Proportionality Coefficient Research Articles

Evaluation of dust production efficiencies in sandy sediments

AbstractSeveral studies have shown that dust emission (vertical flux, F) can be considered a constant fraction (k) of the saltating flux (horizontal flux, Q), that is, . This coefficient of proportionality, or dust production efficiency factor, is often called the ‘k factor’ and is fundamentally related to soil properties especially soil texture. Beyond regional and global modeling applications, a practical utility of k is for air quality regulatory agencies where k can be used to estimate F based on only measurements of Q, which is more easily measured in the field. Only a few studies have directly estimated the k factor from soils within potential dust sources even though dust models that represent the sandblasting process typically utilize k. The goal of this study was to compare two methods to calculate k from sandy sediments and compare those estimates with an empirical method of calculating the k factor. The first method (method 1) used the difference between F calculated from two sets of sediment samplers whereas the second method (method 2) used a set of aerosol monitors to measure F. We found that the range of k values from our study are consistent with soil texture‐based estimates of k and also have the correct order of magnitude. Thus, any of the methods described in our study are appropriate for estimation of k for sandy soils.

Studies on Chemical and Physical Stability of Mayonnaise Prepared from Enzymatically Interesterified Corn Oil-Based Designer Lipids

The objective of current work is to study the physicochemical stability of mayonnaise made from corn oil designer lipid (CODL) and to evaluate the performance of monocaprylin/dicaprylin (80:20) (MD82) as an emulsifier. The oxidative stability, texture, microstructure, and rheological characteristics of CODL-based mayonnaise are evaluated and compared with those of the commercial sample. CODL-based mayonnaise showed good oxidative stability compared to the commercial sample based on established data of acid value, peroxide value, p-anisidine value, and totox value. The firmness of CODL containing mayonnaise (F1) increased, whereas that of F2 mayonnaise (commercial sample) decreased with storage. The creaming indices of the F1 and F2 mayonnaise samples were 0.27 and 3.19%, respectively, after 30 days, indicating higher stability of F1 mayonnaise. The coordination number and proportionality coefficient values for the F1 sample also elucidated a complex network and higher stability of emulsion. The droplet size of F1 mayonnaise was smaller compared to the droplet size of F2 mayonnaise even after 30 days, confirming better stability. It was clearly elucidated that mayonnaise formulated using CODL showed superior physicochemical characteristics and MD82 proved to be an effective emulsifier maintaining a good creaming index.

Power generalization of the linear constitutive equations of heat and mass transfer and the variants of writing the equations of momentum transfer, heat and diffusion arising from them

Currently, when solving problems of heat and mass transfer, linear constitutive equations are used - in hydrodynamics, the viscous stress tensor is proportional to the strain rate tensor (Newton's rheological ratio), in heat transfer, the heat flux density is linearly related to the temperature gradient (Fourier's heat conduction law), in mass transfer, the diffusion flux density proportional to the concentration gradient (Fick's law). When writing these linear governing equations, proportionality coefficients are used, which are called the viscosity coefficient, thermal conductivity coefficient and diffusion coefficient, respectively. Such constitutive equations are widely used to describe the processes of heat and mass transfer in a laminar flow regime. For turbulent flows, these equations are unsuitable, it is necessary to introduce into consideration the empirical turbulent coefficients of viscosity μt, thermal conductivity λt and diffusion Dt. However, to describe turbulent flows, it is possible to go in another way - to modify the linear constitutive relations by giving them a nonlinear power-law form. Two-parameter power-law generalizations of Newton's, Fourier's and Fick's formulas for shear stress, heat flux density and diffusion, which, depending on the value of the exponents, can be used to describe the processes of heat and mass transfer both in laminar and turbulent fluid flow. Also, this generalization can be used to describe the behavior of power-law fluids and flows of polymer solutions exhibiting the Toms effect.

