Horizontal Asymptote Research Articles

On the mechanical behaviour of a coral silt from the South China Sea

During land reclamation on the reef islands, large amounts of silt-sized coral soils were created by segregation and degradation. The accumulation of silt-sized coral soils is fairy uncommon while the research on the geotechnical properties of the coral silt is very limited. In this study, a systematic experimental investigation on the mechanical behaviour of a coral silt obtained from a reclaimed reef island in the South China Sea has been performed, with comparisons to the coral sand collected from the same area. Similar to the coral sand, the coral silt particles also exhibit irregular particle shape and intra-particle pore due to their nature origin. According to the limiting water contents, the coral silt is classified as a low-plasticity clayey silt. Under one-dimensional compression, the coral silt exhibits a much quicker convergence compared to coral sand. Prior to convergence, the compressibility of coral silt is higher. After yielding, the compressibility of coral sand becomes higher due to significant particle breakage. The loose coral silt subjected to undrained shearing at low confining pressures exhibits obvious strain softening behaviour, indicating static liquefaction or flow failure. The peak and critical state friction angles of coral silt are lower than those of coral sand but much higher than those of the other terrigenous clayey silts. A curved critical state line with well-defined horizontal asymptote in the deviatoric stress – mean effective stress plane is identified for coral silt, again indicating higher potential to static liquefaction.

A survey on recent advances in the computation of asymptotes

AbstractIn this paper, we summarize two algorithms for computing all the generalized asymptotes of a plane algebraic curve implicitly or parametrically defined. The approach is based on the notion of perfect curve introduced from the concepts and results presented in Blasco and Pérez-Díaz (Comput Aided Geom Des 31(2):81–96, 2014), Blasco and Pérez-Díaz (Comput Aided Geom Des 31(7-8):345–357, 2014), and Blasco and Pérez-Díaz (J Comput Appl Math 278:231–247, 2015). From these results, we derive a new method that allow to easily compute horizontal and vertical asymptotes.

Iterative nearest neighbour age-height curve adjustment: Addressing the impact of spatial heterogeneity on longitudinal forestry provenance trial data

Spatial heterogeneity in long term forestry genetics trials can obscure genetic variation and influence conclusions made based on the data. Nearest neighbour adjustment methods have been employed to account for spatial patterns, however such methods are limited in their applicability to longitudinal provenance trial data because of the need to account for repeated measures as well as the interest in preserving among-site variation. In this study, a novel approach combining nearest neighbour adjustment techniques with longitudinal data analysis concepts was developed to adjust lodgepole pine (Pinus contorta var. latifola Douglas) provenance trial data for spatial heterogeneity. Individual height-age logistic growth curves were fit to each tree to age 35, and the horizontal asymptote parameters of the height-age curves were adjusted for spatial patterns using iterative nearest neighbour adjustments. The methods developed in this study successfully removed positive spatial correlation and reduced the interaction between block and provenance, thus reducing changes in population ranking among blocks within sites. The adjustments applied caused large shifts in population ranks at many sites, indicating that seed selection decisions based on data not adjusted for spatial heterogeneity could lead to selecting non-optimal populations for a given site. This research provides a methodological framework for adjusting longitudinal genetics trial data for underlying site conditions and spatial patterns. Additionally, a spatially adjusted version of a large and extensively utilized provenance trial dataset was created for use in future analyses.

On Topp-Leone-G Power Series: Saturation in the Hausdorff Sense and Applications

This paper discusses the Topp-Leone-G power series class of distributions. The greatest attention is paid to the investigation of intrinsic characteristic “saturation” to the horizontal asymptote in the Hausdorff sense. Some estimates for the value of the Hausdorff distance are obtained. We present a new family of recurrence generated adaptive functions with corresponding applications. The usefulness of the obtained results is demonstrated in a simulation study of some real data sets from the medical sector and insurance. Some suitable software modules within the programming environment CAS MATHEMATICA are proposed.

