New Set Of Equations Research Articles

Solution of the plane thermoelasticity problems based on a new set of equations

The interaction of thermal and mechanical fields in modern technologies for the synthesis and processing of materials attracts more and more attention. This is due to the need to predict the behavior and properties of new materials and products depending on the conditions of their creation. In the present work, attention is focused on the comparison of the solutions to the thermoelasticity plane problems with and without accounting for the temperature dependence of the material properties. It is assumed that an external heat source traveling over the surface with a specific velocity and following a given trajectory is responsible for a significant temperature increase. It may correspond to a laser source, for example. The new way of problem formulation in stresses is used. The temperature dependence of the characteristics leads to nonlinear thermoelasticity equations when the equilibrium equations, the requirement of strain compatibility, and the Duhamel-Neuman relation for the plane stress state case are combined. To determine the temperature field, a nonlinear thermal conductivity equation is used. To solve the problem numerically, the use of an implicit finite-difference scheme and coordinate splitting for the thermal conductivity equation and the finite-difference method of successive over-relaxation with Chebyshev acceleration for the equations for stresses was made. As a result, the difference in the solution of linear and nonlinear problems is demonstrated for the considered cases. Using the example of a mixture of titanium and aluminum powders, numerical modeling demonstrated that some stress components can reach values up to 3.5 times higher than those obtained in the case of temperature-independent material properties when there is a 500-degree local temperature increase.

Sensitivity Analysis and Uncertainty Quantification on Point Defect Kinetics Equations with Perturbation Analysis

The concentration of radiation-induced point defects in general materials under irradiation is commonly described by the point defect kinetics equations based on rate theory. However, the parametric uncertainty in describing the rate constants of competing physical processes, such as recombination and loss to sinks, can lead to a large uncertainty in predicting the time-evolving point defect concentrations. Here, based on perturbation theory, we derive up to the third-order correction to the solution of point defect kinetics equations. This new set of equations enables a full description of continuously changing rate constants and can accurately predict the solution up to 50% deviation in these rate constants. These analyses can also be applied to reveal the sensitivity of the solution to input parameters and aggregated uncertainty from multiple rate constants.

Combining short-term breath measurements to develop methane prediction equations from cow milk mid-infrared spectra

Predicting methane (CH4) emission from milk mid-infrared (MIR) spectra provides large amounts of data which is necessary for genomic selection. Recent prediction equations were developed using the GreenFeed system, which required averaging multiple CH4 measurements to obtain an accurate estimate, resulting in large data loss when animals unfrequently visit the GreenFeed. This study aimed to determine if calibrating equations on CH4 emissions corrected for diurnal variations or modeled throughout lactation would improve the accuracy of the predictions by reducing data loss compared with standard averaging methods used with GreenFeed data. The calibration dataset included 1 822 spectra from 235 cows (Holstein, Montbéliarde, and Abondance), and the validation dataset included 104 spectra from 46 (Holstein and Montbéliarde). The predictive ability of the equations calibrated on MIR spectra only was low to moderate (R2v = 0.22–0.36, RMSE = 57–70 g/d). Equations using CH4 averages that had been pre−corrected for diurnal variations tended to perform better, especially with respect to the error of prediction. Furthermore, pre−correcting CH4 values allowed to use all the data available without requiring a minimum number of spot measures at the GreenFeed device for calculating averages. This study provides advice for developing new prediction equations, in addition to a new set of equations based on a large and diverse population.

Mesoscale modeling of continuous dynamic recrystallization in Ti-10V-2Fe-3Al alloy

Continuous dynamic recrystallization (CDRX) is the dominant restoration mechanism of near-β titanium alloys during hot deformation. But till now, there is seldom visual modeling of the process which limits its industrial application. Based on CDRX mechanisms characterized by low-angle grain boundaries (LAGBs) formed and partially transformed into high-angle grain boundaries (HAGBs), the present study established a cellular automata (CA) model to investigate the substructure evolution and mechanical response of Ti-10V-2Fe-3Al alloy. Besides, a new set of equations for subgrain rotation considering the effect of the α-phase was integrated into the CA model to improve its applicability in titanium alloy. The model was validated by experimental results and then applied to predict the substructure evolution during hot working. Simulation analysis revealed that, except for high strain rates and temperatures, a high fraction of α/β phase boundaries could also promote the development of CDRX. The proposed CA model provided an effective method for microstructure optimization in hot forging of the Ti-10V-2Fe-3Al alloy.

