asymmetry, have been developed and applied. A specific feature of the proposed approach is the possibility of visualizing the 2D spectral angular diagram of X-ray beam after its interaction with each element of the scheme. The approach makes it possible to perform calculations for a wide range of radiation sources (from an X-ray tube with any anode to a synchrotron radiation source) and X-ray optical elements (slits and monochromators). A comparison of simulation results and experimental data for a Si(110) crystal sample has confirmed adequacy of the proposed approach and its applicability for simulating diffraction patterns recorded in real experiments.

Teaching Air Pollution in an Authentic Context

This paper describes a teaching-learning sequence (TLS) about air pollution and the findings resulting from its implementation by pre-service elementary teachers (PET) currently undergraduate students of the Department of Primary Education in the National and Kapodistrian University of Athens, Greece. The TLS focused on the relation of air pollution with wind and topography in local conditions. An authentic context was provided to the students based on daily up-to-date meteorological data via the Internet in order to estimate air pollution. The results are encouraging given that PET can correlate wind and concentration of air pollutants through reading specialized angular diagrams and weather maps, can recognize the correlation of topography in the concentration of air pollutants, and can describe temperature inversion. However, the PET demonstrated clear difficulties in ability of orientation, in wind naming, and in interpretation of symbols on weather map. Finally, the implications on teaching air pollution are discussed.

Acoustic scattering by elastic cylinders of elliptical cross-section and splitting up of resonances

The scattering of a plane acoustic wave by an infinite elastic cylinder of elliptical cross section is studied from a modal formalism by emphasizing the role of the symmetries. More precisely, as the symmetry is broken in the transition from the infinite circular cylinder to the elliptical one, the splitting up of resonances is observed both theoretically and experimentally. This phenomenon can be interpreted using group theory. The main difficulty stands in the application of this theory within the framework of the vectorial formalism in elastodynamics. This method significantly simplifies the numerical treatment of the problem, provides a full classification of the resonances, and gives a physical interpretation of the splitting up in terms of symmetry breaking. An experimental part based on ultrasonic spectroscopy complements the theoretical study. A series of tank experiments is carried out in the case of aluminium elliptical cylinders immersed in water, in the frequency range 0 ≤ kr ≤ 50, where kr is the reduced wave number in the fluid. The symmetry is broken by selecting various cylinders of increasing eccentricity. More precisely, the greater the eccentricity, the higher the splitting up of resonances is accentuated. The experimental results provide a very good agreement with the theoretical ones, the splitting up is observed on experimental form functions, and the split resonant modes are identified on angular diagrams.

Dependence of Type of Angular Diagrams of Light Backscattering on Direction of Yarn Twist

A method based on analysis of angular diagrams of light backscattering is proposed for the determination of the direction of yarn twist. The efficiency of this method is proved by the example of the study of yarns with various fibre compositions and with various twist counts.

Оптичні властивості серії гальванічних матриць мікрорельєфних світлоповертальних структур

Досліджено оптичні властивості серії гальванічних копій матриць світлоповертальних структур і мікропризмових пристроїв; визначено кутові діаграми світлоповертання для різних матриць світлоповертачів; виконано аналіз можливості використання нікелевих копій матриць-оригіналів для виготовлення світлоповертачів і мікропризмових елементів.

Spectra, thresholds, and modal fields of a kite-shaped microcavity laser

We investigate the lasing spectra, threshold gain values, and emission directionalities for a two-dimensional microcavity laser with a “kite” contour. The cavity modes are considered accurately using the linear electromagnetic formalism of the lasing eigenvalue problem with exact boundary and radiation conditions. We develop a numerical algorithm based on the Muller boundary integral equations discretized using the Nystrom technique, which has theoretically justified and fast convergence. The influence of the deviation from the circular shape on the modal characteristics is studied numerically for the modes polarized in the cavity plane, demonstrating opportunities of directionality improvement together with preservation of a low threshold. These advantageous features are shown for the perturbed whispering-gallery modes of high-enough azimuth orders. Other modes can display improved directivities while suffering from drastically higher threshold levels. Experiments based on planar organic microcavity lasers confirm the coexistence of Fabry–Perot-like and whispering-gallery-like modes in kite-shaped cavities and show good agreement with the predicted far-field angular diagrams.