Effect of Cavitator and Nozzle Parameters on the Efficiency job of the impulse Jet Generator

Studies of fluid jet flows in the presence of a ventilated cavity with a negative cavitation number, carried out at the Institute of Mechanics of Moscow State University, showed that under certain conditions, self-cavitational oscillations with a high intensity of pressure pulsations occur in such a hydraulic system. It was shown that it is possible in principle to use the self-oscillation regime to create periodic impulsed jets during outflow from a converging nozzle into the atmosphere. The influence of the parameters of the cavitator and the outlet nozzle on the intensity of the impact of the outflowing liquid on the screen located perpendicular to the outflow direction is studied. It is shown that an increase in the length of the nozzle can significantly increase the efficiency of the generator, and a smooth narrowing of the channel in front of the cavitator can increase the operating range of the generator in the direction of larger gas blows. It is shown that there is a scale effect - with increasing head pressure, the relative intensity of self-oscillations decreases, but tends to reach a horizontal asymptote.

Water diversion structures and river discharge dictate salinity dynamics on tidal flats of the Fraser River delta, British Columbia

Salinity in estuaries affects numerous ecological processes, and is strongly driven by river outflow interacting with the tide. We used an exponential decay function to model the relationship between salinity and freshwater flow (i.e., river discharge) to characterize and map salinity dynamics over the tidal flats of the Fraser River delta, British Columbia, Canada. The model has three parameters: the horizontal asymptote Asym that represents the average weekly salinity at very high river flows; the theoretical intercept R0 that represents salinity conditions during very low river flows; and the natural log of the rate constant lrc that reflects the relationship between river discharge into the estuary and resultant average salinity. Using data from 47 salinity-monitoring stations deployed from 2015 to 2021, we found that Fraser River discharge had a strong and inverse relationship with average weekly salinity on the outlying tidal mudflats, which is expressed by the lrc value of −8.56. Model estimates indicate that weekly salinity (on the Practical Salinity Scale) at very low discharge rates (R0) had a value of 22.4, which decreased at high discharge rates (Asym) to a value of 3.7. This predictable decrease in salinity for increasing river discharge means that the salinity regime of the Fraser River delta tidal flats is poikilohaline, and undergoes a regular and biologically relevant transition from brackish to nearly fresh water as the river outflow increases and abates seasonally. The resulting spatial gradients in salinity dynamics were associated with distance to river outflows and existing water diversion structures (i.e., jetties and causeways), meaning the timing and extent of this transition varied across the tidal flats. As estuaries become increasingly modified by coastal development and climate change, this simple model can be used to evaluate management interventions and river discharge scenarios that affect salinity gradients over tidal flats.

Is it sufficient? Assessment of two sampling methods for urban plant species richness investigations

Determining adequate sample size (ASS) and minimum plot size (MPS) are two fundamental issues in urban vegetation investigations. To estimate the ASS and MPS of urban plants, we introduced sampling completeness to the MPS calculation based on 54 samples in the urban area of Chongqing, China. Then, we examined the performance of the species-area curve method and CVJack1 (coefficient of variation (CV) for the first-order jackknife estimator (Jack1)) curve extrapolation method. We also tested the effectiveness and error distribution of extrapolating the ASS from CVJack1 curves using 180 samples from the urban area of Chongqing, China, and 222 samples from the urban area of Xiamen, China. The results of the urban plant analyses showed that (1) the constructed species-area accumulation curves fit a logistic function (R2 > 0.990); (2) the MPS increased with sampling completeness, whereas unrecorded species exhibited the opposite trend; (3) the CVJack1 curves fit the allometric1 function (R2 > 0.960) but might fail to reach a CV value of 0.05 for the calculation of ASS if the sample size was too small; and (4) the relative error values were below 5% when the error curves of extrapolation (by CVJack1 curve) approached a horizontal asymptote. The species-area accumulation curve with sampling completeness and the CVJack1 curve extrapolation method were promising approaches for determining the MPS and ASS of urban plants. The results and methods in this study provide a reference for determining the appropriate plot size and sample size for urban plant species richness investigations.

