Linear Dependence Research Articles

Constructing mathematical models of thermal conductivity in individual elements and units of electronic devices at local heating considering thermosensitivity

This paper considers a heat conduction process for an isotropic medium with local external and internal thermal heating. It was necessary to construct linear and non-linear mathematical models for determining the temperature field, and consequently, for the analysis of temperature regimes in these heat-active environments. To solve the linear boundary value problems and the resulting linearized boundary value problems with respect to the Kirchhoff transformation, the Henkel integral transformation method was used, as a result of which the analytical solutions to these problems were obtained. For a heat-sensitive environment, as an example, a linear dependence of the coefficient of thermal conductivity of the structural material of the structure on temperature, which is often used in many practical problems, was chosen. As a result, analytical relations for determining the temperature distribution in this environment were established. To determine the numerical values of the temperature and analyze the heat exchange processes in the given structure, caused by the external heat load, a geometric image of the temperature distribution was constructed depending on spatial coordinates. The resulting linear and non-linear mathematical models testify to their adequacy to the real physical process. They make it possible to analyze heat-active media regarding their thermal resistance. As a result, it becomes possible to increase it and protect it from overheating, which can cause the destruction of not only individual nodes and their elements but the entire structure as well

Constructing mathematical models of thermal conductivity in individual elements and units of electronic devices at local heating considering thermosensitivity

This paper considers a heat conduction process for an isotropic medium with local external and internal thermal heating. It was necessary to construct linear and non-linear mathematical models for determining the temperature field, and consequently, for the analysis of temperature regimes in these heat-active environments. To solve the linear boundary value problems and the resulting linearized boundary value problems with respect to the Kirchhoff transformation, the Henkel integral transformation method was used, as a result of which the analytical solutions to these problems were obtained. For a heat-sensitive environment, as an example, a linear dependence of the coefficient of thermal conductivity of the structural material of the structure on temperature, which is often used in many practical problems, was chosen. As a result, analytical relations for determining the temperature distribution in this environment were established. To determine the numerical values of the temperature and analyze the heat exchange processes in the given structure, caused by the external heat load, a geometric image of the temperature distribution was constructed depending on spatial coordinates. The resulting linear and non-linear mathematical models testify to their adequacy to the real physical process. They make it possible to analyze heat-active media regarding their thermal resistance. As a result, it becomes possible to increase it and protect it from overheating, which can cause the destruction of not only individual nodes and their elements but the entire structure as well

Analysis and Assessment of Knowles' Partitioning in Many-Body Perturbation Theory.

A detailed analysis of a new partitioning in many-body perturbation theory recently proposed by Knowles (J. Chem. Phys. 156, 011101, 2022), termed "perturbation adapted partitioning" (PAPT), is presented. Level shift and orbital rotation effects are identified as gears of the zero-order Hamiltonian. These two components are examined separately, revealing that, in themselves, neither of the two is competitive with the combined effect. The success of PAPT can be attributed to determining a set of molecular orbitals and corresponding orbital energies that can systematically outperform the canonical orbitals and Koopmans' energy-based Møller-Plesset partitioning. The self-consistent version of the method is also tested in terms of energy and convergence. Previous numerical studies are further complemented with an application to an inherent multireference example and an investigation of van der Waals interaction energies. In addition, a rigorous mathematical analysis of the consequence of the linear dependence of projection functions on the solution of the Knowles' equations is provided.

Experimental Measurement of Emissivity of Polished Steel Strips from a Continuous Annealing Line.

