Power Exponential Model Research Articles

Optimal Inflow Performance Relationship Equation for Horizontal and Deviated Wells in Low-Permeability Reservoirs

After Vogel proposed a dimensionless inflow performance equation, with the rise of the horizontal well production mode, a large number of inflow performance relationship (IPR) equations have emerged. In the productivity analysis of deviated and horizontal wells, the IPR equation proposed by Cheng is mainly used. However, it is still unclear whether these inflow performance models (such as the Cheng, Klins-Majcher, Bendakhlia-Aziz, and Wiggins-Russell-Jennings types) are suitable for productivity evaluations of horizontal and deviated wells in low-permeability reservoirs. In-depth comparisons and analyses have not been carried out, which hinders improvements in the accuracy of the productivity evaluations of horizontal wells in low-permeability reservoirs. In this study, exploratory work was conducted in two areas. First, the linear flow function relationship used in previous studies was improved. Based on the experimental pressure-volume-temperature results, a power exponential flow function model was established according to different intervals greater or less than the bubble point pressure, which was introduced into the subsequent derivation of the inflow performance equation. Second, given the particularity of low-permeability reservoir percolation, considering that the reservoir is a deformation medium, and because of the existence of a threshold pressure gradient in fluid flow, the relationship between permeability and pressure was changed. The starting pressure gradient was introduced into the subsequent establishment of the inflow performance equation. Based on the above two aspects of this work, the dimensionless IPR of single-phase and oil-gas two-phase horizontal wells in a deformed medium reservoir was established by using the equivalent seepage resistance method and complex potential superposition principle. Furthermore, through regression and error analyses of the standard inflow performance data, the correlation coefficients and error distributions of six types of IPR equations applicable to deviated and horizontal wells at different inclination angles were compared. The results show that the IPR equation established in this study features good stability and accuracy and that it can fully reflect the particularity of low-permeability reservoir seepage. It provides the best choice of the IPR between inclined wells and horizontal wells in low-permeability reservoirs. The other types of IPR equations are the Wiggins-Russell-Jennings, Klins-Majcher, Vogel, Fetkovich, Bendakhlia-Aziz, and Harrison equations, listed here in order from good to poor in accuracy.

Gastric emptying pattern and disintegration kinetics of cooked rice in a 3D printed in vitro dynamic digestion model ARK®

Abstract Understanding the gastric digestion process is essential for evaluating the bioaccessibility of nutrients from food matrices. The objective of this study was to investigate the kinetics of disintegration and gastric emptying patterns in a 3D printed stomach (ARK®) with white rice as the study sample. Modified power exponential model was used to fit the gastric retention data and the average t 1/2 and t lag values of the solid fractions were found to be 109.22 ± 4.20 and 84.16 ± 5.72 min, respectively. During the disintegration process, the weight percentage of medium size particles (∼0.35 mm) was found to be higher at 30 and 60 min. Moreover, there was a sharp decrease in the percentage of fine particles (<0.125 mm) at 90 and 120 min. The ARK® could effectively mimic the physiochemical process of the human stomach, providing promising insights for future studies on the development of novel and functional food products.

Modeling Urban Growth and Socio-Spatial Dynamics of Hangzhou, China: 1964–2010

Urban population density provides a good perspective for understanding urban growth and socio-spatial dynamics. Based on sub-district data of the five national censuses in 1964, 1982, 1990, 2000, and 2010, this paper is devoted to analyzing of urban growth and the spatial restructuring of the population in the city of Hangzhou, China. Research methods are based on mathematical modeling and field investigation. The modeling result shows that the negative exponential function and the power-exponential function can be well fitted to Hangzhou’s observational data of urban density. The negative exponential model reflects the expected state, while the power-exponential model reflects the real state of urban density distribution. The parameters of these models are linearly correlated to the spatial information entropy of population distribution. The fact that the density gradient in the negative exponential function flattened in the 1990s and 2000s is closely related to the development of suburbanization. In terms of investigation materials and the changing trend of model parameters, we can reveal the spatio-temporal features of Hangzhou’s urban growth. The main conclusions can be reached as follows. The policy of reformation and opening-up and the establishment of a market economy improved the development mode of Hangzhou. As long as a city has a good social and economic environment, it will automatically tend to the optimal state through self-organization.

Achieving realistic gastric emptying curve in an advanced dynamic in vitro human digestion system: experiences with cheese-a difficult to empty material.

