Coefficients Of Equation Research Articles

Shear Elastic Buckling and Resistant Behavior of Single-Side-Stiffened Steel Corrugated Shear Walls

Stiffened steel corrugated shear walls (SSCSWs) have achieved extensive applications in building structures and serve as efficient lateral force-resisting members. Single-side-stiffened steel corrugated shear walls (SS-SCSWs) are more flexible in terms of their structural configuration compared to conventional SSCSWs because this novel structural member effectively reduces wall thickness and simplifies the construction process. In this paper, numerical analyses were carried out to investigate the shear elastic buckling and resistant behavior of SS-SCSWs. A formula for the equivalent flexural stiffness of single-side stiffeners was given based on theoretical analysis. The elastic buckling and elastoplastic analyses of SS-SCSWs were carried out by finite element (FE) models to determine the value of the equivalent flexural stiffness coefficient. Meanwhile, the elastic and elastoplastic transition stiffness ratios of single-side stiffeners were proposed to predict the minimum stiffness required for the stiffener to provide sufficient constraint. The accuracy of the above formulas was verified by calculating the shear elastic buckling loads, the ultimate shear resistance, and the out-of-plane displacements of the SS-SCSWs. Furthermore, parametric analyses were performed to reveal the influences of the aspect ratio and plate thickness on shear resistance capacity. The equivalent flexural stiffness coefficients in both the elastic and elastoplastic analyses were determined to be 0.45 and 0.7, respectively, through curve fitting. The results indicated that the theory of BS-SCSWs could accurately predict the shear elastic and elastoplastic behavior of SS-SCSWs after modifying its expression for flexural stiffness. Consequently, the modified theoretical formulas were demonstrated to be suitable for SS-SCSWs in practical designs.

Research on the approximate equation inversion method for the physical properties parameters of OA media with decoupling of stress and fracture effects

Pre-stack seismic inversion is an effective method for predicting reservoir physical parameters. At the same time, azimuth seismic data is a reliable source of information for predicting underground reservoir elastic parameters, fracture parameters, and interface parameters and has rich underground information. However, it is difficult to determine whether the anisotropy of the reservoir is caused by stress or the original fractures. Therefore, distinguishing the influence of fractures and initial stress in the reservoir from azimuth seismic data is the key to predicting reservoir parameters. Because of the problem of insufficient consideration of the influence of stress and fracture weakness in OA media, based on Born's first-order scattering theory and Bayesian inversion framework, an approximate equation for the reflection coefficient decoupling fracture anisotropy and stress-induced anisotropy was constructed, and a linear inversion method based on the approximate equation was developed, realizing the exploration of methods for predicting fracture weakness and stress action parameters. Model testing and actual work area application have verified the feasibility and practicability of predicting underground medium parameters from seismic response characteristics.

Ground response during of EPB shield shutdown in gravel ground based on coupled CEL-FEM analysis

The shutdown of earth pressure balance (EPB) shield tunneling in gravel stratum can easily lead to significant unexpected ground deformation. In order to study the response of gravel strata during shield shutdown and the characteristic change of soil state in the chamber, this paper establishes a coupled Eulerian-Lagrangian finite element method (CEL-FEM) coupling analysis model that reflects the interaction between the spoiled soil and gravel strata. The plastic flow parameters of CEL spoiled soil are calibrated using the slump method, and a quantitative relationship between the slump value, plastic flow parameters, equivalent coefficient of loosening, and excavation face support pressure is established. The reliability and applicability of CEL method in the simulation of shield shutdown are verified by the field measurements. Results show that: (1) The chamber’s soil equivalent loose coefficient is inversely proportional to the soil slump value which is related to soil’s plastic flow parameters. (2) The shield shutdown in gravel strata has a more significant impact on the deep strata displacement than on the surface. (3) During the shield shutdown stage, the chamber pressure should be dynamically adjusted based on the soil deformation characteristics, and an increase of 16% could result in a stable rebalance.