The long-term use of steel strip in various industries makes it an important semi-finished product, which makes it necessary to improve its chemical composition and mechanical properties, reduce its thickness and weight, expand the range of new types of steel strip and increase its production. This entails a large number of technological operations dependent on precise temperature measurement and control. In some industrial plants, the steel strip is in continuous motion, which makes the use of contact measuring devices impossible. When using non-contact measuring devices such as pyrometers or thermal imaging cameras, the emissivity of the materials being measured is a problematic parameter, as setting an incorrect emissivity value to the measuring device results in inaccurate temperature readings. The essence of this research was to establish a measurement method and to perform experimental measurements of the emissivity of a polished steel strip used in a continuous annealing line, the subsequent processing of the data from these measurements and their evaluation. The emissivity measurements were carried out for 5 types of steel strip of different parameters, while the measurement itself was carried out in the long wavelength range of 7.5-14 µm and at strip temperatures of 100-300 °C. Depending on the type of steel strip, the mean emissivity values ranged from 0.0835- to 0.1143. The emissivity of the steel strip increased with increasing strip temperature, and it was not a linear dependence. The emissivity values determined in this research could be applied to measuring equipment in actual production, which could improve the accuracy of temperature measurement in the heat treatment of polished steel strip. Thermal camera measurements in the long wavelength range, taking thermal images and their processing and determining the emissivity value of polished steel strips are the parts of this research that make it different from other already published research.

Composite "Crosslinked Polyvinyl Alcohol-Magnetite" as a Stimuli-Responsive Matrix for Optical Methods.

The preparation and application of the composite material "crosslinked polyvinyl alcohol-magnetite" as a sensitive matrix for use in digital colorimetry and optical micrometry methods are discussed. The material was synthesized in the form of spherical granules (for micrometry) and thin films (for digital colorimetry). The obtained composites were characterized by the registration of magnetization curves. It was shown that the amount of grown Fe3O4 particles in the polymer gel is in linear dependence with the iron salt concentrations in the impregnating solutions. The composite granules were applied to determining monosaccharides using optical micrometry. The optimal pH value for the total amount of monosaccharides' determination was 8.6. The study of the analytical response of composite granules and films performed with a low limit of detection (7.9 mmol/dm3) of both glucose and fructose and a possibility of the control of high alcohol contention in water media. The granules were used to determine the total carbohydrate content in samples of natural honey and syrups with high fructose contents, while the films were used to control the alcohol content in hand antiseptics. The results obtained are in good agreement with the data provided by the manufacturers.

Weather-dependency of the thermographic flow visualization of the laminar-turbulent transition on wind turbines

Abstract Analyzing the airflow around wind turbines during operation requires an in-process-capable measurement approach that functions without modification of the rotor blade. Infrared–thermographic flow visualization is such a measurement approach. However, its measurement capabilities on wind turbines in operation are highly weather-dependent. Therefore, to understand the expected flow visualization quality in non-laboratory conditions, the dependence of the achievable contrast and contrast-to-noise ratio (CNR) of the laminar-turbulent transition on solar radiation and air temperature is studied, respectively. A linear dependence of the contrast on the absorbed solar radiation is derived as a first estimation from a theoretical study of the heat balance. While the air temperature variations are shown to have no effect under certain conditions. The slope of the linear dependence of about 0.025 m2K W−1 was validated by experiments. To further study the fundamental measurability limit, only the camera noise with constant variance is here applied to determine the achievable CNR, which is thus directly proportional to the contrast. As a result, the achievable contrast and CNR for visualizing the laminar-turbulent flow transition over the year, over the day, and for different yaw angles of the wind turbine are determined. For this investigation, a wind turbine location near in northern Germany, is assumed as an example, and a maximal achievable contrast and CNR of 4.2 K and 122, respectively, are estimated, which agree with previous measurements. The presented method applies to any other wind turbine location and thus enables planning thermographic flow measurements on any wind turbine in the world.

Heterogeneity's impact on the sloshing motion in excited tanks

AbstractThis paper aims to investigate the effect of liquid heterogeneity on sloshing in a two-dimensional rectangular tank. The container is excited horizontally, and the density of the liquid at equilibrium can almost be considered a linear dependence of the depth. The linearized equations representing the sloshing phenomenon are solved numerically using ANSYS 2020 R2 software and analytically using the separation method of variables in conjunction with the Fourier analysis. On the other hand, a comparison study has been carried out between the obtained results and other works related to the same phenomenon. Overall, the results exhibit considerable effects of variation in the Heterogeneity Coefficient β on the free surface's motion and the pressure distribution within the liquid. Furthermore, the free surface of liquid heterogeneity is also affected by the variation of Excitation Frequency Ω and the Filling Rate h of the liquid in the tank.