Energy harvesting using a dynamic weighing system based on piezoelectric materials

Road transport is one of the main energy-consuming sectors. Therefore, the concept discussed in this article is of great interest since it aims to transform this sector into a producer of clean and renewable energy by using piezoelectric conversion. The work carried out in this article concerns the study of the electrical power density recovered by a miniaturized dynamic weighing system using piezoelectric sensors inserted into the road surface and by varying the speed and the weight of the vehicle. The system studied in this article therefore offers the possibility of measuring and then controlling the load of a moving vehicle using the vibrations generated during its passage and then converting them into electricity by direct piezoelectric effect. A mathematical model representing the relationship between the weight of the vehicle and the voltage peaks generated by the passage of the latter over the piezoelectric sensors has been developed. This model was implemented on the Matlab software, which made it possible to carry out, based on several experimental tests, a study of the variation of the coefficients of proportionality according to the weight of the vehicle and its rolling speed. The power density collected by this application at different speeds and masses was then calculated. According to the tests carried out, the recovered power density is approximately 36.06 W/m3 for a travel speed of 0.52 m/s and a vehicle weight equal to 1150 g.

Wind tunnel pressure data analysis for peak cladding load estimation on a high-rise building

A correct evaluation of wind loads on high-rise building cladding panels is essential to ensure safety while avoiding costly over-design. The estimation of peak design loads from wind tunnel tests requires post-processing pressure time histories to remove small-scale fluctuations that do not significantly affect the total load on cladding elements. This post-processing commonly employs a low pass filter with a time-scale that is linearly proportional to the ratio of a reference length scale and velocity. The objective of this study is to analyze the equivalence between the moving-average filter and the spatial averaging procedure, focusing on panels near the top corners and edges of a high-rise building. The real area-averaged pressure is calculated using high-resolution pressure measurements and compared to estimates obtained from moving-average filters with a range of time-scales. The error is within ±1Cp for most pressure tap locations and panels analyzed, although some locations near the top edge result in overestimates of the peak suction up to 3Cp. The optimal value of the proportionality coefficient defining the filter time-scale is shown to be dependent on both pressure tap location and panel size, suggesting that accurate estimates of area-averaged pressures based on single-point measurements require more advanced post-processing techniques.

Processing and evaluation of the results of a psychological experiment using PPP Statistica in the study of the seed separator of oil seeds

As a result of the analysis of technological methods of seed material separation and their technical support it is established that the main trends in the development of precision seed cleaning equipment are the creation of adaptive control systems that allow dynamic optimization of working modes without operator intervention. The process of separation of oilseeds is a complex system that is influenced by a large number of independent variables, and only some of them significantly affect the original parameter studied. Therefore, starting to find the optimal parameters or conditions of the studied phenomenon, it is necessary to determine in advance which independent variables are to be studied. The article presents the definition of the Kendall concordance coefficient and its statistical assessment with a priori ranking of the estimates of the influence of independent variables in a psychological experiment for a multivariate active experiment using Friedman's nonparametric analysis of variance with the use of PPP Statistica in the study of an oilseed separator. A method is proposed for determining the number of significant factors for obtaining the response function by resolving the exponential equations of transgression into areas of fast and slow fall using the proportionality coefficient of the linear equation. It was found that the assessment of the results of the psychological experiment by Friedman's analysis of variance using the PPP Statistica allows us to determine the Kendall concordance coefficient and perform its statistical assessment. To obtain a determination of the number of significant factors of the response function, it is proposed to use the exponential and linear equations of transgression together. So, for the case under consideration with a significance level of p = 0.000001, it can be argued that experts with a concordance coefficient W = 0.66967 argue that four factors - the length of the working chamber of the separator, the air flow speed, the height of the fan and the number of intake chambers most of all affect the performance of the oilseed separator. cultures.

