Slope Of Tangent Research Articles

Bond shear modulus in reinforced concrete at high temperature: General trends from test results

The scanty attention devoted so far to bond shear modulus (secant or tangent slope of the loading branch of the bond-slip curve) limits the ability to numerically model such phenomena as tension stiffening, that controls the stiffness of cracked RC structures even past a fire. To improve the knowledge of bond shear modulus at high temperature, the bond stress-bar slip curves resulting from the tests of eleven selected experimental campaigns spanning a forty-year period are re-examined in this paper. Bond shear modulus is derived as the initial slope of the bond stress-bar slip curves of stressed or unstressed specimens in either hot or residual conditions. The criteria to compare the test results coming from very different experimental campaigns are discussed at length. Bond shear modulus is shown to be a decreasing function of the residual compressive strength of the concrete (at high temperature or past cooling). The envelopes of the test data allow to assess the roles of bar diameter and concrete grade. Trend curves are derived for normal-strength and high-strength/high-performance concretes, as a first necessary step for the formulation of parametric design-oriented laws, that may be useful to model tension stiffening and to describe the distribution of the bond stresses in long anchored bars. A numerical example is also developed and the consistency with EuroCode EC2 is checked.

Light Scattering From High‐Porosity 3D Simulants of the Lunar Regolith at Small Phase Angles

AbstractLunar regolith consists of unconsolidated grains with high porosity, called the fairy castle structure. It is closely linked to the lunar opposition effect, which is the effect where brightness sharply increases as the phase angle approaches 0. However, owing to the Earth's gravity, it is difficult to reproduce the structure to study the physical characteristics of the lunar fairy castle structure in the laboratory. We designed a lunar fairy castle structure model for 3D printing. These models had high porosity and were simplified to tree‐like shapes. Various porous conditions of the surface were considered, represented by the number of trees, maximum trunk length, and maximum branch angle. In this study, a laboratory experiment was conducted to measure the reflectance of simulants with a fairy castle structure within a small phase angle range from 1.4 to 5.0. The result is analyzed for the sample porosity with the tangential slope of the reflectance S, which denotes the strength of the opposition effect. In addition, the results of this study were compared with lunar observation data. The porous samples exhibited a relatively large S value. The influence of branch length and attachment angle was very weak in this study. Samples with a porosity between 0.78 and 0.82 represent the similar S values to the lunar observation data, a mean porosity of lunar regolith. In conclusion, our findings suggest a potential correlation between porosity and the opposition effect in printed samples, proposing a new research approach for understanding the lunar opposition effect.

Characteristics and Mechanism of Downflow in Front of a Cylindrical Pier with Clear-Water Local Scour

Local scour often causes pier instability; however, the characteristics and mechanism of downflow, representing one of the crucial flow structures, are still unclear. In this paper, the interaction between the downflow and the horseshoe vortex system and the role of the downflow under clear-water local scour conditions are discussed, based on the stress distribution obtained via experiments and simulations. In the present experiment, more accurate data are measured by installing suitable sensors on 3D-printed models that reproduce the scour hole conditions at various times. The obtained results reveal that the downflow exhibits a strong interaction with the horseshoe vortex system. From the perspective of flow structures, the flow structures collide and rub against each other, which weakens the effect of the downflow. From the perspective of energy transfer, the horseshoe vortex system absorbs the energy carried by the downflow to develop and reduce the energy introduced into the sediment. In addition, shear stress is a crucial factor in maintaining a high tangent slope. When the shear stress is down to a minimum and is stable, the tangent slope rises with the growth of the pressure stress, which means that the downflow is able to promote scour depth development.