Properties of classical evanescent waves obtained by using the linear independence concept

Normally, the properties of evanescent optical waves are obtained by developing the Fresnel equations that are expressed in the complex numbers field when the incident angle exceeds the critical angle. Instead of using complex numbers, here we use real functions and the mathematical concept of linear independence to obtain all the properties of the evanescent waves.

Analytic Construction of One-Electron Reduced Density Matrices from Electron Densities within Finite Basis Sets.

We show how to construct analytically all one-electron reduced density matrices (1-RDMs) compatible with a given electron density within a finite basis set, provided that the density is specified as a symmetric quadratic form in terms of the basis functions. Contrary to the current belief, exact linear dependencies in the basis function products assist, rather than hinder, such constructions. By applying the N-representability conditions to the analytically reconstructed 1-RDMs, one can perform a constrained search over physically acceptable 1-RDMs that yield a given finite-basis-set density. The discussion is illustrated with worked-out examples.

Feasibility study for the development of multilayered solar cells for proton linear energy transfer depth profile measurement.

Previous study proposed a method to measure linear energy transfer (LET) at specific points using the quenching magnitude of thin film solar cells. This study was conducted to propose a more advanced method for measuring the LET distribution. This study focuses on evaluating the feasibility of estimating the proton LET distribution in proton therapy. The feasibility of measuring the proton LET and dose distribution simultaneously using a single-channel configuration comprising two solar cells with distinct quenching constants is investigated with the objective of paving the way for enhanced proton therapy dosimetry. Two solar cells with different quenching constants were used to estimate the proton LET distribution. Detector characteristics (e.g., dose linearity and dose-rate dependency) of the solar cells were evaluated to assess their suitability for dosimetry applications. First, using a reference beam condition, the quenching constants of the two solar cells were determined according to the modified Birks equation. The signal ratios of the two solar cells were then evaluated according to proton LET in relation to the estimated quenching constants. The proton LET distributions of six test beams were obtained by measuring the signal ratios of the two solar cells at each depth, and the ratios were evaluated by comparing them with those calculated by Monte Carlo simulation. The detector characterization of the two solar cells including dose linearity and dose-rate dependence affirmed their suitability for use in dosimetry applications. The maximum difference between the LET measured using the two solar cells and that calculated by Monte Carlo simulation was 2.34keV/µm. In the case of the dose distribution measured using the method proposed in this study, the maximum difference between range measured using the proposed method and that measured using a multilayered ionization chamber was 0.7mm. The expected accuracy of simultaneous LET and dose distribution measurement using the method proposed in this study were estimated to be 3.82%. The signal ratios of the two solar cells, which are related to quenching constants, demonstrated the feasibility of measuring LET and dose distribution simultaneously. The feasibility of measuring proton LET and dose distribution simultaneously using two solar cells with different quenching constants was demonstrated. Although the method proposed in this study was evaluated using a single channel by varying the measuring depth, the results suggest that the proton LET and dose distribution can be simultaneously measured if the detector is configured in a multichannel form. We believe that the results presented in this study provide the envisioned transition to a multichannel configuration, with the promise of substantially advancing proton therapy's accuracy and efficacy in cancer treatment.

Reductive Immobilization of Hexavalent Chromium in Soil Using Hydrazine – Kinetics, Process Optimization, Sonochemical Enhancement, and Cost Estimation