Light scattering at the boundary between two media

Coefficients of diffuse reflection and transmission of light by smooth Fresnel boundaries of an optically thick layer illuminated by scattered radiation are calculated. Consideration is given to the absorption effect on angular diagrams of light at the boundaries. An analysis is made of asymptotic equations of radiation transfer in a medium with reflecting boundaries, and the range of their applicability is studied. Using methods of geometric optics, coefficients of reflection of directional and diffuse radiation from a rough surface are studied. The results can find use in various areas of science and technology, specifically, in optical diagnostics of biological tissues.

Charge density waves in d-wave superconductors

A self-consistent theory of charge density waves in partially dielectrically gapped superconductors with d-pairing is proposed. The dependences of the dielectric (Σ) and superconducting (Δ) order parameters on the temperature and other parameters of the problem is examined. The corresponding angular diagrams for the gap distribution over the Fermi surface are constructed for the first time. The theory is used to explain the properties of high-temperature oxides. The effect of the displacement angle between the lobes of the order parameters Σ and Δ on the gap distribution in momentum space and on the reentrance phenomenon for Σ with respect to temperature is analyzed.

Coexistence of Charge Density Waves and d-Wave Superconductivity in Cuprates. Sharing of the Fermi Surface

A self-consistent theory that describes charge density waves in a partially dielectrically gapped superconductor with dx2–y2-pairing has been proposed. The dependences of dielectric, Σ, and superconducting, Δ, order parameters on the temperature and other problem parameters have been considered, and the phase diagram has been built. The corresponding angular diagrams for gap distribution over the Fermi surface have been plotted. The developed theory is used for the explanation of properties of high-temperature oxides. The influence of mismatch angle between the lobes of order parameters Σ and Δ on the gap distribution in the momentum space and the reentrance phenomenon for Σ with respect to temperature has been analyzed.

Assessment of surface roughness and reflectance of nonmetallic products upon diamond abrasive finishing

Surface roughness of nonmetallic products machined by various diamond abrasive finishing operations is demonstrated to govern the angular diagrams of reflection and scattering which exhibit a speckle pattern. An indicatrix of scattering is found to form due to light reflection by uniform areas of texture formations on the surface and by their boundaries. A parameter that responds to a change in machined surface roughness is the width of the peak on the indicatrix of scattering, with the pedestal remaining almost unchanged.

Segregation pattern competition in a thin rotating drum

Results are presented of an experimental investigation into patterned size segregation of binary granular mixtures in a thin rotating drum that is half full. It is observed that streaks of small particles are formed within regions of large ones where the integer number of streaks is fixed over a range of rotation rate of the drum. Different patterns form in adjacent parameter ranges and the dynamics associated with the exchange between neighboring states is analyzed using angular spatiotemporal diagrams. These help to reveal properties of the merging mechanism for streaks of small particles. We report experimental evidence that the merging of streaks is mediated by the movement of a surplus material in a direction opposite to that of the rotation of the drum. The excess material is distributed throughout the pattern and the extra streak eventually disappears.

ESR Investigation of Gd3+ Ion Introduction into the Structure of Simple and Double Tungstates

In this paper the spectra of Gd3+ ions studied by electron spin resonance (ESR) in four types of tungstate crystals KY(WO4)2, CdWO4, CsLa(WO4)2 and La2(WO4)3 are discussed. The tungstate crystals were grown by the low-temperature gradient Czochralski technique with Gd2O3 addition in melt. The estimation of spin Hamiltonian (SH) parameters was realized using an original simulation program developed. The parameters of crystalline field in oxide crystals are comparable with Zeeman interaction so the solution of the Schrodinger equation was realized numerically. We have estimated 36 SH parameters from ESR angular diagrams of Gd3+, including gx, gy, gz, gi (where i = 1, …, 6), Bmn, Cmn (where m = 2, …, 6, n = 0 (or 1 for Cmn), …, m), and the Euler angles. The positions of Gd3+ ions in the crystal structures, the charge compensation and the influence of lattice parameters on the SH parameters B20 and B22 are discussed in this paper as well.