Structure Constants Research Articles

Mutual coherence function based topological charge detection in a Gaussian vortex beam optical communication system

We investigate a topological charge (TC) detection schema for an optical communication system employing Gaussian vortex beam (GVB). In this scenario, the transmitter maps the electrical message symbols to the TCs of GVBs. Thus obtained optical signal propagates in turbulent atmosphere arriving at the receiver, where a detection process is implemented to determine the TC of GVB by correlating the imaginary part of the mutual coherence function (MCF) of the incoming beam against the stored profiles. The feasibility of such a schema is firstly established by examining and comparing the analytical formulation of MCF and that of random phase screen setup. The latter is then used to explore the success rate and boundaries of this particular detection schema. Our results show that the proposed detection schema can operate with a error rate of 5% at a link length of 5.5 km and atmospheric turbulence structure constant of 10−14.

Semi-empirical studies on odd parity levels system of manganese atom in multiconfiguration approximation

We present the results of semi-empirical calculations of the fine structure (fs) and the hyperfine structure (hfs) for the odd-parity level system of the manganese atom in a large multiconfiguration basis. Recently, new measurements applying laser induced fluorescence on an atomic beam and in a hollow cathode discharge lamp provided the hyperfine structure constants A and B for altogether 50 odd-parity levels. Therefore, a hyperfine structure many-body parameterization method was successfully used for such complicated system, composed of 71 configurations. In general, a good agreement between the experimental and the calculated values for the fs and hfs fits was obtained.

The Grothendieck Ring of a Family of Spherical Categories

We compute the fusion rule of a one-parameter family of spherical categories constructed by one author from the classification of singly generated Yang–Baxter planar algebras. The structure constant of the fusion rule is expressed in a closed-form formula of Littlewood–Richardson coefficients. We also compute the characters of the simple objects and their generating function in terms of symmetric functions with infinite variables.

Investigation of the anisotropy and scaling of the phase structure function of a spatially coherent light beam propagating through convective air turbulence.

We report on applications of moiré deflectometry in measurements of the anisotropy and scaling of the phase structure function (PSF), obtained after passing a laser beam through an indoor enclosure containing convective air turbulence. We combine the use of two telescopes, with a two-channel wavefront sensor based on moiré deflectometry, to attain high sensitivity and resolution to fluctuations in the wavefront phase, caused by turbulent fluctuations in the enclosure. The measurements of the wavefront PSF along two directions perpendicular to the direction of the light beam propagation at different heater temperatures show that the convective air turbulence is anisotropic turbulence, where the value of the anisotropy increases with increasing temperature gradient. Various models are fitted to the measured PSFs, and we find that the turbulent is also non-Kolmogorov, in which, for the separation distances of two points on the wavefront less than 10 cm, the von Kármán PSF is the best fit to the experimental data. For higher values of separations, the experimental data do not fit with existing models. By fitting the von Kármán PSF on the data, we estimate values of the refractive index structure constant, Cn2, as well as the outer scale of the turbulence. The value of the outer scale decreases with increasing temperature of the heater up to approximately 50°C, where it saturates, while the value of Cn2 monotonically increases. Over the complete range of heater temperatures, from 40°C to 160°C, the Rayleigh number, Ra, for the enclosed air flow varied from 5.80×108<Ra<5.89×109 so that all measurements were conducted in a state of developed convective turbulence.

The limit dynamics for the vacuum Einstein equations in a homogeneous universe

We study the dynamics of the Bianchi IX universe when one of the structure constants tends to zero, i.e. we study the dynamics of the Bianchi VII universe. We prove that there is a surface filled of periodic orbits surrounding an equilibrium point, and that except for another surface filled of equilibria the remainder orbits comes and go to infinity.