1150: OPTIMAL DOSE OF RAPID RESPONSE TEAM ENCOUNTERS FOR CLINICAL EFFECTIVENESS AND PROGRAM EFFICIENCY

Introduction: Although rapid response systems (RRS) are ubiquitous, a consistent reduction in hospital mortality has remained elusive. A minimum threshold for RRS encounters has been observed before arrest reduction can be expected. It is unclear whether this same threshold is associated with a reduction in mortality. In addition, an optimal rate of RRS encounters beyond which additional benefit is minimal has not been identified. Here we explore the relationship between RRS encounters and hospital mortality, hypothesizing that an optimal RRS encounter rate could be identified to ensure both program effectiveness and efficiency. Methods: This was a prospective, observational study performed in a 500-bed urban hospital. A standard RRS existed for several years prior to the intervention, which included transition to a mobile/proactive team and implementation of a novel educational curriculum based on principles of cognitive psychology. The main objective for this analysis was to explore the relationship between RRS patient encounter volume and Risk-Adjusted Mortality Index (RAMI). Data were collected on a quarterly basis over a 4-year period that spanned the intervention. Polynomial regression was used to model the number of RRS encounters as a predictor of RAMI, with r-squared used to quantify the strength of association and statistical significance assumed for p< 0.05 Results: An 80% reduction in non-ICU arrests, a 20% reduction in ICU arrests, and a reduction in hospital mortality were observed following the intervention. A strong nonlinear association was observed between RRS encounter volume and RAMI (r-squared=0.73, p< 0.0001). An initial reduction in RAMI with increasing RRS volume reached a horizontal asymptote at approximately 150 encounters/1000 discharges. Conclusions: We observed a substantial reduction in hospital mortality following transition to a mobile, proactive RRS trained using a novel curriculum. A steep decrease in RAMI with increasing RRS volume was observed up to approximately 150 encounters/1000 discharges, beyond which no additional improvement in RAMI was observed. These data support an “optimal dose” of RRS encounters, potentially representing a target RRS volume for hospitals for both clinical effectiveness and program efficiency.

Comparison between a numerical model and the classic thermal explosion theories for the calculation of the minimum ignition temperature of dust clouds

A numerical model for the calculation of the minimum ignition temperature (MIT) of dust clouds is compared with the classic Semenov and Frank-Kamenetskii thermal explosion theories. The numerical model is developed based on the MIT testing equipment: Godbert-Greenwald furnace. The Semenov theory for uniform temperature system is exploited for the MIT calculation of a single dust particle (MITP). The Frank-Kamenetskii theory for a uniform system with temperature gradient is modified for the MIT calculation of a dust cloud (MITC). At stoichiometric dust concentration with infinite dust cloud residence time, two horizontal asymptotes are discovered along with the variation trend of the numerical ignition temperature against ignition delay time. The higher asymptotic temperature is only discovered for metal dusts. This temperature is almost identical to the MITP value with the Semenov theory. On the other hand, the lower asymptotic temperature for both metal and organic dusts almost equals the calculated MITC value with the Frank-Kamenetskii theory. Thus, there is good agreement between the numerical model and the classic thermal explosion theories. This study can provide reference for the theoretical prediction of the MIT of dust clouds.

The Radial Bulging and Axial Strains of Intervertebral Discs during Creep Obtained with the 3D-DIC System.