Henry’s law constants (IUPAC Recommendations 2021)

Abstract Henry’s law states that the abundance of a volatile solute dissolved in a liquid is proportional to its abundance in the gas phase. It applies at equilibrium and in the limit of infinite dilution of the solute. For historical reasons, numerous different definitions, names, and symbols are used in the literature to express the proportionality coefficient, denoted the “Henry’s law constant”. Here, a consistent set of recommendations is presented. An important distinction is made between two new recommended reciprocal quantities: “Henry’s law solubility constant” (H s) and “Henry’s law volatility constant” (H v). Eight recommended variants of H s and H v are described and relations among them presented.

Degree estimates of one class cut-offs for improper integrals

The paper considers a normalized non-integral integral of the first kind with a variable lower bound. In this case the integrand is a generalization of the standard Gaussian distribution density. Such integrals are often called cutoffs or incomplete functions. The purpose of this paper is to obtain power inequalities for this kind of integrals. The necessity of obtaining this type of estimations is due to the fact that incomplete functions have become widespread in applications and theoretical studies. The peculiarity of the results established in the article consists in the fact that arbitrary degrees of a given integral for any value of an argument are evaluated from above not by means, of the value of integrable functions at a certain point, but by the value of the integral in question at some point proportional to this argument. The coefficient of proportionality, a parameter, can take any value from some closed interval. The main difficulty in obtaining these inequalities is that the integrand is a logarithmically concave function, that is, its logarithm is a concave function. The paper also proves that both limits of the closed interval for the parameter cannot be extended. This shows that the obtained estimates are unimprovable.

Distribution of the Proportionality Coefficient of Winter Route Counting

Distribution of the Proportionality Coefficient of Winter Route Counting

Kinetics and thermodynamics of compound growth due to reactive diffusion between solid Cu and binary Bi-Sn alloys

The growth behavior of compounds for the reactive diffusion between solid Cu and molten binary Bi-Sn alloys was experimentally examined using semi-infinite diffusion couples prepared by an isothermal bonding technique. Isothermal annealing of (Biy-Sn1-y)/Cu diffusion couples with Bi mol fraction of y = 0.27–0.46 was conducted in the temperature range of 453–603 K (180–330 °C) for various times up to 345.6 ks (96 h). In the diffusion couple with y = 0.44, an intermetallic layer composed of Cu6Sn5 with irregular scallop shapes and Cu3Sn with relatively uniform thickness forms at the (Bi-Sn)/Cu interface at 453–523 K (180–250 °C). In contrast, at 563–603 K (290–330 °C), the intermetallic layer consists of only Cu3Sn. Isothermal sections of the equilibrium phase diagram in the ternary Bi-Cu--Sn system were calculated at 453–603 K (180–330 °C) by a CALPHAD (calculation of phase diagrams) method. For the diffusion couple with y = 0.44, the diffusion path passes through the three-phase tie-triangles containing Cu6Sn5 and/or Cu3Sn in the isothermal section at 523 K (250 °C), but through only that containing Cu3Sn in the isothermal section at 603 K (330 °C). As a result, for y = 0.44, the intermetallic layer is composed of Cu6Sn5 and Cu3Sn at 453–523 K (180–250 °C), whereas it consists of only Cu3Sn at 563–603 K (290–330 °C). The mean thickness of the intermetallic layer is proportional to a power function of the annealing time, and the exponent of the power function is mostly smaller than 0.5. Such smaller values of the exponent mean that the layer growth is controlled by boundary diffusion across the intermetallic layer. Adopting the common value of 0.30 as the exponent of the power function for the Cu3Sn layer at 563–603 K (290–330 °C), we obtain a value of 17.9 kJ/mol for the activation enthalpy of the proportionality coefficient of the power function.

