Three-parameter Exponential Function Research Articles

Interference effect of configuration parameters of vertical sand-obstacles on near-surface sand transport

This study investigates the impacts of height (H) and porosity (P) on the structural properties of wind-driven sand flux in vertical sunflower straw sand-obstacles. We conducted an experiment on sand transport within barriers of various configurations within a 1 m proximity to the surface. In tandem, we monitored wind velocity and direction within the barriers, analyzed total sand transport rate, sand-blocking effects, and cumulative sediment transport rate heights for various parameter configurations, and devised a best sand transport flux model for use within the sand-obstacle. The efficacy of vertical sunflower stalk sand-obstacles in mitigating sand movement has been demonstrated to fall within the range of 37.26%–92.31%. This study reveals a significant correlation between barrier height and porosity in achieving this effect (p < 0.05). High and densely configured sand-obstacles lead to an accumulation of intercepted sand material in front of the front row of the sand-obstacle. In contrast, low and sparsely arranged sand-obstacles exhibit a delayed state of sand material accumulation. Furthermore, with an increase in the height of the obstacle and a decrease in porosity, there is a diminishing trend in the sand transport rate within the obstacle. Concurrently, the height of sand transport within the barrier exhibits an upward trend. A three-parameter exponential function has been employed to more precisely simulate the wind-sand flow structure characteristics within a 1-m height range of the barrier. These research findings contribute to an enhanced understanding of the impact of different vertical sand-obstacle configurations on near-surface wind-driven sand transport patterns in active desert areas. Moreover, they furnish both theoretical underpinnings and practical guidance for the scientific configuration of vertical sand-obstacles.

Mathematical determination of the maximum heat release for fly ash cement paste: Effect of heat flow monitoring time, calculation approach and fly ash content

The maximum hydration heat release Qmax is one of the most concerned kinetic parameters for hydration of cementitious materials. In this study, we specially investigated the effect of the mathematical calculation approach, heat flow monitoring time, and fly ash (FA) content on the obtained Qmax values of FA cement paste. The isothermal hydration heat flows of cement paste with 0%, 20%, 40% and 60% FA contents have been monitored for 250 hours at 20°C. Two conventional Qmax calculation approaches, including Knudsen's equation and the three-parameter exponential function, have been utilized to obtain Qmax values for different cementitious systems. The results indicate that irrespective of the calculation approach or monitoring time, mathematically derived Qmax linearly decreases along with the increase of FA content, which is consistent with the determined enthalpy of the binary cement system. Furthermore, the calculated Qmax increases with the extension of heat flow monitoring time, and different calculation approaches can yield varied Qmax values. However, the discrepancies between the two approaches gradually diminish as the monitoring time extends. It is recommended that for cement paste without FA addition, a minimum heat flow monitoring time of 7 days is necessary to obtain a reliable Qmax value using Knudsen's equation, while for the exponential function, a monitoring time exceeding 7 days is advised. For cement paste with FA addition, neither Knudsen's equation nor three-parameter exponential function can derive a relatively accurate Qmax value for FA within the limited heat flow monitoring duration in this study.

Analysis of the isothermal hydration heat of cement paste containing mechanically activated fly ash

Fly ash is a widely used supplementary cementitious material in the world. Mechanical activation, as a potential approach, can realize maximum bulk utilization of fly ash. In this study, the isothermal hydration heat flows of cement paste containing fly ash with or without mechanical activation are tested and modelled by Avrami equation, reaction order model and three-parameter exponential function at different stages. The results indicate that addition of 20% as-received fly ash retards the cement hydration at the nucleation and growth stage, because the aluminate ions in the pore solution might decrease heterogeneous nucleation sites of C-S-H and suppress its growth. Moreover, as-received fly ash impairs the reaction rate of the whole system at final tail stage owing to its low heat release. However, compared with as-received fly ash, mechanically activated fly ash has promoted cement hydration at the very early age due to the enhanced filler effect. More surface area supplied by mechanically activated fly ash promotes C-S-H growth and partially offsets the retarding effect of aluminate ions. The reaction rate of the whole cementitious system at the deceleration stage is also promoted by the improvement of pozzolanic reactivity after mechanical activation. Furthermore, three different mathematical calculation approaches have been adopted to calculate the ultimate hydration heat Qmax of the cementitious systems. In spite of different values for Qmax, the consensus can be achieved that mechanical activation towards fly ash can promote the reaction degree of the system.