Hypersonic similarity for steady compressible full Euler flows over two-dimensional Lipschitz wedges

We establish the optimal convergence rate to the hypersonic similarity law, which is also called the Mach number independence principle, for steady compressible full Euler flows over two-dimensional slender Lipschitz wedges. Mathematically, it can be formulated as the comparison of the entropy solutions in BV∩L1 between the two initial-boundary value problems for the compressible full Euler equations with parameter τ>0 and the hypersonic small-disturbance equations (the scaled compressible full Euler equations with parameter τ=0) with curved characteristic boundaries. We establish the L1–convergence estimate of these two solutions with the optimal convergence rate, which justifies the Van Dyke's similarity theory rigorously for the compressible full Euler flows. This is the first mathematical result on the comparison of two solutions of the compressible Euler equations with characteristic boundary conditions. To achieve this, we first employ the special structures of the two systems and establish the global existence and the L1–stability of the entropy solutions via the wave-front tracking scheme under the smallness assumption on the total variation of both the initial data and the tangential slope function of the wedge boundary. Based on the L1–stability properties of the approximate solutions to the scaled equations with parameter τ>0, a uniform Lipschtiz continuous map with respect to the initial data and the wedge boundary is obtained, which is the first time for the characteristic boundary conditions. Next, we compare the solutions given by the Riemann solvers of the two systems by taking the boundary perturbations into account case by case. Then, for a given fixed hypersonic similarity parameter, as the Mach number tends to infinity, by employing the Lipschitz continuous properties of the map, we establish the desired L1–convergence estimate with the optimal convergence rate. Finally, we show the optimality of the convergence rate by investigating a special solution.

Fluctuation Analysis of Uterine Contractions in Term Pregnancies Using Electrohysterography Signals and Empirical Mode Decomposition-Based Multifractal Features

Investigating the fluctuations of uterine contractions is an indispensable diagnostic practice to evaluate the onset of labor. This work aims to differentiate the fluctuations associated with Term (gestation ≥ 37 weeks) pregnancies during varied gestational ages using electrohysterography (EHG) signals. The signals in the second and third trimesters are subjected to Multifractal-Empirical Mode Decomposition-based Detrended Fluctuation Analysis (MF-EMDDFA). Multifractal spectrum is estimated and features namely, Holder exponents ([Formula: see text], [Formula: see text]), broadness (BD), root slopes (LS, RS) and tangential slopes (TL, TR) are extracted. Machine learning methods, such as Naïve Bayes, adaptive boosting and random forest (RF) classifiers, are utilized to discriminate the contractions during different weeks of gestation. Results show that five multifractal features, namely [Formula: see text], [Formula: see text], BD, LS and TL, show significant differences between the considered gestational ages. An increase in regularity of the uterine contractions is observed as the gestational age increases. These features along with the RF classifier provide an accuracy, sensitivity, precision, recall and F1-score of greater than 98.30%. As the differentiation of uterine contractions during different weeks of gestation is vital to understanding the pregnancy progress, the proposed multifractal features could be used as potential biomarkers in clinical practices.

Dynamical analysis of a network-based SIR model with saturated incidence rate and nonlinear recovery rate: an edge-compartmental approach.

A new network-based SIR epidemic model with saturated incidence rate and nonlinear recovery rate is proposed. We adopt an edge-compartmental approach to rewrite the system as a degree-edge-mixed model. The explicit formula of the basic reproduction number $ \mathit{\boldsymbol{R_{0}}} $ is obtained by renewal equation and Laplace transformation. We find that $ \mathit{\boldsymbol{R_{0}}} < 1 $ is not enough to ensure global asymptotic stability of the disease-free equilibrium, and when $ \mathit{\boldsymbol{R_{0}}} > 1 $, the system can exist multiple endemic equilibria. When the number of hospital beds is small enough, the system will undergo backward bifurcation at $ \mathit{\boldsymbol{R_{0}}} = 1 $. Moreover, it is proved that the stability of feasible endemic equilibrium is determined by signs of tangent slopes of the epidemic curve. Finally, the theoretical results are verified by numerical simulations. This study suggests that maintaining sufficient hospital beds is crucial for the control of infectious diseases.

