Law Coefficient Research Articles

Development of a cyclic semi-circular bending test protocol to characterize fatigue cracking of asphalt mixture at intermediate temperature

The Semi-Circular Bending (SCB) test has been traditionally conducted in a monotonic loading and displacement-controlled mode at intermediate temperature to assess the fatigue crack resistance of asphalt mixtures. However, fatigue damage is essentially deterioration in material integrity as a result of repeated loading. The SCB monotonic loading does not realistically reflect the traffic loading repetition. This may have limitation on mechanism of the fatigue cracking in asphalt mixture. This study aims to develop a cyclic SCB test protocol to characterize the fatigue cracking of asphalt mixtures. Digital Image Correlation (DIC) was utilized to identify crack length associated with the number of loading cycles applied. A full factorial design was conducted for the optimization of testing parameters of the cyclic SCB test, including three levels of notch depth and loading frequency. Two indicators including the number of cycles to failure and Paris’ Law coefficients were used to characterize the fatigue cracking resistance of asphalt mixture. The proposed test protocol of cyclic SCB was validated by three asphalt mixtures of good, medium, and poor cracking performance. The critical strain energy release rate Jc of three mixtures is also measured by the monotonic SCB test for studying the relationship between Jc and Paris’ Law coefficients. The results indicate that Paris’ Law coefficients have relatively low variance compared to the number of cycles to failure and are independent of notch depth and loading frequency. The optimal testing parameter combination of 25 mm notch depth and 10 Hz loading frequency was recommended in perspective of test variance and test practicability. The Paris Law coefficient n ranking was consistent with the one of fatigue cracking resistance of asphalt mixtures evaluated.

Finite Element Analysis of Functionally Graded Sandwich Plates

Computational methods become a necessity at places where the fields of testing as well as lab model testing poses problems or situations demanding large number of test results at low cost. The accuracy of the computational model can be adjusted by convergence study. The present study uses finite element method for finding static behaviour of sandwich plates having functionally graded core. Power law is employed for quantification of the material properties and zig-zag theory is utilized for the analysis. Hamilton’s theorem is exploited for deriving the equation which is resolved by FEM by taking nine-node C-0 iso-parametric FE having 11 DOF/node. Aspect ratio, power law coefficient and skewness of plate are used as variables to study the bending response of the plate. Present results are found to be consistent with the published ones and new results are also presented.

Investigation of entropy generation in power law fluid-filled bulging enclosures: effects of flow and heat transfer

This paper presents a complete investigation into the phenomenon of dual convection flow within a bulging enclosure along with non-Newtonian power-law fluids and employs the Galerkin finite element method for simulation. The main objective is to study the heat and mass transfer and entropy generation within the enclosure. Various factors, such as the Rayleigh number, power law coefficient, Lewis number, and effects of magnetic inclination are evaluated for their influence on flow dynamics and heat distribution. The study also investigates the relationship between these parameters and entropy generation, providing insights into the irreversible processes within the system. A comparative analysis of averaged Nusselt and Sherwood coefficients reveals distinct thermal and fluidic behaviours across varying power-law indices, emphasizing differences between shear thickening, shear thinning, and Newtonian fluid behaviours. The findings provide valuable insights into non-Newtonian power-law fluids in complex flows, enhancing our understanding of flow and heat transfer in bulging enclosures.

Evaluation of Paris law-based approach on asphalt mixture reflective cracking performance modeling

Reflective cracking is a major distress for asphalt pavement overlays. To model asphalt mixture reflective cracking performance, various models and tests have been developed in the past. Among the different methods, Paris law combined with the overlay test has been one of the most popular approaches to assess the reflective cracking resistance of the asphalt mixtures. This study evaluated three variants of ΔK-based Paris law models, specifically Methods A, B, and C, as well as one ΔJR-based Paris law model. The evaluation was conducted using overlay test data from two mixes at three different temperatures. For ΔK-based Paris law, three different models consistently demonstrate that asphalt mixtures have better reflective cracking resistance as temperature increases from 4 °C to 18 °C. However, they diverge in terms of mixture rankings. Specifically, when using the Paris law coefficients to predict the crack growth, Method A matches exactly with the experimental observation since it is a self-validation, while Methods B and C display different crack growth patterns. This may be attributed to the fact that Method A was originally developed based on the overlay test while Methods B and C were calibrated based on the field performance. For ΔJR-based Paris law, inconclusive results have been obtained and the cause of such results are explained on the basis of differences between the experimental details of the present study and the one that originally developed the approach.

