Linear Dependence Research Articles

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.

Bases for optimising stabiliser decompositions of quantum states

Abstract Stabiliser states play a central role in the theory of quantum computation. For example, they are used to encode computational basis states in the most common quantum error correction schemes. Arbitrary quantum states admit many stabiliser decompositions: ways of being expressed as a superposition of stabiliser states. Understanding the structure of stabiliser decompositions has significant applications in verifying and simulating near-term quantum computers.

We introduce and study the vector space of linear dependencies of $n$-qubit stabiliser states. These spaces have canonical bases containing vectors whose size grows exponentially in $n$. We construct elegant bases of linear dependencies of constant size three. 

Critically, our sparse bases can be computed without first compiling a dictionary of all $n$-qubit stabiliser states. We utilise them to explicitly compute the stabiliser extent of states of more qubits than is feasible with existing techniques. Finally, we delineate future applications to improving theoretical bounds on the stabiliser rank of magic states.

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.

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.

First-principles investigation of the thermal properties of XO (X=Be, Mg and Sr) nanosheet

The electronic structures and thermal properties of hexagonal XO ([Formula: see text], Mg and Sr) nanosheets are studied within the density functional theory. The thermal properties are computed using the specified structural parameters of the electronic properties. Thermal properties including entropy, enthalpy, free energy and heat capacity for XO nanosheets are reported. It is found that BeO is an insulator, whereas MgO and SrO are semiconductors based on the energy gap value within GGA and HSE06. The electronegativity and bonding nature of XO nanosheets differ, resulting in considerable variations in thermodynamic parameters that follow a similar pattern as a function of temperature. Enthalpy and entropy increase with temperature whereas free energy falls, owing to a change in the binary oxide internal energy of the system and the electron density distribution. Thermal energy absorbed by the lattices grows with increasing temperature to the point at which all of their modes are activated and the systems start to display unharmonicity deviating from a linear dependence. Variable parameter ranges for XO nanosheets are useful in the development of thermoelectric nanodevices.

The Arsenal of Perturbation Bounds for Finite Continuous-Time Markov Chains: A Perspective

Perturbation bounds are powerful tools for investigating the phenomenon of insensitivity to perturbations, also referred to as stability, for stochastic and deterministic systems. This perspective article presents a focused account of some of the main concepts and results in inequality-based perturbation theory for finite state-space, time-homogeneous, continuous-time Markov chains. The diversity of perturbation bounds and the logical relationships between them highlight the essential stability properties and factors for this class of stochastic processes. We discuss the linear time dependence of general perturbation bounds for Markov chains, as well as time-independent (i.e., time-uniform) perturbation bounds for chains whose stationary distribution is unique. Moreover, we prove some new results characterizing the absolute and relative tightness of time-uniform perturbation bounds. Specifically, we show that, in some of them, an equality is achieved. Furthermore, we analytically compare two types of time-uniform bounds known from the literature. Possibilities for generalizing Markov-chain stability results, as well as connections with stability analysis for other systems and processes, are also discussed.

Two-Point Polynomial Patterns in Subsets of Positive Density in $\mathbb{R}^{n}$

Abstract Let $\gamma (t)=(P_{1}(t),\ldots ,P_{n}(t))$ where $P_{i}$ is a real polynomial with zero constant term for each $1\leq i\leq n$. We will show the existence of the configuration $\{x,x+\gamma (t)\}$ in sets of positive density $\epsilon $ in $[0,1]^{n}$ with a gap estimate $t\geq \delta (\epsilon )$ when $P_{i}$’s are arbitrary, and in $[0,N]^{n}$ with a gap estimate $t\geq \delta (\epsilon )N^{n}$ when $P_{i}$’s are of distinct degrees where $\delta (\epsilon )=\exp \left (-\exp \left (c\epsilon ^{-4}\right )\right )$ and $c$ only depends on $\gamma $. To prove these two results, decay estimates of certain oscillatory integral operators and Bourgain’s reduction are primarily utilised. For the first result, dimension-reducing arguments are also required to handle the linear dependency. For the second one, we will prove a stronger result instead, since then an anisotropic rescaling is allowed in the proof to eliminate the dependence of the decay estimate on $N$. And as a byproduct, using the strategy token to prove the latter case, we extend the corner-type Roth theorem previously proven by the first author and Guo.