Simplified analytical model to predict nonlinear mechanical responses of flexible composite sheet subjected to out-of-plane loading

This paper presents a simplified analytical model for predicting nonlinear mechanical responses of flexible composite sheet (FCS) subjected to out-of-plane loading. New geometric model based on three-parameter exponential function is proposed to depict 3D funnel-like geometric shape of out-of-plane loaded FCS, and nonlinear constitutive model is then derived to describe the load-displacement curves of out-of-plane loaded FCS. Finally, model parameters are determined through the principle of minimum potential energy. In order to verify new models, out-of-plane loading tests are performed on PWF (plain woven fabric) polyester reinforced HNR (hydrogenated nitrile rubber) composite sheets with three length-width ratios of 1, 2 and 3, and the predictions agree well with the experiments, demonstrating the practical and effective use of the proposed model.

A Field Study of Footprint-Scale Variability of Raindrop Size Distribution

Abstract A network of seven two-dimensional video disdrometers (2DVD), which were operated during the Midlatitude Continental Convective Clouds Experiment (MC3E) in northern Oklahoma, are employed to investigate the spatial variability of raindrop size distribution (DSD) within the footprint of the dual-frequency precipitation radar (DPR) on board the National Aeronautics and Space Administration’s Global Precipitation Measurement (GPM) mission core satellite. One-minute 2DVD DSD observations were interpolated uniformly to 13 points distributed within a nearly circular DPR footprint through an inverse distance weighting method. The presence of deep continental showers was a unique feature of the dataset resulting in a higher mean rain rate R with respect to previous studies. As a measure of spatial variability for the interpolated data, a three-parameter exponential function was applied to paired correlations of three parameters of normalized gamma DSD, R, reflectivity, and attenuation at Ka- and Ku-band frequencies of DPR (Z_Ka, Z_Ku, k_Ka, and k_Ku, respectively). The symmetry of the interpolated sites allowed quantifying the directional differences in correlations at the same distance. The correlation distances d0 of R, k_Ka, and k_Ku were approximately 10 km and were not sensitive to the choice of four rain thresholds used in this study. The d0 of Z_Ku, on the other hand, ranged from 29 to 20 km between different rain thresholds. The coefficient of variation (CV) remained less than 0.5 for most of the samples for a given physical parameter, but a CV of greater than 1.0 was also observed in noticeable samples, especially for the shape parameter and Z_Ku.

Dimensionless Effective Flow Work for Estimation of Pier Scour Caused by Flood Waves

AbstractThe pier scour caused by flood waves is analyzed, introducing the dimensionless effective work by the flow on the sediment bed around the pier, W*. The three-parameter exponential function ...

A Field Study of Pixel-Scale Variability of Raindrop Size Distribution in the Mid-Atlantic Region.

The spatial variability of parameters of raindrop size distribution and its derivatives is investigated through a field study where collocated PARSIVEL2 and two-dimensional video disdrometers are operated at six sites in Wallops Island, Virginia from December 2013 to March 2014. The three-parameter exponential function is employed to determine the spatial variability across the study domain where the maximum separation distance was 2.3 km. The nugget parameter of exponential function is set to 0.99 and the correlation distance (d0) and shape parameter (s0) are retrieved minimizing root-mean-square error, after fitting it to the correlations of physical parameters. Fits were very good for almost all fifteen physical parameters. The retrieved d0 and s0 were about 4.5 km and 1.1, respectively, for rain rate (RR) when all twelve disdrometers were reporting rainfall with a rain rate threshold of 0.1 mm h-1 in one-minute observations. The d0 decreased noticeably when one or more disdrometers were required to report rain. The d0 was considerably different for a number of parameters (e.g. mass weighted diameter) but was about the same for the other parameters (e.g. RR) when rainfall threshold was reset to 12 dB for Ka-band and 18 dB for Ku-band reflectivity following the expected Global Precipitation Measurement mission's space-borne radar minimum detectable signals. The reduction of the database through elimination of a site did not alter do as long as the fit was adequate. The correlations of 5-minute rain accumulations were lower when disdrometer observations were simulated for a rain gauge at different bucket sizes.

On the time course of short-term forgetting: a human experimental model for the sense of balance.