Weight calibration in the joint modelling of medical cost and mortality.

Joint modelling of longitudinal and time-to-event data is a method that recognizes the dependency between the two data types, and combines the two outcomes into a single model, which leads to more precise estimates. These models are applicable when individuals are followed over a period of time, generally to monitor the progression of a disease or a medical condition, and also when longitudinal covariates are available. Medical cost datasets are often also available in longitudinal scenarios, but these datasets usually arise from a complex sampling design rather than simple random sampling and such complex sampling design needs to be accounted for in the statistical analysis. Ignoring the sampling mechanism can lead to misleading conclusions. This article proposes a novel approach to the joint modelling of complex data by combining survey calibration with standard joint modelling. This is achieved by incorporating a new set of equations to calibrate the sampling weights for the survival model in a joint model setting. The proposed method is applied to data on anti-dementia medication costs and mortality in people with diagnosed dementia in New Zealand.

Improving Volume and Biomass Equations for Pinus oocarpa in Nicaragua

We present a new set of equations for tree level volume and aboveground biomass estimation for ocote pine (Pinus oocarpa Schiede ex Schltdl). These equation systems are the first developed for this species in Nicaragua. The first system includes a taper function, a merchantable volume equation, and volume equations for stem, coarse branches, and whole trees. The second system estimates whole tree and individual tree component biomass (stem wood, bark, branches, and needles). Data from 112 sampled trees were used for models’ development. Seemingly Unrelated Iterative Regression and the Generalized Method of Moments were used to simultaneously fit the volume and biomass equations systems, respectively; both methods ensure additivity and compatibility between equations. Weighted regression and a second-order continuous autoregressive error structure were used to correct heteroscedasticity and autocorrelation within the hierarchical dataset. The predictive power of the new proposed equations is higher than the currently used models for P. oocarpa in the country. These equation systems represent a scientific advancement that will enhance forest inventories, optimize timber management of the species, and facilitate accurate monitoring of forest carbon dynamics. Additionally, the new equations will contribute to a more precise accounting of CO2 emissions from the country’s forestry sector.

Estimating Effective Hydraulic Conductivity (Ke) for the Rangeland Hydrology and Erosion Model (RHEM)

Highlights Effective hydraulic conductivity (Ke ) predictive equations in all RHEM versions have satisfactory performance. New Ke predictive equations were developed for RHEM applications over broader rangeland conditions. Ke values on most rangelands can be estimated through readily measurable ground cover and soil texture data. Abstract. Effective hydraulic conductivity (Ke) is an important parameter for the prediction of infiltration and runoff by the Rangeland Hydrology and Erosion Model (RHEM). Three sets of equations to predict Ke have previously been used in RHEM. These equations are mainly based on rainfall simulation data representing undisturbed sites and have not undergone comprehensive evaluation for various rangeland conditions, particularly after disturbances. The goal of this research was to evaluate these equations using independent data obtained from rainfall simulations conducted at multiple rangeland sites. Additionally, we developed and evaluated a new set of Ke predictive equations applying readily measurable cover and soils data spanning a wide range of vegetation, soil textures, and disturbance conditions. The results show that all previous Ke equations in RHEM have a “satisfactory” performance with index of agreement (d) > 0.75 and R2 > 0.4. The new Ke approach resulted in “very good” performance with d > 0.9 and R2 > 0.5. The new set of equations enhances RHEM for applications over broader rangeland conditions, including sparse vegetation cover following disturbances or community transitions. Keywords: Disturbed Rangelands, Hillslope Runoff, Infiltration.