Thermal diagnostics of mechanical gear elements of combine harvester

The work carried out practical testing of the technology of thermal diagnostics of belt gear elements of the grating mill drive of the combine harvester. The basis of the technology is the principle of using the coefficient of the temperature ratio on the surface of the diagnosed unit and temperature in the friction zone, expressed through the coefficient of proportionality of the finite element model. The peculiarity of the thermal diagnostics, in this case, is to compare the temperature in the friction zone with the maximum allowable temperature for the direct contact zone in the mechanical transmission unit. The object of the study is the tensioning roller of the drive of the grating mill of the first stage of the CLAAS TUCANO 580 combine harvester with 6203-2RS TIMKEN bearings. The result of the numerical experiment showed a significant effect on the temperature in the friction zone of the operational parameters - radial force and rotational speed. The use of 3D-modeling made it possible to determine the key parameter of the proposed thermal diagnostics technology - the proportionality coefficient of the finite-element model k=0.489. The temperature of the bearing assembly of the tension roller was measured periodically, using a non-contact method during harvesting in the 2020 season. For the period of regular observations of 128 moto-hours, the value of the maximum temperature growth rate in the friction zone Vτ=0.025 °C/min and the maximum temperature in the friction zone 69.5 °C, taking into account the ambient air temperature, were determined. No failures of the diagnosed unit were found. In the process of application of thermal diagnostics technology, no errors of the first kind are recorded, which indicates the effectiveness of the proposed technology.

Разработка математической модели интерферометрической системы определения доплеровского сдвига частоты.

This work presents the result of the received signal measuring system for processing Doppler frequency theoretical research. In the researching device means of controlling laser frequency whose amplitude is proportional to the Doppler frequency shift of the received RF signal is realized. The coherent laser beam is divided in two forming interference pattern. In this case, one of the beams passes through the delay line, which leads to a phase shift in the optical wave. The rate of this phase shift is proportional to the laser frequency, changes in which cause corresponding changes in the interference pattern. Changes in the interference pattern in center analysis makes it possible to determine the changes of the laser frequency, which depends on Doppler frequency shift of the received RF signal. In this work opposition of the requirements for the Doppler frequency shift determination interferometric system parameters (the coefficient of proportionality to conversion Doppler frequency shift of the received RF signal in laser frequency and time delay) is discovered: large dynamic measurement range and high Doppler frequency shift measurement resolution. The processing the received RF signal method is proposed. This method take into consideration these requirements. The proposed measurement algorithm implements the multiscale principle. It is pointed that the proposed processing the measurements results method can be implemented both the parallel processing in channels with different values of conversion coefficients, and sequential – with their iterative change.

Relation between Johnson noise and heating power in a two-terminal conductor

We consider the Johnson noise of a two-dimensional, two-terminal electrical conductor for which the electron system obeys the Wiedemann-Franz law. We derive two simple and generic relations between the Johnson Noise temperature and the heat flux into the electron system. First, we consider the case where the electron system is heated by Joule heating from a DC current, and we show that there is a universal proportionality coefficient between the Joule power and the increase in Johnson noise temperature. Second, we consider the case where heat flows into the sample from an external source, and we derive a simple relation between the Johnson noise temperature and the heat flux across the boundary of the sample.

Exact solution for 1D deep bed filtration with particle capture by advection and dispersion

We consider a one-dimensional (1D) non-linear 2x2 hyperbolic problem of suspension-colloidal-nano transport in porous media, so-called deep bed filtration. The particle capture rate is proportional to the overall particle flux, which includes dispersion. The captured-particle concentration dependency on the proportionality coefficient, which is typical for large captured concentrations, causes the non-linearity of the problem. However, the 1D initial–boundary value problem allows for an exact solution. The introduction of the Riemann invariant converts the 2x2 system into a scalar quasi-linear hyperbolic equation, which is implicitly solved using the method of characteristics. The non-linear equation for particle capture rate yields a limited travelling wave that approximates the exact solution for the initial–boundary problem.