Effects of Fatigue Parameters on Fatigue Crack Growth Rate of Pipe Steels and Girth Weld

Abstract Oil and gas pipeline steels and welds are subjected to a wide variety of cyclic loadings: internal pressure variation, pulsation of gas pressure resulting from the cyclic operation of a reciprocating compressor at a gas compressor station, internal flow-induced vibration resulting from the turbulent flow within the pipe, vortex-induced vibration of a free-spanning section exposed to air (wind) for aboveground pipelines or water for water-crossing pipelines, and cyclic thermal stresses developed by significant changes in temperature due to seasonal changes or changes in operating temperatures. These cyclic loadings are very variable and complex. Considering the fatigue situations, a better understanding of the effects of fatigue test parameters on fatigue behaviors of pipeline steels and welds is required. Hence, in this study, the influences of fatigue test parameters on the Paris law coefficients were studied for pipeline steels and welds. It was analyzed for pipe steels of X65∼X100 and a girth weld of X70. Influences of material strength, crack orientation relative to the pipe axis, and frequency in the range of 1∼30 Hz were insignificant. It was found that the coefficients a1 and b2 of the m-ln(C) relationships linearly relied on the load ratio. The constants (α1, β1, α2, and β2) of these linear relationships between R-ratio and a1 (and b2) were determined for pipe steels.

Scintillation characteristics of the EJ-299-02H scintillator.

A study of the dead layer thickness and quenching factor of a plastic scintillator for use in ultracold neutron (UCN) experiments is described. Alpha spectroscopy was used to determine the thickness of a thin surface dead layer to be 630 ± 110nm. The relative light outputs from the decay of 241Am and Compton scattering of electrons were used to extract Birks' law coefficient, yielding a kB value of 0.087 ± 0.003 mm/MeV, consistent with some previous reports for other polystyrene-based scintillators. The results from these measurements are incorporated into the simulation to show that an energy threshold of (∼9keV) can be achieved for the UCNProBe experiment. This low threshold enables high beta particle detection efficiency and the indirect measurement of UCN. The ability to make the scintillator deuterated, accompanied by its relatively thin dead layer, gives rise to unique applications in a wide range of UCN experiments, where it can be used to trap UCN and detect charged particles in situ.

Initiation and growth of fatigue cracks in sheets with U-shaped notches in the first and mixed modes of fracture

Initiation and growth of fatigue cracks in sheets with U-shaped notches in the first and mixed modes of fracture

Determination of Henry's law coefficient of oxygen in LAB for JUNO

The Jiangmen Underground Neutrino Observatory (JUNO) requires that the detector use liquid scintillator with an extremely low background to achieve the desired measurement accuracy of neutrino mixing parameters. In addition, the production process of the liquid scintillator must avoid radon gas contamination caused by equipment leakage. Direct measurement of radon gas in liquid scintillator is an option for system leak detection. However, considering the low percentage of radon gas and high percentage of oxygen in air, the measurement of oxygen in liquid scintillator will have higher sensitivity. Based on Henry's law and the measuring principle of a dissolved oxygen meter, an experimental device is designed to measure Henry's law coefficient and calibrate the dissolved oxygen meter. Henry's law coefficient of oxygen in linear alkylbenzene (LAB) at 23.6 °C derived from an experimental measurement is 2.09 × 107 ± 2.54 × 106 Pa·L·mol-1. The feasibility of using a dissolved oxygen meter to measure the dissolved oxygen content in LAB is verified by calibrating the dissolved oxygen meter.