Study on the Performance of Nano-Zinc Oxide/Basalt Fiber Composite Modified Asphalt and Mixture

In order to improve the service quality of roads and resolve the problem of defects in the conventional asphalt pavement in service, this paper uses a 5.3% aluminate coupling agent to modify the surface of nano-ZnO and prepares a composite-modified asphalt with nano-ZnO and basalt fiber (BF) as modifiers. First, the basic performance of different types of asphalt was investigated by means of a rotary film oven experiment. Then, a dynamic shear rheology experiment was carried out to analyze the high-temperature anti-rutting performance of the composite-modified asphalt at different temperatures and frequencies. Then, using a bending creep stiffness test, the low-temperature properties of the composite-modified asphalt were investigated. Finally, the microstructure and modification mechanisms of the composite-modified asphalt were analyzed with scanning electron microscopy and infrared spectroscopy. The results indicate that the anti-aging performance of the nano-ZnO/BF composite-modified asphalt is significantly improved after adding fibers to the modified asphalt. The average mass loss ratio is only 0.192%. At 46 °C, the rutting coefficient of the composite-modified asphalt was increased by 62.3%. The frequency master curve is always at the highest position and continues to rise, indicating a significant improvement in the high-temperature anti-rutting performance of the composite-modified asphalt. At 24 °C, the creep stiffness modulus S value of the composite-modified asphalt increased by 24.9%; moreover, there is no obvious effect of improving low temperature, but the variation range of creep tangent slope m of the modified asphalt after aging is decreased, which further shows that the addition of a modifier can decrease the influence of aging on asphalt. Nanoparticles are uniformly dispersed in the asphalt and form a three-dimensional interconnected structure with BF, which effectively improves the overall performance of the asphalt. Nano-ZnO and fibers have weak chemical reactions in matrix asphalt, but they are physically dispersed and compatible.

Study on AE characteristics of concrete with different w/c ratio under uniaxial compression

Concrete material is a three-phase composite material. Its acoustic emission (AE) characteristics are influenced by the properties of its components. The water-cement ratio has significant influence on the mechanical properties and components of concrete. To clarify the relationship between water-cement ratio and AE characteristics of concrete, in this study, AE characteristics of concrete with different water-cement ratio were discussed through parameter analysis and frequency domain analysis. A damage evaluation model of concrete was established based on AE events,cumulative AE ringing count (CR) and cumulative energy (CE).The results show that AE parameters can characterize the three-stage failure process of concrete, namely the initial stage, the stable stage and the active stage.The water-cement ratio has obvious influence on the damage process of concrete and the time distribution of AE parameters.With the development of the damage process, AE signals shift from 30 kHz to 300 kHz and higher frequencies, and the number of main frequency segments increases. On this basis, the evaluation model D of concrete compression damage based on the CR and CE was established. The tangent slope of D was used to observe the change of damage stage, which is in good agreement with the experimental results.

Analysis for temperature distribution of laser cleaning process of curved surface by numerical simulation

Laser cleaning is an advanced cleaning technology which is widely used in the manufacturing industry. Compared with the common planar laser cleaning process, the laser cleaning process of curved surface is difficult to control the completeness and homogeneity of the cleaning layer, which has a great influence on the surface quality and mechanical properties of the cleaned parts. Therefore, a three-dimensional numerical model of the laser cleaning process of the curved surface considering the coordinate system transformation of the heat source is established in this paper to clean the alumina on the surface of the 5754 aluminum alloy. The temperature distribution characteristics for different tangent slopes of the laser cleaning path and the temperature variation with time for different cleaning paths of the laser cleaning process are analyzed. The results show that the proposed method can provide important guiding significance for the practical laser cleaning process of the curved surface.

Bolt body axial stress detection based on nut axial stress

Accurate detection of bolt body axial stress (σb) is a significant means for bolt loosening judgment and bolt fatigue analysis in engineering structures. Strain gauges are widely used in the stress detection of engineering structures and process equipment because of their easy installation, compact structure, and applicability. This paper proposes a method to detect σb using strain gauges based on the nut axial stress. Through theoretical analysis and finite element simulation, it is found that there is a linear relationship between σb and nut surface axial stress (σnx), which is verified by experimental investigations. The results show that the relationship is linearly distributed under static load. However, under dynamic load, the relationship is a flat closed curve due to the relative hysteresis effect of the bolt and nut. The closed curve is less related to the excitation frequency. However, the slope of the curve tangent decreases with the increase of dynamic load, and the decrease gradually slows down. This method is applied to the discharge valve bolt (40CrMoNiA, 10.9) of a compressor in a chemical plant. The detection results show that there is a better linear relationship between σb and σnx. Numerical analysis to suggest nut stress detection positions based on stress signals and dispersion. In summary, the proposed method provides a new way to monitor the bolt connection status, detect bolt loosening, and overcome the short board that the bolt body is inside the machine and cannot directly realize stress measurement.