Факторы и уровни планирования эксперимента, эффективный выбор с учетом ограничений

Исследуется задача планирования эксперимента с ресурсными ограничениями. Для сложной системы, предназначенной для экспериментального исследования, прежде чем использовать известные развитые методы факторного планирования эксперимента, нужно предварительно создать упрощенную математическую модель, представляющую неполное сокращенное описание системы. При этом упрощение из всех объективно существующих независимых параметров системы остаются лишь наиболее значимыми, что является вынужденной процедурой вследствие природных ограничений ресурсов, подобных для выполнения экспериментального исследования. Те же ограничения лимитируют и число значений, назначаемых каждому из параметров (уровню факторов). Статья посвящена модификации существующего метода дискретизации такой модели с рациональным выбором параметров дискретизации в соответствии с существующими ограничениями, однако с крайне ненадежной относительно сходимости итерационной процедурой решения. Главные идеи модифицированного подхода следующие: 1) выбор числа уровней факторов пропорционально значимости соответствующих параметров и сведению задачи к поиску неподвижной точки (как в известном методе); 2) разбиение по вероятности (вместо разбиения на интервалы равной длины) для дискретизации и выбора представительских значений параметра, позволяющего найти точное простое выражение для его энт-ропии Шенона; 3) переход от много- к однопараметрическому (коэффициент пропорциональности как показатель параметризации) представление нелинейного отображения, его декомпозиция и упрощение итерационного процесса; 4) нахождение начального значения коэффициента пропорциональности по фактору с средней релевантностью и расчеты для других факторов с последующим итерационным уточнением. Итерационный процесс гарантированно совпадает, так как рассмотрение малых и больших значений скалярного параметра позволяет использовать теорему с промежуточным значением непрерывной функции. Далее на основе разработанной процедуры решены две задачи о назначении числа уровней факторов для ситуаций с малым и большим ресурсным ограничением, указаны соответствующие усложнения в расчетах и способы их преодоления.

Surface volatilization modeling of (semi-)volatile hydrophobic organic compounds: The role of reference compounds

Volatilization of hazardous hydrophobic organic compounds is often observed in many water, wastewater and soil treatment (bio)processes. Several models have been developed to quantify and predict gas-liquid pollutant transfer, being the proportionality coefficient model (PCM) one of the most commonly used, particularly in wastewater treatment. The PCM is based on the use of oxygen as a reference compound, which has a low resistance to the transfer in the gas phase. However, this resistance might be important for (semi-)volatile organic compounds – or (semi-)VOCs, which may render the use of the PCM model inaccurate. This study proposes an experimental methodology and a modeling approach for the use of the two-reference compound model (2RCM) that considers both the liquid-side and the gas-side resistances, by using water and oxygen as references. Results showed that the 2RCM predicts more accurately the overall mass transfer coefficients than the PCM for a VOC and two semi-VOCs tested in this study. In addition, the 2RCM was found to be a more robust method to estimate mass transfer coefficient of any compound and its use can be extrapolated to all substances. Finally, the relevance and limitations of both models was established.

Prognosis of fatigue cracks in an aircraft wing using an adaptive tunable network and guided wave based structural health monitoring

Due to the stochastic behaviour of fatigue crack propagation resulting from the multifarious uncertainties such as aleatory uncertainty and epistemic uncertainty, a synthetic scheme integrating heterogeneous uncertainty resources is needed to make the prognosis of fatigue crack propagation be accurate. In this paper, an on-line updating strategy combining an adaptively tunable hybrid radial basis function (RBF) network and active Lamb waves based structural health monitoring is proposed for prognosis of fatigue cracks in an aircraft wing. A particle filter and Brownian motion with drift and proportionality coefficients are put forward to dynamically access a posteriori estimation of crack state and model parameters. Because of the advantages of flexibility, electrically stabilized and suitable for complex structure, the sensor layer with an embedded network of distributed piezoelectric transducers is utilized to collect Lamb wave signals describing crack states on-line. A hybrid spatial phase difference-based damage index (DI) is employed to capture the characteristics of Lamb wave signals to quantitatively determine the crack length. Furthermore, fatigue tests on the outboard wing of a real airplane are conducted to substantiate the proposed method. The experimental results demonstrate that the hybrid RBF model can timely trap the dynamic characteristics of sensor signals, and effectively predict the varying tendency of cracks growth. The uncertainties during the prognosis of fatigue cracking propagation can be effectively dealt with by combining the dynamic adjustability and the DIs-based on-line monitoring technique.