On the stability of homogeneous Einstein manifolds II

For any G $G$ -invariant metric on a compact homogeneous space M = G / K $M=G/K$ , we give a formula for the Lichnerowicz Laplacian restricted to the space of all G $G$ -invariant symmetric 2-tensors in terms of the structural constants of G / K $G/K$ . As an application, we compute the G $G$ -invariant spectrum of the Lichnerowicz Laplacian for all the Einstein metrics on most generalized Wallach spaces and any flag manifold with b 2 ( M ) = 1 $b_2(M)=1$ . This allows to deduce the G $G$ -stability and critical point types of each of such Einstein metrics as a critical point of the scalar curvature functional.

Large charges on the Wilson loop in mathcal{N} = 4 SYM. Part II. Quantum fluctuations, OPE, and spectral curve

We continue our study of large charge limits of the defect CFT defined by the half-BPS Wilson loop in planar mathcal{N} = 4 supersymmetric Yang-Mills theory. In this paper, we compute 1/J corrections to the correlation function of two heavy insertions of charge J and two light insertions, in the double scaling limit where the charge J and the ’t Hooft coupling λ are sent to infinity with the ratio J/ sqrt{lambda } fixed. Holographically, they correspond to quantum fluctuations around a classical string solution with large angular momentum, and can be computed by evaluating Green’s functions on the worldsheet. We derive a representation of the Green’s functions in terms of a sum over residues in the complexified Fourier space, and show that it gives rise to the conformal block expansion in the heavy-light channel. This allows us to extract the scaling dimensions and structure constants for an infinite tower of non-protected dCFT operators. We also find a close connection between our results and the semi-classical integrability of the string sigma model. The series of poles of the Green’s functions in Fourier space corresponds to points on the spectral curve where the so-called quasi-momentum satisfies a quantization condition, and both the scaling dimensions and the structure constants in the heavy-light channel take simple forms when written in terms of the spectral curve. These observations suggest extensions of the results by Gromov, Schafer-Nameki and Vieira on the semiclassical energy of closed strings, and in particular hint at the possibility of determining the structure constants directly from the spectral curve.

Structural, Electronic, Mechanical, and Thermodynamic Properties of Na Deintercalation from Olivine NaMnPO4: First-Principles Study.

The impact of Na atom deintercalation on olivine NaMnPO4 was investigated in a first-principle study for prospective use as cathode materials in Na-ion batteries. Within the generalized gradient approximation functional with Hubbard (U) correction, we used the plane-wave pseudopotential approach. The calculated equilibrium lattice constants are within 5% of the experimental data. The difference in equilibrium cell volumes for all deintercalated phases was only 6%, showing that NaMPO4 is structurally more stable. The predicted voltage window was found to be between 3.997 and 3.848 V. The Na1MnPO4 and MnPO4 structures are likely to be semiconductors, but the Na0.75MnPO4, Na0.5MnPO4, and Na0.25MnPO4 structures are likely to be metallic. Furthermore, all independent elastic constants for NaxMPO4 structures were shown to meet the mechanical stability requirement of the orthorhombic lattice system.

Cuprous Oxide Thin Films Implanted with Chromium Ions-Optical and Physical Properties Studies.

Cuprous oxide is a semiconductor with potential for use in photocatalysis, sensors, and photovoltaics. We used ion implantation to modify the properties of Cu2O oxide. Thin films of Cu2O were deposited with magnetron sputtering and implanted with low-energy Cr ions of different dosages. The X-ray diffraction method was used to determine the structure and composition of deposited and implanted films. The optical properties of the material before and after implantation were studied using spectrophotometry and spectroscopic ellipsometry. The investigation of surface topography was performed with atomic force microscopy. The implantation had little influence on the atomic lattice constant of the oxide structure, and no clear dependence of microstrain or crystalline size on the dose of implantation was found. The appearance of phase change was observed, which could have been caused by the implantation. Ellipsometry measurements showed an increase in the total thickness of the sample with an increase in the amount of implanted Cr ions, which indicates the influence of implantation on the properties of the surface and subsurface region. The refractive index n, extinction coefficient k, and absorption coefficient optical parameters show different energy dependences related to implantation dose.