Illustration of the voltage stability by using the slope of the tangent vector component

This Paper is dedicated to the analysis of the evolution of the tangent vector during the Continuous Power Flow (CPF) iterations. The flow of the tangent slope (measured in degrees) is shown through the coefficient of lambda tangent vector component and the maximum voltage tangent vector component. A 17 Node Network was used for the purposes of this Paper. The system was modelled in MATLAB software. The admittance matrix of the node voltage equations was formulated and the functions in MATLAB were developed for the systematic formation of the node admittance matrix. Equations for the calculated network were generated in MATLAB. 32 Iterations were performed. Iterations and corrections of iterations were done manually. Firstly, the results for the tangent vectors calculated through the CPF program were compared to the results for the tangents directly calculated with mathematical formula for the tangent, and both results match. The chart, which contains the classical PV curve and the flow of tangent vectors during the CPF iterations, was developed based on the results obtained. The increase in the slope of the tangent in the PV diagram imposes a clear numerical stability limit by specifying an angle limit value, which can be used to trigger an alarm. In addition to the classic Power-Voltage (PV) curve, this serves as an additional indicator for ensuring voltage stability of the examined system.

Uncertainty analysis for drilled shaft axial behavior using CYCU/DrilledShaft/143

Drilled shaft axial capacities and their uncertainties were evaluated in this paper. A large load test database of drilled shafts labeled as CYCU/DrilledShaft/143 was compiled for this evaluation. All load tests were performed in the field under drained and undrained soil conditions. The database was made available at ISSMGE TC304 database sharing platform 304 dB. Drained and undrained analyses were conducted separately. These load test data were first analyzed using representative interpretation criteria to determine their “capacities”. The results of each of the interpretation criteria were next normalized by a standard interpretation criterion and a predicted capacity to establish the relationships between these various interpretation criteria and to characterize model factors, respectively. The analyses of 143 drilled shafts indicated that L1 and DeBeer interpreted loads can be recommended for the serviceability limit state design. The criteria van der Veen, 4%B, Terzaghi and Peck, slope–tangent, L2, and Fuller and Hoy yielded values that are at the transition region of the load–displacement curve, in which the “ultimate” capacity can be reasonably estimated. The Chin method is not conservative, because it produced a value larger than all of the above interpreted “ultimate” capacities with displacements exceeding 60 mm on the average and beyond the range of the measured load–displacement curve. The scatter in the load–displacement curves is studied by applying different normalization schemes and fitting the normalized curves to a hyperbolic model. The hyperbolic model (curve fitting) parameters are generally negatively correlated. Statistics of these hyperbolic model parameters are shown to be comparable to values reported in previous studies. This hyperbolic model is widely used for reliability-based design at the serviceability limit state. Hence, the statistics of the hyperbolic model parameters presented in this study are useful.

Stable Computer Method for Solving Initial Value Problems with Engineering Applications

Engineering and applied mathematics disciplines that involve differential equations in general, and initial value problems in particular, include classical mechanics, thermodynamics, electromagnetism, and the general theory of relativity. A reliable, stable, efficient, and consistent numerical scheme is frequently required for modelling and simulation of a wide range of real-world problems using differential equations. In this study, the tangent slope is assumed to be the contra-harmonic mean, in which the arithmetic mean is used as a correction instead of Euler’s method to improve the efficiency of the improved Euler’s technique for solving ordinary differential equations with initial conditions. The stability, consistency, and efficiency of the system were evaluated, and the conclusions were supported by the presentation of numerical test applications in engineering. According to the stability analysis, the proposed method has a wider stability region than other well-known methods that are currently used in the literature for solving initial-value problems. To validate the rate convergence of the numerical technique, a few initial value problems of both scalar and vector valued types were examined. The proposed method, modified Euler explicit method, and other methods known in the literature have all been used to calculate the absolute maximum error, absolute error at the last grid point of the integration interval under consideration, and computational time in seconds to test the performance. The Lorentz system was used as an example to illustrate the validity of the solution provided by the newly developed method. The method is determined to be more reliable than the commonly existing methods with the same order of convergence, as mentioned in the literature for numerical calculations and visualization of the results produced by all the methods discussed, Mat Lab-R2011b has been used.