The primary aim of this study was to establish whether the decline of the memory of an angular displacement, detected by the semicircular canals, is best characterized by an exponential function or by a power function. In 27 subjects a conflict was created between the semicircular canals and the graviceptive systems. Subjects were seated, facing forwards, in the gondola of a large centrifuge. The centrifuge was accelerated from stationary to 2.5Gz. While the swing out of the gondola (66°) during acceleration constitutes a frontal plane angular-displacement stimulus to the semicircular canals, the graviceptive systems persistently signal that the subject is upright. During 6 min at 2.5Gz the perceived head and body position was recorded; in darkness the subject repeatedly adjusted the orientation of a luminous line so that it appeared to be horizontal. Acceleration of the centrifuge induced a sensation of tilt which declined with time in a characteristic way. A three-parameter exponential function (Y = Ae−bt + C) and a power function (Y = At−b + C) were fitted to the data points. The inter-individual variability was considerable. In the vast majority of cases, however, the exponential function provided a better fit (in terms of RMS error) than the power function. The mean exponential function was: y = 27.8e−0.018t + 0.5°, where t is time in seconds. Findings are discussed with connection to possible underlying neural mechanisms; in particular, the head-direction system and short-term potentiation and persistent action potential firing in the hippocampus are considered.

An Experimental Study of Spatial Variability of Rainfall

Abstract Spatial variability of rainfall was studied through a gauge network on the Delmarva Peninsula. The gauge network consists of 11 dual- or triple-tipping-bucket sites ranging from 1- to 150-km separation distances. The time of the tip (0.254 mm) was recorded to a datalogger, and a continuous dataset was available from all sites for over 5 yr (May 2005–July 2010). A three-parameter exponential function was fitted to the paired correlations and the resultant correlation distance was 8–13 km during summer and 51–85 km during winter. The correlation distances showed pronounced year-to-year variability as being 8–43 km and 13–67 km during spring and autumn, respectively. The airmass convection was the main weather system during summer while nor’easters played an important role during winter. The 30-min integration and two-tip rain/no-rain threshold was selected for the base of this study. The correlation distance increased with longer integration periods and was 17 and 32 km for 30 min and 1 h, respectively.

Experiment Research of Environment Effect on Mechanical Properties of PMMA

Fatigue properties of the newly-formed and served canopy PMMA, which was applied in a certain airplane, were studied by experimental method. In order to gain the fatigue strength in the designated life, experiments based on up and down method had been conducted. The S-N curves of the PMMA were acquired based on three-parameter exponential function. Fatigue properties of the canopy PMMA in the two different condition of service were discussed. The results of analysis showed that fatigue properties of the served PMMA did not decrease significantly compared to the newly-formed PMMA.

Study of Fatigue Properties of PMMA with Typical Damage

Fatigue properties of canopy PMMA with typical damage, which are two different depth scratches of 0.3mm and 0.4mm, are studied by experimental method. In order to gain the fatigue strength about the depth scratches of 0.3mm in the designated life, experiments based on up and down method had been conducted. The S-N curves of the PMMA about the depth scratches of 0.3mm were acquired based on three-parameter exponential function. Fatigue life of the PMMA with the depth scratches of 0.4mm under different stress levels is obtained by grouping method. Fatigue properties of the canopy PMMA of the two different depth scratches were discussed. The results of analysis showed that compared with the depth scratches of 0.3mm, fatigue properties of canopy PMMA with the depth scratches of 0.4mm decrease significantly.

Analysis and calibration of default steel strip pullout models used in Japan

The calibration of default pullout capacity models for smooth and ribbed steel strip reinforcement, used in reinforced soil walls in Japan, was carried out more than two decades ago and was based on a small number of physical tests available at that time. The writers have collected and organized a much larger database of more than 600 laboratory pullout box and in situ pullout tests from among the Japanese literature. The new database is a useful reference for design engineers to match project-specific soils to previous pullout tests and to check the accuracy of the current lower-bound design curves proposed in the late 70s and 80s. Today, only the ribbed-type steel reinforcement strips are used. The new data show that a three-parameter exponential function better captures the trend in pullout data for ribbed steel reinforcement than the current bi-linear models adopted from European practice. The formulations also have the advantage of being smoothly continuous with depth. Parameter values are determined for default pullout models that can be used in load and resistance factor design (LRFD) and for the current lower-bound (factor of safety) allowable stress design (ASD). The current PWRC model and a newly proposed model for ribbed steel strip reinforcement, that include the soil coefficient of uniformity (Uc) in their formulations, are shown to be no more accurate than the simpler default models without this term.