Development and validation of novel equation for prediction of resting energy expenditure in active Saudi athletes

Being the most stable component of energy expenditure, resting metabolic rate (RMR) is usually used in the calculation of energy requirements for athletes. An adequate energy prescription is essential in supporting athlete development. This work aims to develop and validate an equation for calculating energy requirements for Arabic Saudi athletes. This cross-sectional study included 171 active athletes aged 18 to 45 years. The sample was divided into a development group (n = 127) and a validation group (n = 44). Anthropometry, indirect calorimetry, and body composition analysis via bioelectric impedance analysis were performed on all participants. The novel predictive equations were created by using stepwise linear regression analyses. The accuracy of the novel equations was compared with 10 equations, and Bland and Altman plots were used to estimate the limits of agreement between measured RMR and novel equations. The first novel equation used a set of basic measures, including weight, gender, and age, was [RMR = 1137.094 + (Wt × 14.560)–(Age × 18.162) + (G × 174.917)] (R = 0.753, and R2 = 0.567, wt = weight, G = gender; for male use 1 and female 0). The second equation used fat-free mass, age, and weight [RMR = 952.828 + (fat-free mass × 10.970)–(Age × 18.648) + (Wt × 10.297)] (R = 0.760 and R2 = 0.577). Validation of the second novel equation increased the prediction of measured RMR to 72.7% and reduced the amount of bias to 138.82 ± 133.18 Kcal. Finally, the new set of equations was designed to fit available resources in clubs and showed up to 72.73% accurate prediction and good agreement with measured RMR by Bland and Altman plots.

Improved pool fire-initiated domino effect assessment in atmospheric tank farms using structural response

Domino effects are severe accident scenarios affecting storage tanks and are often initiated by pool fires. Flame engulfment and heat radiation are the two major sources triggering domino effect. Threshold-based and probit-based methods are widely used to assess the possibility and probability of a secondary accident. These methods are also a part of advanced methods devoted to examining synergic or coupling effects. The current work examines (i) how effective the threshold-based methods are and (ii) how accurate the current time to failure (TTF) estimation models are, which are the basis of probit-based methods. The results suggest that threshold-based methods are not pertinent for the quantitative assessment of domino effect and that significant improvement can be made in the existing TTF prediction models using site-specific structural response data. A new set of equations for TTF estimation using data analytics is proposed. Application to 4,080 pool fire scenarios demonstrates that the newly developed model can improve the TTF prediction performance compared to the existing models (around 22% in terms of R2). In addition, a method has been proposed and validated to correlate time with the failure probability for time-dependent domino effect assessment, which is a limitation of probit-based methods.

New Fetch- and Depth-Limited Forecasting Curves Depending on Bed Roughness

ABSTRACT Predicting wind waves within confined and shallow basins is very important, given the decisive role they play in the resuspension mechanisms of sediments and nutrients from the bottom, on which the main morphological and environmental changes depend. Pascolo, Petti, and Bosa (2019) proposed a set of wave forecasting curves for fully developed conditions in finite depth, which consider the bottom roughness as an additional variable, since it plays a fundamental role in the wave energy dissipation during the generation process. The present study incorporates and integrates the results previously obtained by Pascolo, Petti, and Bosa (2019) and provides the growth curves in the complete form, taking into account also the limitation on fetch. A numerical approach on a simplified domain has been adopted and statistical analyses on the fit of the curves to numerical results have been performed. The new set of equations confirms the variability of the wave heights and periods as a function of the bottom conditions, which can change due to the presence of bedforms, vegetation, or particle size differences. Applications at different conditions of depth, fetch, and roughness have been analyzed, in order to confirm the validity of the new growth curves.