IGC investigation of the effect of the length of the n-alkyl substituent in 5-alkylsubstituted norbornenes on solute retention

Polymerization of 5-n-alkyl-substituted 2-norbornenes synthesized a series of polymers having the same structure of the main polymer chain, but differing in the length of the alkyl substituent (up to 14 methylene units). The obtained polymers were studied by the capillary IGC method as a stationary phase during separation of a mixture of normal hydrocarbons C6-C10. Retention data in the form of a logarithm of the retention factor lnk were correlated with the size of the sorbate (via the carbon number of the alkane ZS) and with the size of the n-alkyl substituent in the polymer chain (via the carbon number of the polymer ZP). Correlation of lnk vs. ZS turned out to be linear for all polymers, but the angle of the slope of linear dependence dlnk/dZS increases with a decrease in the carbon number of the polymer ZP. Dependency of dlnk/dZS vs. ZP is not linear and indicates an increase in the retention of sorbates by the stationary phase with a decrease in the length of the alkyl substituent in the polymer chain. The correlation of the retention of lnk analytes with the carbon number of the polymer ZP is not linear and indicates an increase in the sorbate/sorbent interaction with a decrease in the length of the alkyl substituent. Inflection points were found at both correlations with ZP in the region of ZP = 8, which indicates a possible change in the sorption mechanism or a change in the phase state of the polymer. In polymer chemistry, the phase state of a polymer is characterized by the glass transition temperature Tg, the dependence of which vs. ZP turned out to be nonlinear with an inflection point at ZP ∼11. Thus, a decrease in the length of the alkyl substituent leads to the transition of the polymer from a rubbery state to a glassy one at ZP ∼ 11, which in turn, with a further decrease in the carbon number of the polymer to ZP ∼ 8, causes a change in the sorption mechanism from bulk sorption to surface sorption. The change in the sorption mechanism is accompanied by an increase in the interaction of the sorbate with the stationary phase, which manifests itself both in an increase in the retention time of analytes and in an increase in the enthalpy and entropy of sorption. The reason for this increase can be seen in the formation of a microporous structure in 5-alkyl-substituted polynorbornenes in a glassy state.

Towards the understanding of convective dissolution in confined porous media: thin bead pack experiments, two-dimensional direct numerical simulations and physical models

We consider the process of convective dissolution in a homogeneous and isotropic porous medium. The flow is unstable due to the presence of a solute that induces a density difference responsible for driving the flow. The mixing dynamics is thus driven by a Rayleigh–Taylor instability at the pore scale. We investigate the flow at the scale of the pores using Hele-Shaw type experiment with bead packs, two-dimensional direct numerical simulations and physical models. Experiments and simulations have been specifically designed to mimic the same flow conditions, namely matching porosities, high Schmidt numbers and linear dependency of fluid density with solute concentration. In addition, the solid obstacles of the medium are impermeable to fluid and solute. We characterise the evolution of the flow via the mixing length, which quantifies the extension of the mixing region and grows linearly in time. The flow structure, analysed via the centreline mean wavelength, is observed to grow in agreement with theoretical predictions. Finally, we analyse the dissolution dynamics of the system, quantified through the mean scalar dissipation, and three mixing regimes are observed. Initially, the evolution is controlled by diffusion, which produces solute mixing across the initial horizontal interface. Then, when the interfacial diffusive layer is sufficiently thick, it becomes unstable, forming finger-like structures and driving the system into a convection-dominated phase. Finally, when the fingers have grown sufficiently to touch the horizontal boundaries of the domain, the mixing reduces dramatically due to the absence of fresh unmixed fluid. With the aid of simple physical models, we explain the physics of the results obtained numerically and experimentally. The solute evolution presents a self-similar behaviour, and it is controlled by different length scales in each stage of the mixing process, namely the length scale of diffusion, the pore size and the domain height.