Parameters Of Equation Research Articles

Laboratory investigation and prediction of permeability of fresh to five-year-old municipal solid wastes of low and high food contents

The permeability of municipal solid wastes (MSWs) is important for the design and operation of landfills. This study presented the experimental investigation of the permeability of low food content- (LF-) and high food content- (HF-) MSWs prepared in laboratory-scale bioreactors for up to 5 years. The permeability of MSWs with diverse degrees of decomposition (DOBs), void ratios, and permeation liquids was measured (288 tests). The measured permeability was compared to that predicted from the (modified) Kozeny-Carman (K-C) equations in four different forms. The results indicated that the permeability of both LF- and HF-MSWs decreased significantly (p < 0.05) with decomposition under a given void ratio. The predicted permeability using the original K-C equation fitted well with that of fresh MSWs. The permeability of decomposed MSWs was closer to the predicted results using the modified K-C equation with the effective void ratio. This can be attributed to the increase in the fine fractions due to degradation. The reduction in the effective voids was more significant with HF-MSWs. The parameters required in the (modified) K-C equations showed a good correlation with DOB and effective particle size (d10). The predicted permeability based on the relationship between DOB (or d10) and equation parameters was within 3 times the difference compared to the measured values. The above results indicated that the modified K-C equation can be adopted to predict the permeability of fresh and degraded MSWs while more field-scale experiments should be conducted to further evaluate its feasibility.

Assessing local stresses in scanned fillet weld geometry using bagged decision trees

This study addresses the limitations of current parametric equations and artificial neural networks (ANNs) in accurately predicting the stress concentration factor (SCF) of fillet welded joints stemming from the simplification of their real weld profiles. To improve the accuracy, this study introduces bagged trees for estimating local stresses. The dataset used as the foundation for training the bagged trees is extracted from the actual weld geometry of T-shaped joints. It is created via a digitalization process involving the extraction of actual geometric parameters from the joints, which are transformed into finite element models (FEMs). These models are then employed to determine the ratio between the simulated sectional stress and the nominal stress (σsec/∆σnom) under an axial loading condition. A comprehensive comparison is carried out among existing parametric equations, ANNs, and the proposed bagged trees. The results emphasize the inadequacy of idealized geometry models in accurately determining local stresses for real weld profiles. In contrast, bagged trees are a promising method for accurately computing sectional weld stresses (σsec) within real weld geometry.

An artificial neural network model for determining stress concentration factors for fatigue design of tubular T-joint under compressive loads

PurposeThe stress concentration factor (SCF) is commonly utilized to assess the fatigue life of a tubular T-joint in offshore structures. Parametric equations derived from experimental testing and finite element analysis (FEA) are utilized to estimate the SCF efficiently. The mathematical equations provide the SCF at the crown and saddle of tubular T-joints for various load scenarios. Offshore structures are subjected to a wide range of stresses from all directions, and the hotspot stress might occur anywhere along the brace. It is critical to incorporate stress distribution since using the single-point SCF equation can lead to inaccurate hotspot stress and fatigue life estimates. As far as we know, there are no equations available to determine the SCF around the axis of the brace.Design/methodology/approachA mathematical model based on the training weights and biases of artificial neural networks (ANNs) is presented to predict SCF. 625 FEA simulations were conducted to obtain SCF data to train the ANN.FindingsUsing real data, this ANN was used to create mathematical formulas for determining the SCF. The equations can calculate the SCF with a percentage error of less than 6%.Practical implicationsEngineers in practice can use the equations to compute the hotspot stress precisely and rapidly, thereby minimizing risks linked to fatigue failure of offshore structures and assuring their longevity and reliability. Our research contributes to enhancing the safety and reliability of offshore structures by facilitating more precise assessments of stress distribution.Originality/valuePrecisely determining the SCF for the fatigue life of offshore structures reduces the potential hazards associated with fatigue failure, thereby guaranteeing their longevity and reliability. The present study offers a systematic approach for using FEA and ANN to calculate the stress distribution along the weld toe and the SCF in T-joints since ANNs are better at approximating complex phenomena than standard data fitting techniques. Once a database of parametric equations is available, it can be used to rapidly approximate the SCF, unlike experimentation, which is costly and FEA, which is time consuming.