Nowadays, in vitro digestion models have received growing interest in recent years to track the digestive fate of foods in the gastrointestinal tract. A major challenge in the development of more physiologically relevant in vitro gastric models is to simulate realistic gastric emptying. In this study, an advanced dynamic in vitro human gastric system was investigated for its potential in achieving the above. The mechanisms for controlling the gastric emptying rate by modulations of the peristaltic moving distance, the pylorus opening size/frequency, and the stomach tilting angle in relation to time are illustrated. With solid cheese, a difficult food material for emptying, different combinations of the operational parameters of the stomach system were evaluated. The system was steered to attain consistent gastric emptying curve with the theoretical data by optimizing operational parameters. By fitting the gastric retention data with a power-exponential model, which is a common approach for describing gastric emptying, the total meal achieved an average emptying half-time (t1/2) of 84.5 min and a curve shape coefficient (β) of 1.69, similar to the theoretical data reported in the literature, where the values of t1/2 and β were 85 min and 1.8, respectively (p > 0.05). Furthermore, the mean median particle size was significantly decreased from the initial 2.80 mm (cheese cubes) to the final 1.35 mm (p < 0.05). There are few particles greater than 2 mm observed in the emptied cheese digesta throughout the digestion process. These suggest the powerful gastric grinding and sieving capacity exhibited by the in vitro system. The current study demonstrates that a well-considered in vitro system can offer a reasonable approach for tracking the structural and physicochemical changes of foods during digestion in the stomach, which is practically meaningful.

Springback behavior and a new chord modulus model of copper alloy during severe plastic compressive deformation

Abstract The copper alloy in the unloading process after severe plastic compressive deformation (SPCD) exhibits obvious nonlinear stress-strain relationship and hysteresis behavior, and generates severe springback deformation. The severe strain hardening and softening effects occurring in the SPCD and the anisotropy of the material will affect the springback behavior of the material. In this paper, the samples obtained along the different directions (rolling direction, short-thickness direction, transverse direction, and 45° direction) of copper alloy hot-rolled plates were used to perform the quasi-static single pass compression tests with different deformation ratios (0.25 %–90 %). The springback behavior of the copper alloy under the SPCD was investigated. The effects of the strain hardening, strain softening and anisotropy on the springback behavior of the material were revealed. The variation relationships of the instantaneous tangent modulus and the chord modulus in unloading with stress and strain at different deformation stages (elastic stage, yield stage, strain hardening stage, and strain softening stage) were analyzed. A new chord modulus in a power exponential form was proposed. According to the unloading characteristic of the SPCD, the Yoshida-Uemori chord modulus model and the QPE model were modified. The applicability and accuracy of the unloading chord modulus models for the SPCD were evaluated and compared by using the power exponential chord modulus model, the modified QPE chord modulus model, the modified Yoshida-Uemori chord modulus model, and the Yoshida-Uemori chord modulus model, respectively. Besides, based on the proposed chord modulus model in a power exponential form, a 1-D E T model in a power exponential form was also proposed to describe the nonlinear unloading process and the variation of the slope of the unloading curves after the SPCD. The results indicated that the springback behavior of SPCD is obviously different from those of small plastic compressive deformation and elastic compressive deformation. The proposed chord modulus model in a power exponential form can accurately predict the chord modulus and springback strain in the unloading after the SPCD.

Role of collisional matter in the framework of extended teleparallel theory

The purpose of this work is to examine the cosmic evolution in the presence of collisional matter (CM) with and without radiations in a modified Teleparallel theory involving a generic function [Formula: see text] which depends on the scalar torsion [Formula: see text] and the boundary term associated to the divergence of torsion [Formula: see text]. We select seven novel [Formula: see text] models including power law, logarithmic models and exponential models, some of these reported in [S. Bahamonde, M. Zubair and G. Abbas, Phys. Dark Univ. 19 (2018) 78; S. Bahamonde and S. Capozziello, The Eur. Phys. J. C. 77 (2017) 107; C. Escamilla-Rivera and J. L. Said, Class. Quantum Grav. 37 (2020) 165002] and discuss the evolutionary scenario. The behavior of deceleration parameter [Formula: see text], Hubble parameter [Formula: see text], Equation-of-state (EoS) for dark energy (DE) and effective EoS is presented. [Formula: see text]CDM epoch and crossing of phantom divide line (approaching to phantom era) is observed in scenarios like noncollisional matter (NCM) with radiation, CM with and without radiation. Results are found to be adequate with recent cosmic observations.