Creep-associated changes in disc bulging and axial strains are essential for the research and development of mechano-bionic biomaterials and have been assessed in various ways in ex vivo creep studies. Nonetheless, the reported methods for measurement were limited by location inaccuracy, a lack of synchronousness, and destructiveness. To this end, this study focuses on the accurate, synchronous, and noninvasive assessment of bugling and strains using the 3D digital image correlation (3D-DIC) system and the impact of creep on them. After a preload of 30 min, the porcine cervical discs were loaded with different loads for 4 h of creep. Axial strains and lateral bulging of three locations on the discs were synchronously measured. The three-parameter solid model and the newly proposed horizontal asymptote model were used to fit the acquired data. The results showed that the load application reduced disc strains by 6.39% under 300 N, 11.28% under 400 N, and 12.59% under 500 N. Meanwhile, the largest protrusion occurred in the middle of discs with a bugling of 1.50 mm, 1.67 mm, and 1.87 mm. Comparison of the peer results showed that the 3D-DIC system could be used in ex vivo biomechanical studies with reliability and had potential in the assessment of the mechanical behavior of novel biomaterials. The phenomenon of the largest middle protrusion enlightened further the strength of spinal implants in this area. The mathematical characterizations of bulging and strains under different loads yielded various model parameters, which are prerequisites for developing implanted biomaterials.

Optimization of ethylene dichloride (EDC) and ethane concentrations to maximize catalytic ethylene oxide production rate and yield: Experimental study and modeling

Simultaneous optimization of EDC and ethane concentrations to maximize ethylene oxide production rate (rEO) over a commercial catalyst at 17.4 bar, 213–240 °C and in the GHSV range of 3000–5000 h−1 was done in this study. The feed composition and operating conditions were chosen similar to those in the industry, so that the findings are practical. EDC and ethane concentrations in the feed are merged into a practical parameter referred to as equivalent EDC (EDCeq) in this study which is indicative of the chlorinating power of the gas mixture. It was noticed that the higher the temperature, the higher the optimum EDCeq to maximize rEO. Although rEO had a decreasing trend versus EDCeq for 213 °C, it showed a maximum with EDCeq for 225 and 240 °C. While CO2 production rate (rCO2) monotonically decreased with EDCeq, EO selectivity experienced an upward trend with EDCeq, approaching a horizontal asymptote.

Continued Fraction Interpolation of Preserving Horizontal Asymptote

The classical Thiele‐type continued fraction interpolation is an important method of rational interpolation. However, the rational interpolation based on the classical Thiele‐type continued fractions cannot maintain the horizontal asymptote when the interpolated function is of a horizontal asymptote. By means of the relationship between the leading coefficients of the numerator and the denominator and the reciprocal differences of the continued fraction interpolation, a novel algorithm for the continued fraction interpolation is constructed in an effort to preserve the horizontal asymptote while approximating the given function with a horizontal asymptote. The uniqueness of the interpolation problem is proved, an error estimation is given, and numerical examples are provided to verify the effectiveness of the presented algorithm.

Optimization of the CRTM process by means of monitoring techniques

In this work the feasability of the monitoring system, composed of flow-rate and injection pressure sensors, in addition to the pressure sensors integrated in the mold, is demonstrated to determine the optimal process window of the CRTM (Compression Resin Transfer Molding). The sensors of the injector allow monitoring of the injection phase, while the pressure sensors integrated in the mold allow the phases of the compression and the curing to be followed. In order to relate the pressure sensor variations with the curing phase, an electric current sensor has been used. The increase of the resistance, associated with the beginning of curing, corresponds in time with the pressure drop, which in turn is justified by the contraction generated during curing. This pressure drop reaches a horizontal asymptote which corresponds to a conversion rate of 40%. Based on this behavior of the pressure sensor, it is possible to determine the minimum time for the demoulding of each of the pieces. Finally, the system has been used to monitor the manufacturing of prototypes with curing temperatures between 80-120 &ordm;C, and it has been confirmed that the sensors identify the parts that are inside the process window and those that are not.