Transverse flow distributions in ice‐covered channels

AbstractTraditional discharge measurements in ice‐covered river channels are time‐consuming and costly, thus limiting the elucidation of flow patterns during winter. This study proposes an analytical model for quantifying the transverse distributions of the unit‐width discharge and the depth‐averaged streamwise velocity in ice‐covered channels by extending an existing stream‐tube method to include the effects of cover and bed roughness and cross‐sectional geometry. A new set of equations are obtained for this extended method. An empirical coefficient α is included to lump the effects of the shape and friction factors of the ice cover and the channel bed. The model is compared with flume experiments and field data for fully and partially ice‐covered flows to examine the variation of the coefficient α.

Non-linear modeling parameters for new construction RC columns

Modeling parameters (MP) of reinforced concrete columns are a critical component of performance-based seismic assessment methodologies because in these approaches damage is estimated based on element deformations calculated using non-linear models. To ensure model fidelity and consistency of assessment results, performance-based seismic assessment methods in ASCE 41, ACI 369.1, and ACI 374.3R prescribe modeling parameters calibrated using experimental data. This paper introduces a new set of equations to calculate reinforced concrete column non-linear modeling parameters optimized for design verification of new buildings using response history analysis. Unlike modeling parameters provided in ACI 369.1 and ASCE 41, intended for columns of older non-ductile buildings, the equations for modeling parameters anl and bnl presented in this study were calibrated to simulate the load-deformation envelope of reinforced concrete columns that meet the detailing requirements of modern seismic design codes. Specifically, the proposed equations are intended for use with provisions in ACI 374.3R, Chapter 18 and Appendix A of ACI 318-19 and Chapter 16 of ASCE/SEI 7-16. The proposed equations were calibrated using the ACI Committee 369 column database, which includes column configuration parameters, material properties, and deformation capacity modeling parameters inferred from the measured response of columns under load reversals. Dimension reduction techniques were applied to visualize different clusters of data in 2D space using the negative log-likelihood score. This technique allowed decreasing the non-linearity of the problem by identifying a subset of columns with load-deformation behavior representative of new construction conforming to current codes requirements. A Neural Network model (NN) was calibrated and used to perform parametric variations to identify the most relevant input parameters and characterize their effect on modeling parameters, and to stablish the degree of non-linearity between each input variable and the model output. Developing equations for modeling parameters applicable to a wide range of columns is challenging, so this research considered subsets of the database representative of new construction columns to calibrate simple practical equations. Linear regression models including the most relevant features from the parametric study were calibrated for rectangular and circular columns. The proposed linear regression equations were found to provide better estimates of new construction column modeling parameters than the available tables in ACI 374.3R and ASCE 41-13, and the equations ASCE 41-17.

The carbonate system and air-sea CO2 fluxes in coastal and open-ocean waters of the Macaronesia

The CO2 system, anthropogenic carbon (Cant) inventory and air-sea CO2 fluxes (FCO2) were analysed in the archipelagic waters of the Macaronesian region. The (sub)surface data were collected during POS533 (February and March, 2019) in coastal areas leeward of Cape Verde (CV), Canary Islands (CA) and Madeira (MA) and through the vessel track. The CO2 variability was controlled by changes in temperature, biological activity and advection processes forced by spatial heterogeneities in the Canary Upwelling System, the mixed layer depth, the mesoscale activity and the circulation patterns. The surface fCO2,sw variability was driven by biological production and CO2-rich water injection in tropical waters and by temperature fluctuations in subtropical waters. The factors controlling the upper ocean changes in the total inorganic carbon normalized to a constant salinity (NCT) were assessed. The uptake and storage of anthropogenic carbon, calculated by using the TrOCA 2007 approach described, as an upper limit, > 60% (>90% above the MLD) of the NCT increase from preformed values. The organic carbon pump accounted 36.6-40.9% for tropical waters and lose importance for subtropical waters (7.5-11.6%), while the carbonate pump has a minimal contribution (<4.2%). The upper-ocean Cant inventory in coastal areas of CV (8,570 Km2), CA (7.960 Km2) and MA (1,250 Km2) was 7.57 x 103, 9.26 x 103 and 8.86 x 103 µmol kg-1, respectively (0.51, 0.58 and 0.09 Tg C, respectively). In terms of FCO2, the CV, CA and MA behaved as a winter CO2 sink (-4.74, -3.90 and -8.34 mmol m-2d-1, respectively) while a strong outgassing was detected over the Cape Blanc filament (20-25 mmol m-2d-1). The total average FCO2 for the ocean area of the three archipelagos (371,250 Km2) was -28.27 Gg CO2 d-1. The POS533 data were compared and compilated with SOCAT and GLODAP data and a new set of equations was provided to calculate the fCO2,sw, Cant and FCO2 in the Macaronesian region based on physical and biogeochemical properties.