New Tsallis holographic dark energy with Granda–Oliveros as IR-cutoff

In the current study, a theoretical model for non-interacting new Tsallis holographic dark energy is constructed using the Granda–Oliveros as the IR cutoff with specified scale factor [Formula: see text]. The time-dependent deceleration parameter, with appropriate assumptions, yields this scale factor. The features of the deceleration parameter, equation of state parameter, density parameter, and jerk parameter are then investigated for this model. According to our findings, the cosmos has a normal thermal history, dark matter and dark energy eras occurring one after the other until dark energy eventually takes over entirely in the far future. Additionally, the evolution of the potential and pressure to indicate the universe’s accelerated expansion by using our model are studied. We investigate the evolution trajectory of statefinder parameters, which is consistent with ΛCDM model.

CURLING – I. The influence of point-like image approximation on the outcomes of cluster strong lens modelling

ABSTRACT Cluster-scale strong lensing is a powerful tool for exploring the properties of dark matter and constraining cosmological models. However, due to the complex parameter space, pixelized strong lens modelling in galaxy clusters is computationally expensive, leading to the point-source approximation of strongly lensed extended images, potentially introducing systematic biases. Herein, as the first paper of the ClUsteR strong Lens modelIng for the Next-Generation observations (CURLING) program, we use lensing ray-tracing simulations to quantify the biases and uncertainties arising from the point-like image approximation for JWST-like observations. Our results indicate that the approximation works well for reconstructing the total cluster mass distribution, but can bias the magnification measurements near critical curves and the constraints on the cosmological parameters, the total matter density of the universe Ωm, and dark energy equation of state parameter w. To mitigate the biases, we propose incorporating the extended surface brightness distribution of lensed sources into the modelling. This approach reduces the bias in magnification from 46.2 per cent to 0.09 per cent for μ ∼ 1000. Furthermore, the median values of cosmological parameters align more closely with the fiducial model. In addition to the improved accuracy, we also demonstrate that the constraining power can be substantially enhanced. In conclusion, it is necessary to model cluster-scale strong lenses with pixelized multiple images, especially for estimating the intrinsic luminosity of highly magnified sources and accurate cosmography in the era of high-precision observations.

Isotropic compact stars admitting Heintzmann solution in Rastall gravity

This paper is devoted to observe the physical attributes of static spherically symmetric isotropic compact stellar candidates in the context of Rastall theory of gravity. In order to inspect the structural composition of compact objects, the Heintzmann ansatz is taken into account. The unknown parameters associated with Heintzmann ansatz are evaluated through matching conditions with derived values of radii and masses of some specific star models. The consistency of the adopted ansatz is analyzed via graphical interpretation of matter variables, equation of state parameter, mass components, energy constraints, causality condition, stellar equation and adiabatic index for several choices of Rastall parameter. It is observed that the stars under consideration manifest stable structures corresponding to Heintzmann ansatz in this framework. Moreover, it is shown that for vanishing Rastall coupling parameter, the standard outcomes of general relativity can be retrieved.

A numerical investigation into the equivalent parameters of a compressible soil treated by stone columns

A series of triaxial test simulations are adopted to estimate the equivalent strength parameters for compressible soil samples reinforced with stone columns. The simulations utilize the finite difference code, Fast Lagrangian Analysis of Continua in three dimensions FLAC3D. An elasto-plastic model is applied to utilize a Mohr-Coulomb yield criterion. The equivalent strength parameters are estimated using newly proposed formulas for geo-composite materials. The researchers compare the obtained results to the analytical formulas proposed in the literature. Additionally, the equivalent parameters are used in equivalent area models. This study investigates the effect of the replacement area ratio. This study offers two applications. Firstly, it evaluates the safety factor of embankments constructed on compressible soil improved with stone columns. Secondly, it estimates the bearing capacity of strip footings on compressible soil treated with stone columns. In all applications, both individual column and equivalent area models are considered. The proposed equations for the equivalent elastic parameters (E, ν) and the mechanical properties, equivalent cohesion, and internal frictional angle (c and φ) give results that agree with the solutions reported in the existing literature.