Estimating the long-term strength and time-to-failure of brittle rocks from laboratory testing

The long-term strength and time-to-failure of brittle rocks has become increasingly important with the increased interest in the storage of used nuclear fuel in deep geological repositories . This paper critically reviews and analyzes the currently available time-to-failure data for various brittle rock types. The current best approach on estimating time-to-failure of rock samples at the lab scale under a constant stress is using semi-log data based on the driving stress ratio and the logarithm of time. In most studies, the applied driving stress ratio is calculated based on the average strength of the rock, however, sample strength can vary up to 15%. Therefore, it is proposed that the crack-initiation stress threshold for each sample be used to calculate sample specific ultimate strengths based on relationships determined in literature. It is proposed that if a sample fails during a long-term strength test within the first 1–10 s, the applied stress for that test can be assumed equivalent to the ultimate strength. Additionally, a modified exponential function with a horizontal asymptote at the crack-initiation threshold is explored as an alternative to the typical log-linear approach. The exponential approach is non-linear in semi-log space and does not require an arbitrary cut-off for time-to-failure at the static fatigue limit of the rock as is the case of the semi-log approach. Ultimately, it is shown that although the exponential function does usually provide a better overall fit to data at relatively short times (<1,000,000 s), there is little evidence to justify the asymptotic behaviour in the longer term. Common practice has been to present the driving stress ratio as a function of time-to-failure, however, in theory these axes should be reversed as the variable of interest to the reader is the time-to-failure based on in-situ stresses. The consequence of plot orientation and subsequent error calculation are explored. The goal of this paper is to provide users and researchers with a reliable methodology to predict time-to-failure of brittle rocks both at the lab and excavation scale as well as a basis for incorporating explicit time-to-failure calculations into a continuum numerical model.

Over 55 years of critical power: Fact or artifact?

This report aims to generate an evidence-based debate of the Critical Power (CP), or its analogous Critical Speed (CS), concept. Race times of top Spanish runners were utilized to calculate CS based on three (1500-m to 5000-m; CS1.5-5km ) and four (1500-m to 10000-m; CS1.5-10km ) distance performances. Male running world records from 1000 to 5000-m (CS1-5km ), 1000 to 10,000-m (CS1-10km ), 1000-m to half marathon (CS1km-half marathon ), and 1000-m to marathon (CS1km-marathon ) distance races were also utilized for CS calculations. CS1.5-5km (19.62kmh-1 ) and CS1.5-10km (18.68kmh-1 ) were different (p<0.01), but both approached the average race speed of the longest distance chosen in the model, and were remarkably homogeneous among subjects (97%±1% and 98%±1%, respectively). Similar results were obtained using the world records. CS values progressively declined, until reaching a CS1km-marathon value of 20.77kmh-1 (10% lower than CS1-5km ). Each CS value approached the average speed of the longest distance chosen in the model (96.4%-99.8%). A power function better fitted the speed-time relationship compared with the standardized hyperbolic function. However, the horizontal asymptote of a power function is zero. This better approaches the classical definition of CP: the power output that can be maintained almost indefinitely without exhaustion. Beyond any sophisticated mathematical calculation, CS corresponds to 95%-99% of the average speed of the longest distance chosen as an exercise trial. CP could be considered a mathematical artifact rather than an important endurance performance marker. In such a case, the consideration of CP as a physiological "gold-standard" should be reevaluated.

Insight into t->m transition of MW treated 3Y-PSZ ceramics by grazing incidence X-ray diffraction

The influence of a microwave hybrid heat treatment (MHH) on the surface and in-depth mineralogical transformation of pre-sintered 3Y-PSZ was investigated. 3Y-PSZ samples were prepared by slip casting and sintered by conventional firing (1270 °C). Then, different MHH treatments from 5 to 15 min. at 1200 °C were applied to obtain a fully stabilized 3Y-TZP. The monoclinic fraction depth profiles in the first micrometres (up to 5) of thickness were investigated by means of the grazing incident X-ray diffraction technique (GIXRD). A good sintering degree with practically nil closed porosity and grain growth was achieved after MHH of 15 min. MHH increases the tetragonal phase content both in the surface and in-depth, reducing completely the monoclinic phase shell typically found after conventional sintering. A new parabolic model is proposed for the convoluted monoclinic fraction depth profile, which through the value of its horizontal asymptote allows the determination of the monoclinic shell thickness.