HALF EXPONENTIAL POWER MODEL FOR THE FIRST TIME FAILURE OF POWER DISTRIBUTION TRANSFORMERS IN NIGERIA

Transformer failure is a major problem confronting the Nigerian power sector, hindering the transmission and distribution of electric power to various households, institutions, and industries. Many of these transformer developed problem due to the old age of the transformers, overloading, in-availability of technical expertise, poor maintenance culture, manufacturer's faults, just to mention few. The present research focuses on providing half exponential power model for the failure of already installed transformers, with respect to years of installation up to the time of the first failure, using secondary data from the south western part of Nigeria as a case study. The results obtained showed that half exponential power performed better in modeling the first time failure of power transformers. This was possible because of the present of shape parameter which gives flexibility to half exponential power when compared with a half normal distribution.

A non-probabilistic time-variant method for structural reliability analysis

Time-variant reliability problems commonly occur in practical engineering due to the deterioration in material properties, external disturbance and other uncertain factors. Considering the non-probabilistic method can effectively deal with the uncertainties in reliability analysis. Based on the stress–strength interference method and interval method, a time-variant stress–strength interference interval model is established by considering the stress and strength as time-variant intervals. And then, the stress and strength intervals are converted into the normalized intervals to define the non-probabilistic time-variant reliability index [Formula: see text] according to the different relationships between the limit state function and the normalized intervals. The structural state at any time can be described by the non-probabilistic time-variant reliability index [Formula: see text]. In addition, a strength power exponential degradation model is given as an example to clearly verify the non-probabilistic time-variant method, and the analysis results are compared with the interval method, the uniform distribution stress–strength interference method and the normal distribution stress–strength interference method, which confirm that the non-probabilistic time-variant method is feasible and valid to analyze the structural time-variant reliability without the probability density functions of the parameters.

Study of a Prediction Method of the Failure Time and Failure Voltage of Generator Stator Bars Under the Electrical Stress Test

A method for predicting the failure time and failure voltage of generator stator bars under the electrical stress test was proposed. The method established a general life prediction theory model for the electrical stress test based on the negative power-exponential model, and this model could predict the insulation life of stator bars under the electrical aging test and breakdown test. Then, we utilized Weibull distribution theory to estimate the life factor in the model and predict the failure time and failure voltage of the stator bars under the step-by-step test. The test results were consistent with the estimated results, and the correctness of the proposed method was verified.

Tensile strength prediction of natural fiber and natural fiber yarn: Strain rate variation upshot

Fibers are the main load-carrying member in composites. Hence, it is required to examine the behavior of fiber against different strain rate (SR). In present study, the behavior of natural fiber (NF) and Natural fiber yarn (NFY) is investigated by varying the SR at lower SR: 0.17 × 10−4 s−1 to 1.25 × 10−4 s−1 (crosshead speed (CHS): 0.1 to 0.75 mm/min) and higher SR: 1.25 × 10−4 s−1 to 25.00 × 10−4 s−1 (CHS: 0.75 to 20 mm/min) and measure its effect on tensile strength (TS). Here, the range is proposed for SR of lower SR and higher SR. NF: hemp fiber, sisal fiber and banana fiber and NFY: flax fiber yarn, bamboo fiber yarn and cotton fiber yarn are procured for the tensile testing. The mathematical models: exponential model (EM), linear model (LM), logarithmic model (LOM), polynomial model (PM) and power model (POM) are also proposed to predict the TS at different SR. The paper signifies the outcome as: TS increases gradually at lower SR and decreases gradually at higher SR; PM is advised to use in the prediction of TS at lower SR and higher SR for NF and NFY.

A new method for evaluating loess collapsibility and its application

Collapsibility affects loess engineering stability. Currently, there are two methods used to determine the collapsibility of loess: the traditional indoor collapsibility test (indoor test) method and the field immersion test (field test) method. However, for the same loess site, the collapse values under overburden pressure obtained by the two methods are quite different. For sites that cannot be tested in situ, it is easy to misjudge the collapsibility of the loess foundation when depending only on indoor test results. To improve the accuracy of the indoor collapsibility determination, the characteristics of the compression curves obtained from confined compression tests at six different loess sites are analyzed in this paper. The compression curves of loess under different states are normalized and described by the composite power exponential model. The collapsibility of loess is closely related to its structure. A new method for analyzing and evaluating the collapsibility of loess is proposed; the method combines the relationship between the compression characteristics and initial structural properties of loess and the relationship between the initial structural properties and physical comprehensive indexes. To verify the applicability and accuracy of the new method, the collapse values under overburden pressure of two test sites along the Xi'an Metro Line 5 were calculated using the physical indexes of loess at different depths and compared with the values calculated from the indoor test and field-measured values. The results show that the calculated value of the new method is closer to the measured value of the field test than is the calculated value of the indoor test, and the new method can correctly determine the collapsibility type and grade of the site. The new method provides a simple and feasible means by which to correctly and quickly evaluate site collapsibility in loess engineering, which is beneficial for conducting loess site collapsibility evaluations under full operation to develop and implement the measures of foundation treatment in loess areas. The method can be used as a reference at loess sites where field tests cannot be performed.