Performance of a free-space optical communication system employing receive diversity techniques in anisotropic atmospheric non-Kolmogorov turbulence

In this paper, bit error rate (BER) performance of a free-space optical communication (FSOC) system operating in anisotropic non-Kolmogorov weak turbulence is investigated together with the spatial diversity techniques. The spatial diversity techniques are implemented as maximum ratio combining (MRC), equal gain combining (EGC), and selection combining (SC) and applied to the receiver. The propagating beam is the Gaussian beam wave, and the modulation scheme is binary phase-shift keying (BPSK). Results are obtained for various parameters such as the anisotropy factor, non-Kolmogorov power law exponent, photodetector responsivity, equivalent load resistor, electronic bandwidth, Gaussian beam radius, wavelength, propagation distance, and turbulence structure constant. It is found that the spatial diversity technique used at the receiver causes significant improvement in the performance of an FSOC system under the conditions of anisotropic non-Kolmogorov atmospheric turbulence. It is also observed that BER performance improves as the atmospheric turbulence becomes more anisotropic. Among the spatial diversity techniques, SC is inferior to EGC and EGC is inferior to MRC in terms of BER performance.

Predicting the thermal conductivity of Bi2Te3-based thermoelectric energy materials: A machine learning approach

Bi2Te3-based materials are remarkable thermoelectric renewable energy harvesters. The measurement of their thermal conductivity (κ) is a critical phase toward the realization of the material's energy conversion efficiency. However, the experimental techniques involved in the measurements of κ, particularly for thin films, are incredibly challenging. Herein, we introduce a pioneering technique using support vector regression and decision tree regression machine learning models where the values of κ can be predicted based on the structural crystal lattice constants of the material and its electrical properties. A decision tree regression (DTR) and support vector regression (SVR) models using both radial basis function (RBF) and polynomial kernels were developed. The performance of the models was evaluated based on the correlation coefficient (CC) between the predicted and actual values of κ, R2 values, mean absolute error (MAE), and mean square error (MSE). Our results revealed that the DTR outperforms the SVR models in estimating the values of κ with CC of 98.7% and R2 of 97.5% for the testing phase. The models were validated by solving some real-world problems such as predicting the thermal conductivity of transition metal-doped Cu–Bi2Te3, effects of doping non-metals (Se–Bi2Te3), and the role of toxic elements (Pb–Bi2Te3) on the values of κ. The model was further employed to investigate the effects of pulsed laser deposition substrate temperature on the thermal conductivity of Bi2Te3. The performance of the models in predicting the thermal conductivity of Bi2Te3-based materials makes it a useful tool for thermoelectric energy research.

Wigner crystallization at large fine structure constant

We consider the fate of the Wigner crystal state in a two-dimensional system of massive Dirac electrons as the effective fine structure constant $\ensuremath{\alpha}$ is increased. In a Dirac system, larger $\ensuremath{\alpha}$ naively corresponds to stronger electron-electron interactions, but it also implies a stronger interband dielectric response that effectively renormalizes the electron charge. We calculate the critical density and critical temperature associated with quantum and thermal melting of the Wigner crystal state using two independent approaches. We show that at $\ensuremath{\alpha}\ensuremath{\gg}1$, the Wigner crystal state is best understood in terms of logarithmically interacting electrons, and that both the critical density and the melting temperature approach a universal, $\ensuremath{\alpha}$-independent value. We discuss our results in the context of recent experiments in twisted bilayer graphene near the magic angle.

Abnormal Extremals of Left-Invariant Sub-Finsler Quasimetrics on Four-Dimensional Lie Groups with Three-Dimensional Generating Distributions

We find the three-dimensional subspaces of four-dimensional Lie algebras which generate the algebras, as well as abnormal extremals on the connected Lie groups determined by these algebras and endowed with the left-invariant sub-Finsler quasimetrics defined by seminorms on the subspaces. Using the structure constants of Lie algebras and dual seminorms, we establish a criterion for the strict abnormality of the extremals.