A Reduced Kinetics Model for the Oxidation of Transcritical/Supercritical Gasoline Surrogate/Ethanol Mixtures Using Real Gas State Equations

ABSTRACT Efforts to combat the harmful effects of vehicle emissions on our environment and health include exhaust emissions and fuel efficiency regulations. One promising solution is direct fuel injection in supercritical conditions, where the fuel mixture is above critical temperature and pressure. This study presents a reduced kinetics mechanism (129 species and 1015 reactions) utilizing real gas equations to simulate the combustion of supercritical/transcritical gasoline surrogate/ethanol blends. It was developed by combining two reduced models – a Toluene reference fuel (TRF) with a Diisobutylene (DIB) and an ethanol model – and validated through simulations of ignition delay time (IDT). The Arrhenius parameters of key reactions for each fuel component were modified to improve accuracy. An adjusted Redlich-Kwong cubic state equation was employed to segregate each surrogate mixture tested as supercritical, transcritical, or subcritical. The new mechanism was then validated against experimental results using high-pressure conditions and the cubic Peng-Robinson and Redlich-Kwong equation of state parameters. Critical properties of each species were obtained through Joback’s Group Method and the Ambrose-Walton vapor pressure equation. The TRF/DIB/E mechanism results were consistent with shock tube experimental data at high pressure, indicating a potential for modeling combustion in ultra-high pressure direct injection engines.

Characterization of torsion plate energy-absorbing members and multi-objective optimization of mechanical properties

In order to prevent damage to the support equipment caused by rock burst, a torsion plate energy absorption member is designed to be used with hydraulic columns. Explicit dynamic simulation is used and compared with the tests. The equations of structural parameters to the mean value of the reaction force (Fmean), specific energy absorption (SEA), and mean squared deviation (σ) are constructed based on the response surface method. The structural parameters are optimized using MOPSO. The results indicate that the torsion plate exhibits excellent energy absorption characteristics. The error rate of the simulation compared to the test is less than 5%, indicating a high level of simulation accuracy. All three sets of response fitted equations have R2 above 0.97, indicating a good fit. The three evaluation indexes demonstrate a trend of increasing then decreasing as the torsion angle increases. The wall thickness is positively correlated with the influence of each parameter index, while the effect of fillet radius is reversed. The maximum relative error of the predicted value is 9.50%. After optimization, the Fmean is effectively increased by more than 78%, the SEA is increased by more than 24.72%. The σ is increased by 8.31%, the optimization effect is remarkable.

A method for predicting the yield strength of AZ31 magnesium alloy bars processed by ambient extrusion

Magnesium alloys have strong mechanical properties anisotropy due to their universal basal texture. This study develops a novel method for predicting the yield strength of AZ31 extruded bars with basal fiber texture. From series tensile and compressive tests on ambient extruded bars with different loading direction, the relationship between yield strength, loading direction and extrusion strain was summarized. With varying loading direction, tensile and compressive yield strength can be fitted by linear and nonlinear equations in a strength coordinate system where yield strength can be calculated on different loading direction. Furthermore, parameters of yield strength equations can also be fitted by different equations. Then, from the parameter equations to yield strength equations, tensile and compressive yield strength can be predicted on different loading direction for extruded bars with different extrusion strain.

Impact of [formula omitted] theory on the geometry of charged stellar objects

The main objective of this article is to study the viable charged compact stellar structures in f(R,φ,χ) theory, where R, φ and χ denote the Ricci scalar, scalar field and kinetic term, respectively. For this purpose, a static spherical metric with anisotropic matter configuration is considered to analyze the compact stellar structures. We consider a particular model of this modified theory to formulate the explicit expressions of energy density and pressure components that govern the relationship between matter and geometry. The unknown constants in the Finch–Skea solutions are determined by the smooth matching of interior and exterior spacetimes to analyze the configuration of the proposed stellar structures. Physical parameters such as matter variables, energy bounds and equation of state parameters are analyzed to examine the viability of the considered stellar objects. Further, we use sound speed and adiabatic index methods to examine the stability of the compact objects. The rigorous analysis and satisfaction of necessary conditions lead to the conclusion that the stellar objects studied in this framework are viable and stable in the presence of charge.