The exponentiated power exponential regression model with different regression structures: application in nursing data

ABSTRACTWe define the exponentiated power exponential distribution and propose a regression model with different systematic structures based on the new distribution. We show that the new regression model can be applied to dispersion data since it represents a parametric family of models that includes as sub-models some widely-known regression models. It then can be used more effectively in the analysis of real data. We use maximum likelihood estimation and derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes. Some global-influence measurements are also investigated and simulation studies are performed to evaluate the accuracy of the estimates. We provide an application of the regression model with four systematic structures to nursing activities score data in the Unit of the Medical Clinic of University of São Paulo (USP) Hospital.

Energy-Efficient MTC Data Offloading in Wireless Networks Based on K-Means Grouping Technique

Machine-type communication (MTC) devices provide a broad range of data collection especially on the massive data generated environments such as urban, industrials and event-enabled areas. In dense deployments, the data collected at the closest locations between the MTC devices are spatially correlated. In this paper, we propose a k-means grouping technique to combine all MTC devices based on spatially correlated. The MTC devices collect the data on the event-based area and then transmit to the centralized aggregator for processing and computing. With the limitation of computational resources at the centralized aggregator, some grouped MTC devices data offloaded to the nearby base station collocated with the mobile edge-computing server. As a sensing capability adopted on MTC devices, we use a power exponential function model to compute a correlation coefficient existing between the MTC devices. Based on this framework, we compare the energy consumption when all data processed locally at centralized aggregator or offloaded at mobile edge computing server with optimal solution obtained by the brute force method. Then, the simulation results revealed that the proposed k-means grouping technique reduce the energy consumption at centralized aggregator while satisfying the required completion time.

A Testing Method of Probability Weighting Functions From an Axiomatic Perspective

The aim of this study is to present a testing method to examine various models of probability weighting functions that are considered nonlinear functions of probability in behavioral decision theory, such as prospect theory. Although there are several empirical psychometric tests to examine probability weighting functions, there is no concrete method to examine these functions’ axiomatic properties. We propose axiomatic properties and a testing method to examine the generalized hyperbolic logarithmic model, power model, and exponential power model of the probability weighting functions, and provide an illustrative example of the testing method.

Expenditures of 50+ Households on transport and communications - statistical analysis

The dynamics and structure of consumption are influenced by demographic changes in the world. One of the most important is the phenomenon of aging society. The study covered households in Poland where the head of the household was at the age of 50 or more, according to the World Health Organization experts, they were people who had entered at least in the first year of presenile. The goal of this article is to analyse and model expenditure on transport and communication of these households. The analyses were carried out on the basis of a set of non-identifiable data of households budget which were bought from Central Statistical Office. Based on the estimated power-exponential model, it was found that the largest positive impact on transport and communications spending was the level of total expenditures per person. The diversification of the preferences of expenditure depending on the number of people in the family, the class of place of residence, socioeconomic group membership and the subjective assessment of the material situation of the households was also found important. In addition, it was found that the expenditures also depends on the characteristics of the household head: they decrease with age and the increase with level of education.

Non-destructive evaluation of nano silica-modified roller-compacted rubbercrete using combined SonReb and response surface methodology

Roller-compacted concrete (RCC) is being widely used in highway construction industry (for pavement applications) due to its enormous advantages over conventional concrete rigid pavement. However, the major problems related to RCC pavement are the rigidity and relative tendency to crack due to low tensile strength. To address this problem, crumb rubber (CR) can be added as partial replacement of fine aggregate. High elastic and deformation properties of CR will increase the ductility of RCC pavement to absorb the deformation and strain energy caused by traffic loads. However, incorporating CR to RCC pavement leads to a reduction in mechanical properties which needs to be addressed for proper utilisation. Therefore, in this study, roller-compacted rubbercrete (RCR) was produced by partially replacing fine aggregate with CR. Nano silica was used as an additive to cement to mitigate the loss of mechanical properties in RCR caused by incorporation of CR. The non-destructive tests, that is, rebound hammer test and ultrasonic pulse velocity (UPV) were used to evaluate the performance of RCR. Response surface methodology was then used to develop models for predicting the 28 days UPV and rebound number (RN) of RCR. Combined UPV–RN (SonReb) models for predicting the 28 days strength of RCR based on combining UPV and RN were developed using multivariable regression (double power, bilinear, and double exponential models). From the combined SonReb models formulated, it is concluded that the double exponential model has better accuracy for predicting the 28 days compressive strength of RCR compared to the double power models recommended by RILEM 43-CND for conventional concrete.