The generation of mass in a non-linear field theory

Abstract The mass spectrum of elementary particles is calculated in a new approach, based on B. Heim’s quantum field theory, which manifests in a non-linear eigenvalue equation and merges into the Einstein field equation in the macroscopic limit. The poly-metric of the theory allows spacetime and matter to be described in a unified formalism, representing a radical geometrisation of physics. The calculated mass energies are in very good agreement with the empirical data (error &lt; 1 % ${&lt; }1\%$ on average) if the mass scale is gauged to the electron as lowest mass and the second main parameter, determining the strength of obtained mass hierarchy levels, is close to the half inverse of the fine structure constant, describing the difference in strength between the electromagnetic and the strong interaction. The obtained hierarchy levels are not identical to the particle generations of the Standard Model; however, show a self-similarity typical for non-linear theories. For higher values of the main quantum number N, the calculated mass formula becomes identical to the phenomenological formulae of Nambu, respectively, Mac Gregor.

Evolution of the structure and properties of (Zr1-xHfx)B2 solid solution ceramics from first-principle theory

As typical ultra-high temperature ceramics, both ZrB2 and HfB2 have unique properties such as excellent mechanical performance and oxidation resistance, are promising candidates for the aerospace industry. In this work, the phase stability, electronic, mechanical and thermodynamic properties of (Zr1-xHfx)B2 solid solution ceramics were systematically studied performing by first-principles calculations. The calculated results of structural optimization and elastic constants are in good agreement with the experimental values, which confirms the reliability of the proposed model. The lattice parameters of the optimized (Zr1-xHfx)B2 solid solution ceramics are linearly related to the Hf content, while a decrease is detected as the increasing Hf content. The calculated elastic constants show that the addition of Hf is beneficial in improving the mechanical properties of the (Zr1-xHfx)B2 solid solution, including the elastic modulus, hardness and fracture toughness. In addition, the (Zr1-xHfx)B2 solid solution was found to be kinetically stable. From the trend of the calculated value of the Debye temperature, it can be found that the addition of Hf can effectively reduce the thermal conductivity of solid solution materials. Our work introduced an important theoretical framework, which is of great significance for the development of solid solution diboride material systems with adjustable composition and properties.

Macroscopic flexotronics enhanced controllable piezotronic-like response by flexual semiconductor devices

Interface engineering to modulate electronic transport is a pivotal technological and scientific endeavour. Herein, regardless of the macroscopic or microscopic aspects, we successfully demonstrate the piezotronic-like response in bulk bending centrosymmetric semiconductors single crystal Si strip with more flexibility and flexure in the home-built fixed platform. The flexoelectric potential and flexotronics could be dramatically enhanced by bending single crystal Si strip due to the change of the crystal structure and lattice constant. Besides, the flexoelectric polarization direction can be tuned by changing the bending direction. Moreover, the thinner the bending material is, the greater the SBH change rate. Theoretically, the working mechanism of flexoelectricity induced by the synergistic contribution consequence of the surface piezoelectric effect and bulk flexoelectric effect is elucidated.

High-temperature orthorhombic phase of Cu2HgGeS4: Electronic structure and principal optical constants as evidenced from the experiment and theory

We report on successful synthesis of single-phase high-temperature (HT) orthorhombic modification of Cu2HgGeS4 and studies of its electronic and optical properties from a viewpoint of experiment and theory. In particular, we have made measurements of the XPS core-level and valence-band spectra of the HT-Cu2HgGeS4 modification and calculated density of states. The calculations are carried out within a framework of density functional theory and using varieties of techniques. We have realized that the best agreement of the theory and experiment is observed when we use in the calculations the modified Becke-Johnson (mBJ) functional as refined by Tran-Blaha and consider also the Hubbard correction parameter U and spin-orbit coupling (SOC). The calculations demonstrate that main contributions of sulfur 3p states occur near the topmost and upper part of the HT-Cu2HgGeS4 valence band, copper 3d states dominate in its central part, the lower part is prevailed by contributions of mercury 6s and germanium 4p states, whereas near the valence band bottom the biggest contributions come from mercury 5d states. The theoretical predictions are verified experimentally. The calculations reveal that the HT-Cu2HgGeS4 modification is a direct band gap semiconductor. The principal optical constants are elucidated following first-principles calculations of the quaternary sulfide under consideration.