Enhancing fatigue reliability prediction of offshore wind turbine jacket joints through individual uncertainties for each degree of freedom of stress concentration factor

This paper presents the fatigue reliability prediction for welded planar tubular joints of offshore fixed jacket support structures. A coupled model is employed to calculate the dynamic response of the jacket support structure under wind and wave loads. Stress concentration factors (SCFs) are evaluated using Efthymiou parametric equations, and the hot-spot stresses at eight locations on the chord and brace of the tubular joints are derived by summing the stress components from axial, in-plane, and out-of-plane actions. The stress distribution is determined using the rainflow counting method, fatigue damage from an S–N curve, and Miner’s rule. Uncertainties associated with the fatigue lifetime evaluation procedure are identified, quantified, and modeled. The focus is specifically given to modeling the uncertainty related to the SCFs, and a framework is proposed to evaluate the fatigue reliability of the joint by incorporating individual uncertainties for each degree of freedom of the SCFs (i.e., axial load crown, axial load saddle, in-plane bending moment, and out-of-plane bending moment). The results reveal that assuming the same uncertainty level (Coefficient of Variation of 0.2) as recommended by DNV-RP-C210 for each degree of freedom of the SCFs and including the uncertainty after obtaining the stress distribution from rainflow counting does not consistently yield conservative reliability index values, as it depends on the critical hot spot. It is essential to note that the simplified assumptions derived from the oil and gas sector may not directly translate to the offshore wind industry due to differences in loading conditions. A reduction of up to approximately 24% in the reliability index is observed for one critical hot spot, while an increase of up to 20% was observed for another. Overall, this paper provides valuable insights into the complex interplay of factors affecting the reliability of joints in offshore fixed jacket support structures, shedding light on the need for tailored approaches to address uncertainties in the specific context of the offshore wind industry.

Effects of the Flying Start on Estimated Short Sprint Profiles Using Timing Gates.

Short sprints are predominantly assessed using timing gates and analyzed through parameters of the mono-exponential equation, including estimated maximal sprinting speed (MSS) and relative acceleration (TAU), derived maximum acceleration (MAC), and relative propulsive maximal power (PMAX), further referred to as the No Correction model. However, the frequently recommended flying start technique introduces a bias during parameter estimation. To correct this, two additional models (Estimated TC and Estimated FD) were proposed. To estimate model precision and sensitivity to detect the change, 31 basketball players executed multiple 30 m sprints. Athlete performance was simultaneously measured by a laser gun and timing gates positioned at 5, 10, 20, and 30 m. Short sprint parameters were estimated using a laser gun, representing the criterion measure, and five different timing gate models, representing the practical measures. Only the MSS parameter demonstrated a high agreement between the laser gun and timing gate models, using the percent mean absolute difference (%MAD) estimator (%MAD < 10%). The MSS parameter also showed the highest sensitivity, using the minimum detectable change estimator (%MDC95), with an estimated %MDC95 < 17%. Interestingly, sensitivity was the highest for the No Correction model (%MDC95 < 7%). All other parameters and models demonstrated an unsatisfying level of sensitivity. Thus, sports practitioners should be cautious when using timing gates to estimate maximum acceleration indices and changes in their respective levels.

Novel path planning algorithm for laser powder bed fusion to improve the scan quality of triply periodic minimal surface structures

Traditional path planning methods, such as contour and raster methods, suffer from problems like uneven filling, overfilling, and underfilling in the sliced layers, resulting in poor continuity of the lattice melt pool, internal porosity defects, and severe powder adhesion at the contour edges, while research on path planning for three-periodic minimal surfaces lattices is relatively limited. In this study, a scanning path planning method based on lattice equations control is proposed, which differs from traditional contour paths and raster paths. The new paths are controlled by the isosurface parameters of the lattice equation and optimized using the traveling salesman problem, resulting in more uniform scanning paths. The new paths avoid the underfilling issue present in raster path and the sawtooth-shaped borders of raster path. Additionally, they circumvent the nonuniform scanning path problem caused by uneven wall thickness in contour path. Through visualizing the paths and conducting printing experiments on the lattice, it is found that the new path is more uniform compared to contour paths, effectively addressing the issue of overfilling. Compared to raster paths, the new path has smoother boundaries and reduces internal porosity and powder adhesion within the lattice. This research has important value in reducing internal porosity and external powder adhesion issues in three-period minimal surface (TPMS) lattice printing processes, further enhancing the manufacturing quality of TPMS lattices.