The use of solution microcalorimetry to evaluate chemically modified fish scales as a viable adsorbent for heavy metals

Here, we report for the first time the direct and simultaneous determination of kinetic and energetic parameters of Cr(VI) sorption on chemically modified fish scales (GA-scale) using solution microcalorimetry. Characterization has suggested that electrostatic interactions between scales collagen positive charges and chromate negative charges constitute the majority of the interactions. The microcalorimetric kinetic data of Cr(VI) sorption on GA-scale were successful adjusted to a three-parameter exponential function. The enthalpies of Cr(VI) sorption on GA-scale are highly exothermic (from −226.43 to −183.79 kJ mol−1), and Cr(VI) interaction energies decrease as initial Cr(VI) in solution increases. The kinetic and thermodynamic from solution microcalorimetry results suggest that the interactions GA-scale/Cr(VI) occur mainly by surface reactions. The maximum adsorption capacity of GA-scale for Cr(VI) was found to be comparable with some commercial adsorbent samples.

Decay properties of the foamed bitumens

This paper presents study on decay properties of two foamed bitumens. Foaming tests under various conditions were carried out to investigate decay properties of two types of bitumen: Penetration-grade 60 (PG 60) and Penetration-grade 100 (PG 100). Decay data were recorded and analyzed. It is found that water content has a significant effect on the bitumens’ decay, and the time at which the maximum expansion ratio appears advances with an increase of temperature. PG 60 achieves the maximum expansion ratio at an earlier time than PG 100. The effect of viscosity on the two bitumens’ decay properties was discussed and explained; and the observation of the tests confirms this explanation is rational. For developing the bitumens’ decay functions, a four-parameter power function and a three-parameter exponential function were selected to fit the testing data of PG 60 and PG 100 bitumen, respectively. Two bitumens’ decay functions were established by a two-stage method. Non-linear fitting analysis exhibits that two functions can well fit the data of the foaming tests. Decay functions’ parameters were obtained by using the best subset regression method. Two decay functions can be used to calculate the maximum expansion ratios and half-lives of PG 60 and 100 bitumen under various conditions.

Chromium and nickel in roadside grapes.

Chromium and nickel concentration in roadside unwashed wine grapes and leaves is considered as a function of the distance from the suspected source, an isolated straight road. The analyses were performed with electrothermal atomization in a graphite furnace. The decrease in the concentration of the element can be described by means of a three-parameter exponential function c = A + (B - A)exp(-Cd), which allows the determination of the asymptotic level far from the emitting source (C infinity) and the pollution level (C0) at the edge of the road (d = 0). Least-squares nonlinear regression gives the estimation of the parameters A, B, and C. The results indicate that an effect is detectable up to a distance of about 50 m.

DISTRIBUTION OF ATTACKS ON SPRUCE STUMPS BY THE SPRUCE BEETLE, DENDROCTONUS RUFIPENNIS (KIRBY) (COLEOPTERA: SCOLYTIDAE), AND EFFECTS ON THE LENGTH OF EGG GALLERIES

AbstractThe distribution of spruce beetle attacks and length of associated egg galleries were investigated on 21 spruce stumps over a 4-year period in central British Columbia. Attack density formed a distinct vertical gradient which peaked near the duff line at about one-third stump height above the mineral soil. The proportion of attacks on the stumps that were located below the duff was linearly related to the ratio of stump height below duff and total stump height above mineral soil. Attack density was significantly higher below the duff than above. A three-parameter exponential function gave satisfactory fit to the attack density gradient on normalized stump height. A discrete-step theoretical model was also developed based on assumptions regarding beetle behavior during landing and imitation of the egg gallery and the physical characteristics of the host. This model gave an excellent fit to the attack density gradient as an average process over all stumps. Average egg gallery length was a curvilinear function of attack density with maximum average egg gallery length occurring at about 0.33 attacks per 100 cm2.

A comparison of pressure-volume models in hydrocephalus.

Traditional descriptions of the pressure-volume properties of the craniospinal axis have expressed pressure as a function of volume. This study develops a theoretical and practical rationale for expressing volume as a function of pressure. We tested the rationale by comparing the two functions using pressure and volume data collected from 37 hydrocephalic patients during ventricular fluid removal. Two equivalent expressions were evaluated, one expressing pressure as an exponential function of volume and one relating volume as an exponential function of pressure. Each expression had three parameters, adjustable to the specific case. We used a nonlinear curve-fitting algorithm to determine the best estimate of the parameters. We could fit three-parameter exponential functions of either type to the data in all cases. We found a superior goodness-of-fit to aggregated data when expressing volume as a three-parameter exponential function of pressure changes. This finding is discussed in the context of the preferable number of parameters in a model and the interpretation of the terms in the models. This "reversed" volume-pressure relationship has importance in the development of more complicated models involving these same relationships.