Structural and defect changes in black carbon charcoal irradiated with gamma ray

This study investigates the use of black carbon charcoal as passive radiation dosimetry, offering low dependence on photon energy and near soft tissue effective atomic number with state-of-the-art techniques. Regression analyses have now been conducted using graphite manufactured commercially in the form of charcoal from three different types: mangrove, coconut, and green charcoal recycled from sawdust, working with photon-mediated interactions at radiotherapy dose levels. Explorations of changes in Raman spectroscopic characteristics, and photoluminescence dose dependence have been performed with a focus on the relationship between absorbed radiation energy and induced material changes, using a 60Co gamma-ray source doses ranging from 0 to 10 Gy. Raman spectroscopy has established to be an effective method for exploring defects in carbon-based materials due to its high sensitivity, most commonly focusing on the use of ID/IG parameter. While photoluminescence analysis will provide information on electronic properties and the band gap energy. The crystal structure of the black charcoal samples was characterised using X-ray diffractometry, with the goal of determining the degree of structural order, atomic spacing, and lattice constants of the various irradiated charcoal samples, supported by crystallite size assessments. The findings of this study could pave the way for a low-cost yet highly effective system for studying radiation-induced changes in carbon, as well as offering a viable alternative to current commercial dosimeters, well suited to applications in radiotherapy.

Structures, phase transitions, thermodynamic properties, and structural dynamics of eco-friendly hybrid perovskite NH3(CH2)3NH3CoCl4 and NH3(CH2)5NH3CoCl4 crystals

The present study investigates the structures, phase transition temperatures, thermodynamic properties, and structural dynamics of the organic–inorganic perovskite NH3(CH2)nNH3CoCl4 (n = 3 and 5) crystals according to the number of carbon atoms. The structure and lattice constants were confirmed by single-crystal X-ray diffraction (XRD) at 298 K. From differential scanning calorimetry and XRD powder patterns, the phase transition temperature TC obtained at 483 K for n = 3 was isostructural without changing the crystal structure, whereas the TC for n = 5 was obtained at 494 K with change in the crystal structure. The thermodynamic properties of the two crystals studied by thermogravimetric analysis exhibited relatively high thermal stability at 600 K. From the spin-lattice relaxation times (T1ρ) according to the temperature change for n = 3 and 5, it was determined that the energy transfer, demonstrating a small thermal displacement around the 1H and 13C atoms of the cation, was minuscule. The effects of T1ρ for 1H and 13C were insignificant, indicating a minor change in the N–H⋯Cl hydrogen bond related to the coordination geometry of the CoCl4 anion. Thus, the obtained results for NH3(CH2)nNH3CoCl4 (n = 3 and 5) can be helpful for future research on the application of eco-friendly organic–inorganic hybrid perovskite materials.

On the tau function of the hypergeometric equation

The monodromy map for a rank-two system of differential equations with three Fuchsian singularities is classically solved by the Kummer formulæ for Gauss’ hypergeometric functions. We define the tau-function of such a system as the generating function of the extended monodromy symplectomorphism, using an idea recently developed. This formulation allows us to determine the dependence of the tau-function on the monodromy data. Using the explicit solution of the monodromy problem, the tau-function is then explicitly written in terms of Barnes G-function. In particular, if the Fuchsian singularities are placed to 0, 1 and ∞, this gives the structure constants of the asymptotical formula of Iorgov–Gamayun–Lisovyy for solutions of Painlevé VI equation.