ABSTRACT The presence of hexavalent chromium in soil poses a grave hazard to the environment and human health. This study explores the effectiveness, mechanism, and economic viability of remediation of Cr(VI)-contaminated soil by hydrazine. Soil-phase batch kinetic experiments were performed to examine the feasibility of reducing Cr(VI) while finding the effects of relevant process parameters, such as initial Cr(VI) concentration, hydrazine dosage, pH, soil-to-water ratio, and temperature. The materials were thoroughly characterized to gain insight into the mechanism. TCLP tests were done to affirm the immobilization stability. Complete Cr(VI) reduction was achieved within 3 h using a moderate 326% excess of hydrazine at neutral pH. Sonication of the soil mixed with hydrazine using a probe-type sonicator accelerated the reduction of Cr(VI) to Cr(III). Kinetic data could be adequately fitted in a second-order rate model, where the rate constant shows a linear dependency on the soil-to-water ratio. Additionally, the logarithmic rate constant demonstrates linearity within the pH range. The leaching toxicity of Cr(VI) and Crtotal complied with the USEPA regulatory limit and remained stable for 75 d. Hydrazine alone and its combination with ultrasound are sustainable and economically feasible for effective remediation of Cr(VI)-contaminated soil. The statistical analysis using RSM indicated a 99.4% reduction, aligning closely with the calculated optimized value. The optimal process conditions are easy to implement for field application at a competitive cost compared to other reductants. A simplified economic analysis was done to check the competitive acceptability of the technique, considering the construction cost of the remediation plant and its daily operational and maintenance expenses. The results show that the proposed technique will be a competitive one for field applications for the remediation of soil contaminated with Cr(VI). The data and kinetic rate equation will be useful for the process design of the remediation of soil contaminated with Cr(VI).

2D-network of boron-functionalized N-doped graphene quantum dots for electrochemical sensing of dopamine

A glassy carbon electrode (GCE) modified by boron-functionalized N-doped graphene quantum dots (B-GQDs) was employed for the electrochemical determination of dopamine (DA), a neurotransmitter. The B-GQDs were obtained by hydrothermal etching of GO with H2O2 and NH3 in the presence of H3BO3. By using various techniques, including transmission electron microscopy, atomic force microscopy, molecular absorption spectrometry, fluorescence, ICP-MS, and zeta potential analysis, it was demonstrated that B-GQDs are self-organized in 2D-network, being N-doped GQDs nanoparticles crosslinked by H3BO3. The GCE modification was carried out using the drop-casting method with B-GQDs in Nafion®, previously dispersed through ultrasonication. For the first time, the synthesized nanomaterial was tested in the electroanalysis of neurotransmitters. The B-GQDs/Nafion®/GCE modification led to a significant increase in peak currents in the presence of DA. The electrochemical and interfacial characteristics of the sensors were evaluated by cyclic voltammetry (CV). Under optimized square wave voltammetry and supporting electrolyte conditions, a linear dependence between the anodic peak current and DA concentration was observed in the range of 0.7 to 188 μmol L−1 (R2 = 0.9991). The limit of detection (LOD) was estimated at 0.05 μmol L−1. Selectivity was confirmed in the presence of potential interferents found in urine, with interference response below 12 %. The sensor exhibited excellent intra-day and inter-day repeatability, with a relative standard deviation of 4.12 % and 4.66 %, respectively. Electrochemical determination of DA was conducted in artificial urine samples (Surine®), with recovery values of 90–101 %. The new analytical platform B-GQDs/Nafion®/GCE demonstrated promising characteristics for application in biological and/or pharmaceutical analysis.

Stochastic Averaging of Radiative Transfer Coefficients for Relativistic Electrons

Synchrotron emissivities, absorptivities, and Faraday rotation and conversion coefficients are needed in modeling a variety of astrophysical sources, including Event Horizon Telescope (EHT) sources. We develop a method for estimating transfer coefficients that exploits their linear dependence on the electron distribution function, decomposing the distribution function into a sum of parts each of whose emissivity can be calculated easily. We refer to this procedure as stochastic averaging and apply it in two contexts. First, we use it to estimate the emissivity of an isotropic κ distribution function with a high-energy cutoff. The resulting coefficients can be evaluated efficiently enough to be used directly in ray-tracing calculations, and we provide an example calculation. Second, we use stochastic averaging to assess the effect of subgrid turbulence on the volume-averaged emissivity and along the way provide a prescription for a turbulent emissivity. We find that for parameters appropriate to EHT sources turbulence reduces the emissivity slightly. In the infrared, turbulence can dramatically increase the emissivity.