Fractal permeability model for a complex tortuous fracture network

The complex fracture network in unconventional oil and gas reservoirs is the main channel for the fluid flow, and effective prediction of fracture network permeability is the basis for further accurate assessment of oil and gas productivity. On the basis of the traditional parallel-plate cube law, we introduce the tortuosity fractal dimension DTf to characterize the tortuosity of fractures. Then, combined with fractal theory, a permeability model is derived for a complex tortuous discrete fracture network (DFN). A pixel probability decomposition algorithm is used to generate ten random DFNs that conform to the fractal scale relationship, and the effectiveness of the proposed model is verified by numerical simulation. The fracture geometry parameters are further analyzed and their effect on permeability discussed. The results show that the permeability K of a fracture network increases with an increase in porosity ϕ (0.117–0.292), fractal dimension Df (1.635–1.824), maximum fracture length lmax (3.337–7.472 m), and proportionality coefficient β (0.00108–0.0164), but decreases with the increasing tortuosity fractal dimension DTf (1.0018–1.0196) and fracture dip angle θ (10°–80°). Among these parameters, Df, DTf, and β have the greatest influence on the permeability of the fracture network, followed by θ, lmax, and ϕ.

Toward an Integrated View of Ionospheric Plasma Instabilities: 6. Analytic Analysis of Thermal Effects

AbstractThermal effects in the ionospheric plasma instabilities including the Farley‐Buneman instability (FBI), the gradient‐drift instability (GDI), and the ion‐thermal instability (ITI) are analyzed, focusing on analytic analysis of the previously obtained general expression of the combined instability growth rate. It is shown that thermal effects lead to generally nonmonotonic behavior of the growth rate with the background electric field or, equivalently with the plasma drift speed , in contrast with the conventional quadratic (FBI) or linear (GDI) dependence. The threshold electric field for FBI is demonstrated to exist at all altitudes, although at higher altitudes and/or at longer wavelength the threshold fields become too high to be observed in the ionosphere. The GDI growth rate is shown to be significantly modified by the thermal effects at long wavelengths. In the absence of thermal effects, the growth rate is proportional to a cosine of the flow angle, the angle between the differential plasma drift and the wavevector. Thermal effects result in an additional phase shift that maximizes at an altitude around 120 km, using representative high‐latitude ionospheric parameters, and in an increase in the proportionality coefficient by up to a factor of 2. The study highlights the usefulness of an analytic treatment for revealing additional insights into the instability behavior in the broad range of ionospheric parameters that may remain hidden using only numerical treatment.

Spherical Indentation of a Micropolar Solid: A Numerical Investigation Using the Local Point Interpolation–Boundary Element Method

The load-penetration curve in elastic nanoindentation of an elastic micropolar flat by a diamond spherical punch is analyzed. The presented results are obtained by a specifically developed numerical tool based on a judicious combination of the conventional boundary element method and strong form local point interpolation method. The results show that the usual linear relationship between the material depression and the square of the radius of the contact area is also valid in this case of micropolar elastic material. It is also shown that the relation between the indentation stress (applied load over the contact surface) and the indentation strain (ratio of contact radius by the punch radius) is linear. The proportionality coefficient which is none other than the indentation stiffness varies with the coupling factor of the micropolar elastic medium. A relation between the indentation stiffness of a micropolar solid and that of a conventional solid with the same Young modulus and Poisson ratio is derived.