Strength of AAAS Composites with Ceramic Precursor over Time

The paper deals with the approximation of the time evolution of the strengths of selected alkali-activated aluminosilicate (AAAS) composites based on ceramic precursors. Composites made of brick dust as a precursor and an alkaline activator with a silicate modulus of Ms = 0.8, 1.0, 1.2, 1.4, and 1.6 were investigated. The filler consisted of standard quartz sand in one case, and crushed brick in the other. The test specimens had nominal dimensions of 40 × 40 × 160 mm and were tested in three-point bending after 7, 28, 90, and 300 days of maturation. From each composite, 3 specimens were tested and the compressive strength was determined from the 6 specimen parts that remained after the bending tests. The obtained flexural and compressive strength values for the abovementioned 4 composite ages were approximated by the exponential function , where the coefficient a represents a horizontal asymptote to the approximation curve, i.e. the theoretical strength of the composite at time t = ∞; the exponential term of the approximation with the coefficients b and c expresses the degree of the time-dependent change of the respective compressive strength in the interval t = (0, ∞). The approximation was performed with the least squares method using genetic algorithms implemented in the Java GA package with open source code.

THE ODD WEIBULL-TOPP-LEONE-G POWER SERIES FAMILY OF DISTRIBUTIONS

In 2021 Oluyede, Chipepa and Wanduku \cite{Olu} developed a new generalization of the Weibull--Topp--Leone--G family of distributions called the odd Weibull--Topp--Leone--G--power series (OW--TL--GPS) family.In the paper we study one of the important characteristics saturation of this new family of cumulative functions to the horizontal asymptote with respect to Hausdorff metric. We prove estimates for the Hausdorff approximation of the Heavisidestep function by means of this family.Also we construct and study families of recurrence generatedadaptive functions based on the odd Weibull-Top-Leone-G power series family. In additional we consider a new adaptive model with “polynomial variable transfer”.Some numerical examples and simple programming modules, illustrating the new results are given.

Fatigue of wire+arc additive manufactured Ti-6Al-4V in presence of process-induced porosity defects

Currently, additive manufactured titanium alloy Ti-6Al-4V predominantly fails from process-induced defects, when subjected to cyclic loading in the polished condition. These defects not only lead to premature failure, but also contribute to the significant dispersion of fatigue life commonly seen in metal additive manufacturing. In this work, we have studied the source of dispersion and the influence of pore size on fatigue life using samples from the standard processing route and samples with intentionally introduced porosity defects. According to the fracture surface study, contrary to the common belief, the source of dispersion is primarily the pore location, e.g. surface or embedded pore, rather than the pore size. In the case of embedded pores as the failure source, a threshold pore size of approximately 85 μm was observed, below which the wrought level fatigue performance was achieved. For surface pores above the threshold size, fatigue life was reduced by two orders of magnitude, but remained unchanged, even though crack initiating pore size increased roughly by a factor of four. This experimental observation was supported by local elastic stress analysis, which indicated that pores above a certain size could behave like micro-notches suggesting the popular Kitagawa-Takahashi diagrams should be presented with a horizontal asymptote for this alloy.

Some Notes on the Omega Distribution and the Pliant Probability Distribution Family

In 2020 Dombi and Jónás (Acta Polytechnica Hungarica 17:1, 2020) introduced a new four parameter probability distribution which they named the pliant probability distribution family. One of the special members of this family is the so-called omega probability distribution. This paper deals with one of the important characteristic “saturation” of these new cumulative functions to the horizontal asymptote with respect to Hausdorff metric. We obtain upper and lower estimates for the value of the Hausdorff distance. A simple dynamic software module using CAS Mathematica and Wolfram Cloud Open Access is developed. Numerical examples are given to illustrate the applicability of obtained results.