Exploiting indirect linear correlation for label distribution learning

Label distribution learning represents the relevance of labels to samples using description degree, which can provide richer semantic information, thus finding wider applications. Exploiting label correlations is an effective approach to narrow down the hypothesis space of label distribution learning models. In existing works that utilize low-rank assumptions or label linear dependence to mine correlations, it is assumed that a label can be linearly expressed by other labels. However, this assumption can only be satisfied when there are linear dependency relationships between labels, thus the label correlation obtained by such methods is subject to certain distortion. To address this issue, this paper assumes that labels can be linearly represented by the same set of bases. The correlation between labels is represented by sharing common bases. Specifically, the paper employs matrix factorization to extract bases that can be used to represent all labels. And then designs a label distribution learning algorithm based on the property of sharing the same set of bases of the ground truth label distribution and predict label distribution. The effectiveness of the algorithm is verified through experimental validation. Generally speaking, the algorithm presented in this paper achieves optimal performance at 73.15% of the cases, with the best average ranking. In the two-tailed t-test, the algorithm in this paper exhibits statistical superiority compared to all comparison algorithms.

ОПРЕДЕЛЕНИЕ ТЕМПЕРАТУРЫ ТЕПЛОНОСИТЕЛЯ В МЕТАЛЛИЧЕСКИХ И ПЛАСТИКОВЫХ ТРУБАХ ПО ТЕМПЕРАТУРЕ ИХ НАРУЖНЕЙ ПОВЕРХНОСТИ

To determine the coolant temperature by the pipe wall temperature, mutual dependences between the temperatures of the wall, coolant and air, flow velocity, and pipe dimensions are revealed. It is established that the flow velocity of the coolant in the pipeline affects the heat flux density only in the laminar flow regime characterized by low velocity. A linear dependence between the wall temperature, air temperature and coolant temperature has been found. A nomogram allowing to determine the coolant temperature in polypropylene pipes by their wall temperature has been constructed. It is shown that the surface temperature of steel pipes can be considered equal to the temperature of the coolant.

Optimizing misfit dislocation glide kinetics for enhanced threading dislocation density reduction in Si1−xGex/Si(001) layers through dynamic growth rate control

Relaxed Si1−xGex layers on Si(001) serve as virtual substrates for strained Si or Ge layers. However, plastically relaxed layers inevitably contain misfit and threading dislocations, negatively affecting devices. Deposition of a SiGe layer on the backside of the substrate introduces a dislocation reservoir at the wafer edge that can reduce the threading dislocation density (TDD) of Si0.98Ge0.02/Si layers, as these preexisting dislocations start gliding toward the wafer center upon reaching the critical thickness. Here, we show that this low-strain system can be used effectively to study dislocation glide kinetics. In agreement with the literature, dislocation glide is a thermally activated process with an activation energy of 2.12–2.16 eV. Near the critical thickness, relaxation is sluggish and inefficient due to the linear dependence of the glide velocity on excess stress. At lower growth rates, dislocations from the edge reservoir are activated in a lower density due to the increase in the critical thickness through partial strain relaxation by already activated dislocations. Contrary to common models, here, the lowest possible growth rate is not essential for minimizing the TDD. Instead, a careful balance between low and high growth rates is beneficial. Overcoming the initial sluggish and inefficient relaxation phase is critical while also avoiding accumulation of strain energy, and, therefore, the activation of dislocation sources. Only in a later stage of buffer growth, the growth rate should be reduced to a minimum. With this method, the TDD of strain relaxed Si0.84Ge0.16 layers is reduced to 7 × 104 cm−2.