A new set of estimated cardiorespiratory fitness equations are associated with cognitive performance in older adults

This study aimed to develop new equations to estimate cardiorespiratory fitness specifically for older adults and, secondly, to analyze the associations of cardiorespiratory fitness, both objectively measured and estimated using new equations, with cognitive performance. Ninety-two older adults (41 females, 65–75 years) from baseline data of a randomized controlled trial were analyzed (“ClinicalTrials.gov” Identifier: NCT03923712). Participants completed 4 measurement sessions including (i) physiological and health indicators in a laboratory setting, (ii) field-based fitness tests, (iii) sociodemographic and physical activity questionnaires, and (iv) a battery of neuropsychological tests to evaluate cognitive performance. The main findings were as follows: (i) a set of new equations with good predictive value for estimated cardiorespiratory fitness were developed (74–87%), using different scenarios of complexity and/or equipment requirements, and (ii) higher estimated cardiorespiratory fitness, even using its simplest equation (eCRF = − 1261.99 + 1.97 × 6 min walking test (m) + 1.12 × bioimpedance basal metabolic rate (kcal/day) + 5.25 × basal heart rate (bpm)), was associated with better cognitive performance evaluated by several neuropsychological tests (i.e., language, cognitive flexibility, fluency, attention, and working memory), similar to using objectively measured cardiorespiratory fitness. In summary, a new set of estimated cardiorespiratory fitness equations have been developed with predictive values ranging from 74 to 87% that could be used based on necessity, availability of equipment, resources, or measurement context. Moreover, similar to objectively measured cardiorespiratory fitness, this measure of estimated cardiorespiratory fitness was positively associated with performance on language, fluency, cognitive flexibility, attention, and working memory, independently of sex, age, and education level.

Unbalance compensated distance relay for active distribution networks

Integration of Distributed Energy Resources (DER) into the Active Distribution Networks (ADN) causes issues in conventional overcurrent protection. Additionally, another conventional protection, such as the distance function, has been used, but ADN characteristics require new well-fitted approaches. This paper proposes a strategy to improve conventional distance relays when applied in unbalanced distribution lines. The strategy is based on the relay’s current and voltage measurements and the line series impedance matrix. Different overhead line cases are studied considering several pole geometrical arrangements and fault types. Based on the results, the new set of equations for distance-based protection can achieve a more accurate fault impedance estimation, with a maximum error of 0.1% in the analysed situations and despite the fault conditions. The high proposal performance and the straightforward application make this proposal suitable for the nowadays ADN protection.

Pure azimuth passive positioning in attempted UAV formation flight

In order to maintain the formation of UAVs during flight, pure azimuthal passive positioning is generally used to adjust the position of UAVs. In order to accurately perform UAV positioning, this paper establishes a single-objective optimization model of UAV with passively received signals based on the polar coordinates of UAVs, combined with geometric knowledge such as the sine theorem and triangle properties. And then the model is optimized and improved, i.e., when the position information of two UAVs is known, how many additional UAVs are needed to perform UAV localization. Therefore, it was found that two additional UAVs with unknown numbers were needed to determine the UAV position by establishing a new set of equations to achieve the positioning of the UAVs with slightly deviated positions. The model is important to achieve effective positioning of UAVs and adjust the solution.