Underestimation of soil respiration in a desert ecosystem

Soil respiration (Rs), conventionally considered as net soil CO2 flux, is an important link in the terrestrial carbon cycle. However, existing estimates of Rs in drylands may be erroneous, because of the abiotic soil CO2 flux. This may seriously hamper our understanding of the carbon cycle of desert ecosystems. In this study, we monitored CO2 flux of natural and sterilized soils, and obtained the net and abiotic soil CO2 flux in a desert ecosystem in Ningxia, China, and then computed Rs by using these data. Daily Rs was much larger than the net soil CO2 flux both in the growing and non-growing season. Further analysis indicated that Rs was controlled by soil temperature (Ts) over the annual cycle, and an exponential model could provide a good prediction of Rs. During the growing season, Rs increased significantly with rising soil water content (VWC) (P<0.05). A bivariate (Ts and VWC) exponential–power model had a better performance for predicting Rs in the growing season than a Ts-only model. However, during the non-growing season, this model failed to simulate Rs. Our results suggest that Rs is greatly underestimated, and the exponential model is more applicable for annual Rs prediction.

Model Selection in Continuous Test Norming With GAMLSS.

To compute norms from reference group test scores, continuous norming is preferred over traditional norming. A suitable continuous norming approach for continuous data is the use of the Box-Cox Power Exponential model, which is found in the generalized additive models for location, scale, and shape. Applying the Box-Cox Power Exponential model for test norming requires model selection, but it is unknown how well this can be done with an automatic selection procedure. In a simulation study, we compared the performance of two stepwise model selection procedures combined with four model-fit criteria (Akaike information criterion, Bayesian information criterion, generalized Akaike information criterion (3), cross-validation), varying data complexity, sampling design, and sample size in a fully crossed design. The new procedure combined with one of the generalized Akaike information criterion was the most efficient model selection procedure (i.e., required the smallest sample size). The advocated model selection procedure is illustrated with norming data of an intelligence test.

Reliability analysis using an exponential power model with bathtub-shaped failure rate function: a Bayes study.

Models with bathtub-shaped hazard function have been widely accepted in the field of reliability and medicine and are particularly useful in reliability related decision making and cost analysis. In this paper, the exponential power model capable of assuming increasing as well as bathtub-shape, is studied. This article makes a Bayesian study of the same model and simultaneously shows how posterior simulations based on Markov chain Monte Carlo algorithms can be straightforward and routine in R. The study is carried out for complete as well as censored data, under the assumption of weakly-informative priors for the parameters. In addition to this, inference interest focuses on the posterior distribution of non-linear functions of the parameters. Also, the model has been extended to include continuous explanatory variables and R-codes are well illustrated. Two real data sets are considered for illustrative purposes.

Brownian Integrated Covariance Functions for Gaussian Process Modeling: Sigmoidal Versus Localized Basis Functions

ABSTRACTGaussian process modeling, or kriging, is a popular method for modeling data from deterministic computer simulations, and the most common choices of covariance function are Gaussian, power exponential, and Matérn. A characteristic of these covariance functions is that the basis functions associated with their corresponding response predictors are localized, in the sense that they decay to zero as the input location moves away from the simulated input sites. As a result, the predictors tend to revert to the prior mean, which can result in a bumpy fitted response surface. In contrast, a fractional Brownian field model results in a predictor with basis functions that are nonlocalized and more sigmoidal in shape, although it suffers from drawbacks such as inability to represent smooth response surfaces. We propose a class of Brownian integrated covariance functions obtained by incorporating an integrator (as in the white noise integral representation of a fractional Brownian field) into any stationary covariance function. Brownian integrated covariance models result in predictor basis functions that are nonlocalized and sigmoidal, but they are capable of modeling smooth response surfaces. We discuss fundamental differences between Brownian integrated and other covariance functions, and we illustrate by comparing Brownian integrated power exponential with regular power exponential kriging models in a number of examples. Supplementary materials for this article are available online.