Design and synthesis of Co@NiSe catalyst for efficient 2e− ORR in neutral electrolyte: Effect of electronic structure engineering

Two-electron oxygen reduction reaction (2e− ORR) generating hydrogen peroxide (H2O2) in neutral electrolytes is currently encountering significant scientific challenges. Here, we adopted a direct electron transfer and defect engineering approach for synthesizing a Co-doped NiSe hybrid catalyst to boost the efficiency of this reaction system. The Co@NiSe catalyst with long-term stability over 160 h showed a 53.1 % increase in H2O2 selectivity comparing with the pristine NiSe material in neutral electrolyte, indicating the effective modulation of the electronic structure of NiSe via Co doping. Impressively, the 2e− ORR catalytic activity of the catalysts exhibited a positive linear dependence on the content of Ni2+ species. The present research proved the possibility for improving the activity of transition metal-based catalysts in neutral electrolytes via hetero-atom doping, which had built basic structure-function relations for designing highly efficient 2e− ORR system.

Study of 10 kW Vanadium Flow Battery Discharge Characteristics at Different Load Powers

Vanadium redox flow batteries are promising energy storage devices and are already ahead of lead–acid batteries in terms of installed capacity in energy systems due to their long service life and possibility of recycling. One of the crucial tasks today is the development of models for assessing battery performance and its residual resource based on the battery’s present state. A promising method for estimating battery capacity is based on analyzing present voltage and current values under various load conditions. This paper analyzes the discharge characteristics of a 10 kW all-vanadium redox flow battery at fixed load powers from 6 to 12 kW. A linear dependence of operating voltage and initial discharge voltage on load power is established. It is also determined that the slope of the discharge curve linear section does not increase linearly in absolute value, and the Box–Lucas model can be used to describe it. Models for predicting current VRFB capacity based on different curve fitting functions are proposed. These models can be used to roughly estimate battery capacity at different load powers.

Fabrication of ZnO/ Bi2O3/PVA coated glass for X-ray detection and measurement

Electrospun ZnO/Bi2O3/PVA-coated glass samples were fabricated using electrospinning method, with varying ZnO molarities (0 M, 5 M, and 7 M) and Bi2O3 weight percentages (wt%) to assess their potential for x-ray detection and measurement. Sample morphology and elemental composition analysis revealed well-distributed nanofiber strands on the glass substrate, with even dispersion of elements within the nanofiber across all samples. The effective atomic number (Zeff) of the sample is consistently enhanced with the addition of Bi2O3 and higher ZnO molarity, where sample with 7 wt% Bi2O3 own a greater Zeff value (41.56–44.12) than sample with 5 wt% Bi2O3 (37.22–40.54). All samples except Sample A0 and B0 exhibited strong absorbance between wavelength range of 360 nm–400 nm. Sample A0 and B0 yielded energy band gaps (Eg) of 2.39 eV and 2.37 eV, respectively, whereby samples with ZnO exhibit energy gaps of Eg = 3.29 eV (Sample A1), Eg = 3.27 eV (Sample A2), Eg = 3.25 eV (Samples B1 and B2). All samples underwent x-ray exposure at various tube voltages (40–60 kVp) to assess their attenuation ability for x-ray detection and measurement. Sample B2 (5 wt% Bi2O3 and 7 M ZnO) exhibited the most favorable linear response, while Sample B1 (5 wt% Bi2O3 and 5 M ZnO) displayed favorable energy dependency. Thus, the electrospun ZnO/Bi2O3/PVA-coated glass with these compositions are proposed as potential dosimetry material due to their favorable linear response and energy dependency characteristics.

Observation of Linear Magnetoresistance in MoO2.

Magnetoresistance, the change in resistance with applied magnetic fields, is crucial to the magnetic sensor technology. Linear magnetoresistance has been intensively studied in semimetals and semiconductors. However, the air-stable oxides with a large linear magnetoresistance are highly desirable but remain to be fully explored. In this paper, we report the direct observation of linear magnetoresistance in polycrystalline MoO2 without any sign of saturation up to 7 T under 50 K. Interestingly, the linear magnetoresistance reaches as large as 1500% under 7 T at 2 K. The linear field dependence is in great contrast to the parabolic behavior observed in single-crystal MoO2, probably due to phonon scattering near the grain boundaries. Our results pave the way to comprehending magneto-transport behavior in oxides and their potential applications in magnetic sensors.