Analytic solutions of Brans–Dicke cosmology: Early inflation and late time accelerated expansion

In this paper, we investigate the most general exact solutions of Brans–Dicke cosmology by choosing the scale factor “a” as the new independent variable. It is shown that a set of three field equations can be reduced to a constraint equation and a first-order linear differential equation. Thus this new set of equations is solvable when one supplies one of the following pairs of functions: ([Formula: see text], [Formula: see text]), ([Formula: see text], [Formula: see text]) or ([Formula: see text], [Formula: see text]). A universe with a single component energy-matter density, the early universe with constant energy density and radiation and the present universe with constant energy density and matter are studied. It is seen that in all cases initial values of the universe cause [Formula: see text] potential and a constant term in the Hubble function which causes an exponential expansion of the universe. The relation between cosmological constant and initial values of the universe is found.

Application of the imaginary time hierarchical equations of motion method to calculate real time correlation functions.

We investigate the application of the imaginary time hierarchical equations of motion method to calculate real time quantum correlation functions. By starting from the path integral expression for the correlated system-bath equilibrium state, we first derive a new set of equations that decouple the imaginary time propagation and the calculation of auxiliary density operators. The new equations, thus, greatly simplify the calculation of the equilibrium correlated initial state that is subsequently used in the real time propagation to obtain the quantum correlation functions. It is also shown that a periodic decomposition of the bath imaginary time correlation function is no longer necessary in the new equations such that different decomposition schemes can be explored. The applicability of the new method is demonstrated in several numerical examples, including the spin-Boson model, the Holstein model, and the double-well model for proton transfer reaction.

Estimating unconfined compressive strength and Young’s modulus of carbonate rocks from petrophysical properties

Geomechanical studies in carbonate rocks often require the use of log relations to obtain mechanical properties when laboratory measurements are not available. This study presents a new set of equations to predict the unconfined compressive strength (UCS) and Young’s modulus (E) for three carbonate lithologies: limestone, dolomite, and chalk. The equations are developed based on more than 700 mechanical-physical tests of carbonate rocks across different geological settings and geographical locations. The obtained results confirmed that petrophysical properties are consistent in determining the carbonate mechanical properties. The relations are developed based on either a single parameter or multiple parameters where coefficient of determination was improved for the multiple parameter relations. Scattering in the prediction of UCS and E is expected due to the carbonate heterogeneity in mineralogy, porosity, fabric as well as testing conditions. Thus, the applicable range of each relation is investigated. To test whether improved fits are achieved in this study, the relations are compared with the literature, and they showed a higher coefficient of determination. The proposed relations can be generally used as a starting point for UCS and E estimate when carbonate mechanical properties from laboratory tests are not available.

A three-dimensional Lagrangian particle tracking model for predicting transport of eggs of rheophilic-spawning carps in turbulent rivers

Grass carp, bighead carp, and silver carp spawn in flowing water. Their eggs, and then larvae, develop while drifting. Hydraulic conditions and water temperature control spawning locations, egg survival, and the downstream distance traveled before the hatched larvae can swim for low velocity nursery habitats. Existing egg drift models simulate the fluvial transport of carp eggs but have limitations in capturing the effect of localized turbulence on egg transport due to inadequate dimensions of hydrodynamics and/or empirical parameterization of river dispersion. We present a three-dimensional Lagrangian particle tracking model that uses fully resolved river hydrodynamics and a continuous random walk algorithm driven by local turbulent kinetic energy and its dissipation rate. We incorporate a new set of equations to compute evolving egg characteristics with fully resolved 3-D hydrodynamics. To demonstrate the performance of the model, we conducted a case study in an eight-kilometer reach of the Missouri River at the discharge of approximately 25% daily flow exceedance. Three-dimensional river hydrodynamics was modeled, calibrated, and evaluated with measurement data. Egg drift was modeled and compared using fully three-dimensional, depth-averaged two-dimensional, and zone-averaged one-dimensional hydrodynamics. The comparison shows a generally good agreement among models of downstream egg transport due to advection but a different dispersion pattern of eggs in the river, as a result of turbulent diffusion and shear induced dispersion.