Experimental Study on Permeability and Gas Production Characteristics of Montmorillonite Hydrate Sediments Considering the Effective Stress and Gas Slippage Effect

Summary Gas permeability in hydrate reservoirs is the decisive parameter in determining the gas production efficiency and gas production of hydrate. In the South China Sea (SCS), the gas flow in tight natural gas hydrate (NGH) silty clay reservoirs is significantly affected by the gas slippage effect and the effective stress (ES) of overlying rock. To improve the effectiveness of hydrate exploitation, it is necessary to understand the influence of gas slippage in hydrate reservoirs on the permeability evolution law. For this paper, the gas permeability characteristics and methane production of hydrate montmorillonite sediments were studied at different pore pressures and ESs. Experimental data revealed that the gas permeability of montmorillonite samples before methane hydrate (MH) formation is seriously affected by the Klinkenberg effect. The gas permeability of montmorillonite sediments before hydrate formation is generally smaller than that after hydrate formation, and the gas slippage effect in the sediments after hydrate formation is weaker than that before hydrate formation. With the change in ES, the intrinsic permeability of sediment has a power law relationship with the simple ES. The ES law coefficient n was determined using the response surface method to eliminate the influence of gas slip on gas permeability. As pore pressure decreases and MH decomposes, montmorillonite swelling seriously affects gas permeability. However, the gas slippage effect has a good compensation effect on the permeability of montmorillonite sediments after MH decomposition under low pore pressure. The multistage depressurization-producing process of MH in montmorillonite sediments is mainly 3 MPa depressurization-producing stage and 2 MPa depressurization-producing stage. In this paper, the influence mechanism of gas slippage effect of hydrate reservoir is studied, which is conducive to improving the prediction accuracy of gas content in the process of hydrate exploitation and exploring the best pressure reduction method to increase the gas production of hydrate in the process of exploitation.

A semi-empirical model of the calendar ageing of lithium-ion batteries aimed at automotive and deep-space applications

Lithium-ion batteries are highly affected by calendar ageing effects, which can lead to capacity loss even when the battery is not used at all. The current literature proposes plenty of semi-empirical models to predict the calendar ageing of the lithium-ion batteries, which are mostly based on Arrhenius functions for temperature dependency, exponential models for state of charge dependency and power laws for time dependency. Those models are easy to calibrate, and they provide a sufficiently precise prediction of capacity loss over time. However, it might be difficult to find a physical meaning to the parameters determined in these models, due to their lumped nature and the optimization process used. Therefore, in this work a semi-empirical model able to predict the capacity degradation over time with physically meaningful parameters is proposed. The dependency on temperature is considered by a pre-exponential factor whereas the dependency on state of charge is considered by a power law coefficient. A two-step constrained optimization process is considered to calibrate the model parameters. The model allows to predict the capacity loss over a wide range of different temperature and state of charge conditions, and it is calibrated for 4 different cell chemistries: LMO-NMC, LFP, NCA, and NMC. It was found that the worst storing condition is given by the highest temperature and state of charge conditions. The capacity degradation is provided over a period of 50 years. Two end-of-life conditions were analyzed: a loss of capacity of 20 % as representative of an end-of-life condition for automotive applications, and a loss of capacity of 50 % as an end-of-life condition for deep-space applications. In both cases, it was observed that NMC provided the best performance (the slowest ageing over time) for storing temperatures below 15 °C and storing state of charge below 10 %, whereas for temperatures higher than 15 °C and state of charge higher than 10 %, the LFP chemistry resulted to be the most longevous.

Modeling Henry's law and phase separations of water-NaCl-organic mixtures with solvation and ion-pairing.