Reliability of HCT-based Soil Water Retention Curves

The measurement of SWRCs using HCTs has been the subject of several recent studies. Consequently, there have been several design and experimental procedures developed. However, despite these developments, the accuracy, range and duration of HCT-based measurement is still largely characterized by uncertainties and inconsistencies, thereby, reducing the reliability of the obtained SWRCs. In this work, an experimental program is designed to address these uncertainties. SWRCs of reconstituted London clay were measured using the continuous drying method with evaporation rate control. The obtained SWRCs were analysed based on the maximum suction value recorded by HCTs (smax), the obtained air-entry value (saev), the suction at inflection point (si), the water content at inflection point (wi), and the slope of tangent to inflection point (mi). A percentage uncertainty of ±4% was obtained for the saev and si values. Similarly, percentage uncertainties of ±6% and ±0.5% were obtained respectively for the mi and wi values. These results were further compared with parametric analysis of the reported SWRCs of the same soil in the literature. Given the observed tolerance ranges, cautions must be taken in selecting values for these parameters e.g. as input values in mathematical curve fitting equations for prediction of the entire SWRC, or in unsaturated constitutive modelling, to enhance reliability of the outputs.

Analysis of Factors Influencing Wave Overtopping Discharge from Breakwater Based on an MIV-BP Estimation Model

Aiming at the problem of calculating the overtopping of single-slope breakwaters, a mean impact value-backpropagation (MIV-BP) estimation model for predicting overtopping was established. Experimental data from the Tianjin Research Institute of Water Transport Engineering (TIWTE) were utilized to further enrich the dataset of the CLASH project for single-slope wave overtopping discharge. This paper established a comprehensive prediction model based on an ensemble learning average method combination strategy. There are 10 input parameters in the model, including the offshore effective wave height, average wave period, offshore water depth, toe submergence, toe width, slope tangent, armor rock surface roughness factor, crest height with respect to the static water level, wall height with respect to the static water level, and crest width; the output parameter is the mean overtopping discharge. Subsequently, a comparative analysis was conducted between this estimation model, the Chinese standard formula calculation model, and the European Van der Meer formula calculation model. Compared with the two formulas mentioned above, this estimation model’s coefficient of correlation increased by 0.23 and 0.26, respectively. Finally, a weight evaluation analysis of the 10 main factors affecting overtopping was carried out based on a MIV-BP neural network model. In the analysis, a positive correlation was found for factors, such as the wave height, average wave period, and water depth at the structure toe; a negative correlation was found for factors, such as the slope, crest height with respect to the static water level, wall height with respect to the static water level, and crest width. Overall, the results provide a significant basis and reference for optimizing the design of the wave overtopping control.

A Model-Constrained Tangent Slope Learning Approach for Dynamical Systems

Real-time accurate solutions of large-scale complex dynamical systems are in critical need for control, optimisation, uncertainty quantification, and decision-making in practical engineering and science applications, especially digital twin applications. This paper contributes in this direction a model-constrained tangent slope learning (mcTangent) approach. At the heart of mcTangent is the synergy of several desirable strategies: (i) a tangent slope learning to take advantage of the neural network speed and the time-accurate nature of the method of lines; (ii) a model-constrained approach to encode the neural network tangent slope with the underlying governing equations; (iii) sequential learning strategies to promote long-time stability and accuracy; and (iv) data randomisation approach to implicitly enforce the smoothness of the neural network tangent slope and its likeliness to the truth tangent slope up second order derivatives in order to further enhance the stability and accuracy of mcTangent solutions. Rigorous results are provided to analyse and justify the proposed approach. Several numerical results for transport equation, viscous Burgers equation, and Navier–Stokes equation are presented to study and demonstrate the robustness and long-time accuracy of the proposed mcTangent learning approach.