Semiglobal interval observer‐based robust coordination control of multi‐agent systems with input saturation

AbstractThis paper investigates the problem of robust coordination control based on interval observers for multi‐agent systems in the presence of input saturation and disturbances. Firstly, in the scenario where the system state is not directly measurable, two types of interval observers are, respectively, constructed by resorting to the upper and lower bounds on external perturbances as well as the output information. Secondly, a parametric Lyapunov equation‐based low‐gain feedback control method is proposed to guarantee semiglobal bounded consensus. In contrast to the conventional approach based on parametric algebraic Riccati equations, the proposed method offers the advantage of allowing the parameters to be determined in advance. Finally, a simulation example and a practical electrical circuit model are conducted to verify the theoretical results.

Reaction calorimetry and structural crystal properties of non-ideal binary rhabdophane solid solutions (Ce1−xREExPO4·nH2O)

Rhabdophane is a hydrous phosphate that commonly replaces monazite as a weathering product in critical mineral deposits during the alteration of rare earth elements (REE) bearing carbonatites and alkaline igneous complexes. It is an important host to the light (L)REE (i.e., La to Gd) but the stability and structure of binary solid solutions between the Ce and the other LREE endmembers have not yet been determined experimentally. Here we present room temperature calorimetric experiments that were used to measure the enthalpy of precipitation of rhabdophane (Ce1−xREExPO4·nH2O; REE = La, Pr, Nd, Sm, Eu, and Gd). The solids were characterized using X-ray diffraction, scanning electron microscopy, Raman spectroscopy, and the role of water in the rhabdophane structure was further determined using thermogravimetric analysis coupled with differential scanning calorimetry. The calorimetric experiments indicate a non-ideal behavior for all of the binary solid solutions investigated with an excess enthalpy of mixing (ΔHex) described by a 2- to 3-term Guggenheim parameters equation. The solid solutions were categorized into three groups: 1) binary Ce-La and Ce-Pr which display positive ΔHex values with a slight asymmetry; 2) binary Ce-Nd and Ce-Sm which display negative ΔHex values with a nearly symmetric shape; 3) Ce-Eu and Ce-Gd which display both negative and positive ΔHex values with nearly symmetric shape. The excess Gibbs energy (ΔGex) of the solid solutions was further investigated using a thermodynamic analysis approach of aqueous-solid solution equilibria and the optimization programs GEMS and GEMSFITS. The resulting ΔGex values combined with the calorimetric ΔHex values indicate that there is likely an excess entropy contribution implying important short-range structural modifications in the solid solutions dependent on the deviation of the REE ionic radii from the size of Ce3+. These observations corroborate with the trends in the Raman v1 stretching bands of the PO4-site. The excess molar volumes determined from X-ray diffraction analysis further indicate an overall asymmetric behavior in all of the studied binary solid solutions, which becomes increasingly important from La to Gd. The pronounced short-range order–disorder occurring in groups 2 and 3 solid solutions mimics some of the behavior observed from previous studies in anhydrous monazite solid solutions. This study highlights the potential to use the chemistry and the structural modifications of rhabdophane as potential indicators of formation conditions in geologic systems and permits improving our modeling capabilities of REE partitioning in critical minerals systems.

Effect of volumetric deformation on saturation of unsaturated soils under constant suction

The soil–water retention curve (SWRC) represents a fundamental relationship in the study of unsaturated soils, where volumetric deformation plays a crucial role in shaping the water retention characteristics by impacting the pore size distribution. This study conducted a thermodynamic analysis to derive a relationship between the effective stress parameter and the water retention properties of unsaturated soils. Consequently, a streamlined formula was introduced to forecast the impact of volumetric deformation on saturation at constant suction. This formula, incorporating a singular parameter from the effective stress parameters equations, can be seamlessly integrated with any prevailing SWRC model to characterize the influence of volume deformation on the SWRC. The effectiveness of the proposed model was corroborated through seven sets of experimental data spanning various soils, affirming its capability to precisely describe the water retention behavior of deformable soils under deformation.