Empirical measurements of solution vapor pressure of ternary acetonitrile (MeCN) H2O-NaCl-MeCN mixtures were recorded, with NaCl concentrations ranging from zero to the saturation limit, and MeCN concentrations ranging from zero to an absolute mole fraction of 0.64. After accounting for speciation, the variability of the Henry's law coefficient at vapor-liquid equilibrium (VLE) of MeCN ternary mixtures decreased from 107% to 5.1%. Solute speciation was modeled using a mass action solution model that incorporates solute solvation and ion-pairing phenomena. Two empirically determined equilibrium constants corresponding to solute dissociation and ion pairing were utilized for each solute. When speciation effects were considered, the solid-liquid equilibrium of H2O-NaCl-MeCN mixtures appear to be governed by a simple saturation equilibrium constant that is consistent with the binary H2O-NaCl saturation coefficient. Further, our results indicate that the precipitation of NaCl in the MeCN ternary mixtures was not governed by changes in the dielectric constant. Our model indicates that the compositions of the salt-induced liquid-liquid equilibrium (LLE) boundary of the H2O-NaCl-MeCN mixture correspond to the binary plateau activity of MeCN, a range of concentrations over which the activity remains largely invariant in the binary water-MeCN system. Broader comparisons with other ternary miscible organic solvent (MOS) mixtures suggest that salt-induced liquid-liquid equilibrium exists if: (1) the solution displays a positive deviation from the ideal limits governed by Raoult's law; and (2) the minimum of the mixing free energy profile for the binary water-MOS system is organic-rich. This work is one of the first applications of speciation-based solution models to a ternary system, and the first that includes an organic solute.

The Signature of Climate in Fluvial Suspended Sediment Records

AbstractArid regions are often characterized by exceptionally high rates of fluvial sediment transport, but the processes responsible for this apparent connection between climate and sediment transport remain unclear. We examined decades of continuous flow records and suspended sediment concentrations from 71 rivers across the United States by comparing the suspended sediment rating curve behavior, quantified using power law coefficients and exponents, to an aridity index. Results indicate that higher aridity correlates with both greater overall suspended sediment concentration and lower sensitivity of concentration to changes in discharge, demonstrating that rivers in arid locations on average have greater suspended sediment transport efficiency across most discharges, and achieve high transport rates at a relatively lower discharge than rivers in temperate climates. Furthermore, based on additional analyses of the Normalized Difference Vegetation Index, specific suspended sediment yield, and a hydrograph flashiness index, we attribute the relationships between sediment transport and climate primarily to differences in vegetation density, precipitation, and runoff, variables that all influence both sediment supply and riverbed grain sorting. Finally, we note that the observed contrasts in sediment transport behavior likely represent climate‐driven differences in the magnitude and frequency of sediment supply rather than annual suspended sediment load, which does not depend significantly on climate. This study highlights a critical connection between multiple interrelated climatic factors and sediment transport, an important finding for future hazard mitigation in a changing climate with rapidly shifting vegetation patterns and hydrology.

Determining Which Sine Wave Frequencies Correspond to Signal and Which Correspond to Noise in Eye-Tracking Time-Series.

The Fourier theorem states that any time-series can be decomposed into a set of sinusoidal frequencies, each with its own phase and amplitude. The literature suggests that some frequencies are important to reproduce key qualities of eye-movements ("signal") and some of frequencies are not important ("noise"). To investigate what is signal and what is noise, we analyzed our dataset in three ways: (1) visual inspection of plots of saccade, microsaccade and smooth pursuit exemplars; (2) analysis of the percentage of variance accounted for (PVAF) in 1,033 unfiltered saccade trajectories by each frequency band; (3) analyzing the main sequence relationship between saccade peak velocity and amplitude, based on a power law fit. Visual inspection suggested that frequencies up to 75 Hz are required to represent microsaccades. Our PVAF analysis indicated that signals in the 0-25 Hz band account for nearly 100% of the variance in saccade trajectories. Power law coefficients (a, b) return to unfiltered levels for signals low-pass filtered at 75 Hz or higher. We conclude that to maintain eyemovement signal and reduce noise, a cutoff frequency of 75 Hz is appropriate. We explain why, given this finding, a minimum sampling rate of 750 Hz is suggested.