Validation of the “stage – diffuser” system numerical study and its use for design modernization

The efficiency of a gas turbine largely depends on the aerodynamics and pressure recovery capacity of the diffuser. For reliable numerical simulation of the flow in the diffuser, the model must be validated on the basis of experimental data on the flow structure. An experimental and numerical study of the stage diffuser system was carried out. The results of this investigation are as follows: the area of applicability of the numerical method for assessing the flow in the stage diffuser system was determined; recommendations for preparing a numerical model and transferring boundary conditions from domain to domain were developed; the importance of profiling the last turbine stage to ensure unseparated flow entry into the diffuser is indicated; the influence of the hub length and the geometry of the struts on the losses in the diffuser and its pressure recovery capacity is determined. It is shown that increasing the hub length to certain limits improves the pressure recovery ratio of the diffuser. The smallest thickness of the struts gives the best results; the tangential and axial slope of the struts does not make a significant contribution in the nominal operating mode of the gas turbine.

Optimization Analysis of Two-Factor Continuous Variable between Thread Depth and Pitch of Microimplant under Toque Force.

Microimplant, an anchorage device, is widely applied in clinical orthodontic treatment. Since tooth torque is required to be controlled during orthodontic tooth movement, a novel microimplant needs to be developed to apply better torque force during orthodontic. In this study, the optimal value ranges of thread depth and pitch under toque force were studied for choosing microimplant with relevant value ranges in clinical design from biomechanical perspective. Finite element analysis (FEA) and optimization design technology were used for accessing the optimal value ranges of thread depth and pitch under toque force. Thread depth (D) (0.1 mm to 0.4 mm) and pitch (P) (0.4 mm to 1 mm) were used as continuous variables, with the other parameters as constant, and the optimal value ranges were obtained by analyzing the tangent slope and sensitivity of the response curve. When a torque force of 6 Nmm was applied on the microimplant, the maximum equivalent stress (Max EQV) of cortical bone and maximum displacements (Max DM) of microimplant were analysis indexes. When 0.55 mm ≤ P ≤ 1 mm, the Max EQV of cortical bone was relatively smaller with less variation range. When 0.1 mm ≤ D ≤ 0.35 mm, the Max DM of microimplant was relatively smaller with less variation range. So in conclusion, the initial stability of microimplants with pitch 0.55 mm ≤ P ≤ 1 mm and thread depth 0.1 mm ≤ D ≤ 0.35 mm was better with the torque force applied.

Mathematics Students’ Characteristics of Basic Mental Models of the Derivative

The concept of derivative is characterised with reference to four basic mental models. These are described as theoretical constructs based on theoretical considerations. The four basic mental models—local rate of change, tangent slope, local linearity and amplification factor—are not only quantified empirically but are also validated. To this end, a test instrument for measuring students’ characteristics of basic mental models is presented and analysed regarding quality criteria.Mathematics students (n = 266) were tested with this instrument. The test results show that the four basic mental models of the derivative can be reconstructed among the students with different characteristics. The tangent slope has the highest agreement values across all tasks. The agreement on explanations based on the basic mental model of rate of change is not as strongly established among students as one would expect due to framework settings in the school system by means of curricula and educational standards. The basic mental model of local linearity plays a rather subordinate role. The amplification factor achieves the lowest agreement values. In addition, cluster analysis was conducted to identify different subgroups of the student population. Moreover, the test results can be attributed to characteristics of the task types as well as to the students’ previous experiences from mathematics classes by means of qualitative interpretation. These and other results of students’ basic mental models of the derivative are presented and discussed in detail.

Study on volume and pressure of scroll compressor constructed from involute of variable radii circle with line-arcs modification

The working chamber volume and pressure constructed from involute of variable radii circle with line-arcs modification are calculated accurately by equivalent translation area method avoiding complicated piece-wise integration and Green’s theorem. The influence of modified distance is divided into two benchmarks to investigate because the interval length of the discharge process is always 2 π. The increase of modified distance will decrease the working chamber volume before the discharge process and increase the volume in the discharge process. Afterward, the volume change rate is proposed to study the tangent slope of volume curve, which is also meaningful for discussing the working chamber pressure. Finally, the working chamber pressure is obtained by the working chamber volume. The increase of modified angle and distance will increase the working chamber pressure in the same orbiting angle before the discharge process, but decrease the discharge pressure and advance the discharge process. Furthermore, the influences of modified parameters on the working chamber pressure in the discharge process are qualitatively studied. The increase of modified parameters will decrease the working chamber pressure in the discharge process.