Optimization-based planning of speech articulation using general Tau Theory

This paper presents a model of speech articulation planning and generation based on General Tau Theory and Optimal Control Theory. Because General Tau Theory assumes that articulatory targets are always reached, the model accounts for speech variation via context-dependent articulatory targets. Targets are chosen via the optimization of a composite objective function. This function models three different task requirements: maximal intelligibility, minimal articulatory effort and minimal utterance duration. The paper shows that systematic phonetic variability can be reproduced by adjusting the weights assigned to each task requirement. Weights can be adjusted globally to simulate different speech styles, and can be adjusted locally to simulate different levels of prosodic prominence. The solution of the optimization procedure contains Tau equation parameter values for each articulatory movement, namely position of the articulator at the movement offset, movement duration, and a parameter which relates to the shape of the movement’s velocity profile. The paper presents simulations which illustrate the ability of the model to predict or reproduce several well-known characteristics of speech. These phenomena include close-to-symmetric velocity profiles for articulatory movement, variation related to speech rate, centralization of unstressed vowels, lengthening of stressed vowels, lenition of unstressed lingual stop consonants, and coarticulation of stop consonants.

Dominance of polarization modes and absorption on self-focusing of laser beams in collisionless magnetized plasma

This work investigates the polarization modes i.e., Extraordinary (E-mode) and Ordinary (O-mode) on self-focusing of higher-order mode of elegant Hermite-cosh-Gaussian (EHChG) laser beams within collisionless magnetized plasma medium. In this study, the authors have taken transverse electromagnetic ([Formula: see text]) mode with mode indices (0, 4) and explored. The ponderomotive force is primarily responsible for the dielectric constant’s nonlinearity in this context. Also, WKB and paraxial approximations via the parabolic wave equation approach are used to establish the general form of differential equations for beam-width parameters in both transverse dimensions of the beam. In this paper, the authors have theoretically investigated the dominance of polarization modes and absorption coefficient on self-focusing. The final results show good enhancement of laser propagation through collisionless plasma medium.

A Force Function Formula for Solutions of Nonlinear Weakly Singular Volterra Integral Equations

In this paper, we examine the nonlinear Weakly Singular Volterra Integral Equation(WSVIE), $u(x)=f(x)+\int_{0}^{x}\frac{t^{\mu-1}}{x^\mu}[u(t)]^\beta dt$. AL-Jawary and Shehan used Daftardar-Jafari Method(DJM) and solved the above integral equation for the investigation parameter $\mu&gt;1$ using specific force functions with $\mu$ and $\beta$ values and obtained unique solutions. We have discovered a force function $f(x)=x^{k_1}-{\frac{x^{\gamma k_1}}{\gamma k_1+\mu}}$, that allows the introduction of noise terms phenomena discovered by Wazwaz; that cancel out the terms of the power series in the successive solution terms $u_m$, $m=0,1,2,...,n$: we thus obtain a maximum finite power series terms for each solution term called truncation point and denoted by $x^{g(n)}$. Such that the integral solution can be written as $u(x)=u_0+\sum_{m=1}^{n}u_m$, where $n$ is finite. Simplifying the solution terms we get the unique solution $u(x)=x^{k_1}$, irrespective of $n-$value in the truncation point. We discovered a formula relation between the last solution term $u_n$ and the truncation point as $u_n=a_nx^{g(n)}$. Our results confirm the results of the two solution examples of AL-Jawary and Shehan for the investigation parameter $\mu&gt;1$. We extend the parameter range to include $\mu&gt;1$ and $0&lt;\mu\leq 1$ for our solution. In addition, for any chosen rational parameter $k_1$, the solution $u(x)=x^{k_1}$ is extrapolated to be valid for all integer parameter values $\beta\geq 2$, and positive rational parameter value $\mu&gt;0$ and for any finite value of $n\geq2$.