Thermodynamic and economic evaluation of a non-cascaded dual-temperature compression–absorption–resorption refrigeration system

Thermal processes in many industries require simultaneous cooling at multiple temperatures, highlighting the need for an efficient and cost-effective dual-temperature refrigeration system. This study proposes two novel non-cascaded dual-temperature ejector-assisted compression–absorption–resorption refrigeration cycles (ECARC) to deliver simultaneous refrigeration effects at -5°C and 7°C. These cycles are classified based on the compressor staging with an ejector as ECARC-1 and ECARC-2. The performance simulations of the proposed cycles were carried out at the design conditions and a detailed parametric study was performed to determine the influence of the key operating parameters on the first and the second law coefficients of performance. The proposed novel cycles are more efficient and utilise heat more effectively by consuming up to 60 % less electricity than the conventional multi-evaporator compression refrigeration system, for the same operating conditions and refrigeration capacity. These cycles are also more cost effective with a reduction in their unit production cooling cost by up to 50 % and 25.5% as compared with the state-of-the-art double-effect absorption refrigeration system and the multi-evaporator compression refrigeration system, respectively. Thus, the proposed cycles show excellent thermal and economic advantages for a potential dual-temperature refrigeration system, and the development of these systems contribute towards the decarbonisation of the industrial cooling and heating sector.

Data reduction methods in the fatigue analysis of the Double Cantilever Beam, Part II: Evaluation and case studies

The characterization of high-cycle crack growth properties of bonded joints is an important research field with a direct impact on the practical engineering and designing of structures. Regardless, to date, no standard exists to evaluate the Mode-I fatigue properties of adhesively bonded joints nor for delamination of composite structures. In part II of this work, virtual fatigue tests are used to explore several reduction schemes that have been employed by researchers to characterize the Paris law coefficients. The results show that different reduction methods can yield different Paris curves when the measurement of the actual crack size is used, and the discrepancy among the methods increases as the global stiffness of the joint increases. However, when the concept of equivalent crack is used, the performance of most reduction methods increases significantly. The results show that the use of the equivalent crack concept combined with an appropriate reduction method can yield very accurate results, sparing cumbersome crack length measurements altogether.

Development of word count data corpus for Hindi and Marathi literature

India has a huge diversity of languages, and Hindi and Marathi are the most spoken languages in the northern and western parts of India. Hindi and Marathi have more than 528 million and 83 million speakers, respectively. The paper describes the development of the Hindi Word Corpus (Hindi WordCorp) and the Marathi Word Corpus (Marathi WordCorp), reporting the frequency of single words (1-gram) used in written texts of the respective languages using the bag-of-words model (BoW). The word frequencies are provided for eleven decades (pre-1920, 1920 to 2020). These texts include books (fiction, non-fiction, history, autobiographies, etc.) and magazines. Academic and reference books were not used. The Hindi WordCorp and Marathi WordCorp used 640 and 712 texts, respectively. An analysis was employed to check whether the texts used were enough to stabilize the rank-order of the total frequencies of the words. Zipf's and Heaps’ law coefficients indicated the sufficiency of the texts. Researchers in various areas like linguistics, social sciences, text mining, machine learning, etc., can use the dataset to answer research questions about language and culture. Some demonstrative examples are provided for using the datasets in the two languages. The dataset is made available on an open data repository. The paper is an account of dataset creation for Hindi and Marathi WordCorp. Hence, no empirical results or conclusions are made based on the data created. A WebApp named Indian Languages Word Corpus (ILWC) has been developed for users. Future directions for text mining and language models are discussed.

Tracking control of nonlinear systems actuated by saturated oscillatory force generator

This research has been devoted to the construction of a permanent-stable algorithm for tracking control of a nonlinear 1-degree of freedom (DOF) mechanical system affected by a second-order vibratory constrained actuator. The dynamics of the actuator is involved in governing equation of the mechanical system, and using the two-step Adams-Bashforth and Adams-Moulton methods, the resultant continuous-time model is formulated in the discrete-time domain. The discrete-time model of the whole system is then employed in a discrete-time power reaching law-based controller architecture. Using the reaching law strategy and considering the saturation boundaries of the actuation system, various available bounds of position and velocity control signals can be determined with respect to the reaching law coefficients. Then, special optimization algorithms are employed to determine the optimal value of position and velocity power reaching law coefficients as well as the optimally modified trajectory references. The position and velocity control commands resulting from the concept of optimal trajectory reference, along with the optimal reaching law coefficient, ensure the permanent-stable tracking control of both position and velocity modes regarding the actuation constraint. In the next step, another concept, namely the optimal combined position-velocity controller, is taken into account, which is a Gaussian-weighted average of the position and velocity control commands to form the main control command of the proposed controller. Consequently, the designed controller will be a permanent-stable control approach that never violates the actuation constraint. Finally, numerical simulations are conducted to evaluate the performance of the proposed method for two types of desired inputs, including piecewise-step and harmonic trajectories. The results suggest the proposed controller efficiency in satisfying pre-determined characteristics.

Droplet Evaporation Process of a Fluorobenzene + n-Octane + Polystyrene Mixture.

The vapor-liquid equilibrium of the fluorobenzene-polystyrene binary polymer solution at 303.15 K was measured using a static pressure device. The vapor-liquid equilibrium of the fluorobenzene-n-octane-polystyrene ternary solution in a partial concentration range under normal pressure was determined using an improved Othmer equilibrium still, in which the octane concentration was low. Three activity coefficient models, poly-NRTL, UNIQUAC, and M-UNIQUAC-LBY, were utilized to correlate the experimental data of binary and ternary solutions, and the component activities of the fluorobenzene-n-octane-polystyrene solution at 303.15 K were predicted. A mathematical model based on the Stefan flow was developed to simulate the evaporation process of composite spherical droplets. The activity predicted by the activity coefficient model was used for numerical simulations, and compared with simulations using the activity following Raoult's law. The comparative analysis revealed that simulations based on Raoult's law and activity coefficient models yielded similar results when the mass fraction of fluorobenzene exceeded 0.6. However, in the later stages of evaporation, the calculations based on Raoult's law predicted a 10% shorter drying time for fluorobenzene. The activity coefficient models provided a better approximation and exhibited similar droplet diameter shrinking behaviors to the actual evaporation process.

Non-destructive estimation of conductive network constructed by 1D fillers in polymer composites via small angel X-ray scattering

Efficient and non-destructive estimation of conductive network in conductive polymer composites is now becoming an urgent issue than ever owing to the rapid rise of modern electronic industry. Nevertheless, traditional observation and estimation method inevitably cause damage and distortion to sample, demanding urgent development of a non-destructive fidelity detection methodology. In this study, the degree of network formation of carbon nano-fibers in polymer matrix was calculated based on small-angle X-ray diffraction (SAXS). The degree of fiber network construction based on the power law coefficient (A) has been proved to be valid and effective in comparison with other testing methods. Moreover, a mathematical model was established to predict the electrical conductivity of the conductive polymer composite. This study not only solves the problem of non-destructive testing of fiber network construction, but also provides theoretical guidance for the design of conductive polymer composites.

Continuous Control Set Model Predictive Control for the optimal current control of Permanent Magnet Synchronous Motors

This paper proposes a Continuous Control Set Model Predictive Control (CCS-MPC) for controlling the internal loop of Permanent Magnet Synchronous Motors (PMSMs). The proposed controller has the ability to track the references with zero steady-state error and provides a fast dynamic response. The performance of the internal loop affects the motor currents and torque ripples. The obtained Total Harmonic Distortion (THD) with the same switching frequency is much lower than Finite Control Set Model Predictive Control (FCS-MPC), which is mostly used in controlling the internal loop.The control parameters are selected with a sensitivity analysis to provide a reasonable phase margin and gain margin. Furthermore, to overcome the nonlinearity of the model, the controller is designed beforehand for different speed setpoints, and the control law coefficients are saved in a look-up table. Then, in each sampling time, the speed is measured, the coefficient is interpolated, and the control law is updated.All the optimization of the proposed controller is performed offline and the output is some simple expressions thus the control law is not computationally expensive. In addition, the controller output is voltage in the continuous space that is applied to the inverter by a standard algorithm and works with a fixed switching frequency.The simulation and experimental results are presented to validate the proposed controller’s appealing features.