Measurement of the equivalent friction coefficients of ball bearings based on the variations in kinetic energy

Measurement of the equivalent friction coefficients of ball bearings based on the variations in kinetic energy

DEPENDENCE OF THE EFFICIENCY OF A VORTEX CHAMBER EJECTOR ON ITS GEOMETRIC PARAMETERS

The wear and decreased efficiency of superchargers with moving impellers make using jet devices in many technological processes advisable. Using the properties of swirling flows, such as reduced axial pressure, has created vortex ejectors. Still, their energy performance and efficiency are reduced compared to classical direct-flow jet pumps and ejectors. The solution to this problem may be the use of more advanced energy transfer principles and technical solutions in the design of vortex chamber-based jet superchargers. Such superchargers are vortex chamber superchargers, which, due to the use of centrifugal force, have better energy efficiency than vortex ejectors. The aim of this work is to determine the dependence of the efficiency of a vortex chamber ejector on its geometric parameters based on the design of the experiment. The study consisted of three stages: an experimental study of the vortex chamber ejector operation in a homogeneous medium with the initial geometric parameters of the vortex chamber and the supply and discharge channels for optimization. In the second stage, mathematical modeling was performed based on solving the Reynolds equations using the SST turbulence model. Next, the experimental data were compared with the calculation results. The optimization of parameters using the second-order model allowed us to find the maximum value of the efficiency of the vortex chamber ejector, which is equal to 16 %. The geometric parameters selected as factors are the relative height and diameter of the vortex chamber, the relative diameter of the supply channel. The relative height of the vortex chamber has the greatest influence on the efficiency. The significance of the obtained coefficients of the regression equations was tested using Student's t-test.

The effect of cuboid explosive shape on the dimension of damaged area in masonry walls subjected to contact explosions

Cuboid explosives are commonly available in both military and civilian markets. Masonry walls are among the most prevalent structural elements utilized in buildings worldwide. This study numerically investigates the response of masonry walls subjected to blast loads generated by cuboid explosives. The LS-DYNA software was employed to create numerical models, which were subsequently validated against experimental data. The shape of the cuboid explosives is characterized by its three-dimensional dimensions: length ([Formula: see text]), width ([Formula: see text]), and height ([Formula: see text]). To maintain a constant mass of explosives, two distinct scenarios were considered. In the first scenario, the explosive’s shape was altered by adjusting the height-to-length ratio ([Formula: see text]) while keeping [Formula: see text] equal to [Formula: see text]. In the second scenario, the length-to-width ratio ([Formula: see text]) was modified while maintaining a constant height ([Formula: see text]), leading to changes in the explosive’s shape. The effects of both the [Formula: see text] ratio and the [Formula: see text] ratio on the dynamic responses of the masonry walls were investigated. The results indicate that the dimensions of both the ejection crater and the spalling crater on the masonry wall initially increased and then decreased as the [Formula: see text] ratio increased. Furthermore, the size of the breached hole gradually diminished with an increasing [Formula: see text] ratio. In terms of changes to the [Formula: see text] ratio, the damage area of the masonry wall took on an elliptical shape, with the dimensions of this elliptical damage area exhibiting regular variations. This study aimed to equate cuboid explosives (with [Formula: see text] and [Formula: see text]) to cubic explosives (where [Formula: see text]) of the same mass. The equivalent cubic shape coefficients ([Formula: see text]) for the cuboid explosives were evaluated and calculated based on the dimensions of the damage area on the masonry wall. Furthermore, four coefficients ([Formula: see text] to [Formula: see text]) were proposed to estimate the dimensions of the masonry wall damage area when subjected to contact explosions from arbitrarily shaped cuboid explosives. The applicability of these coefficients was validated through numerical simulations.

Deriving improved plasma fluid equations from collisional kinetic theory

IntroductionDeveloping a quantitative understanding of wave plasma processes in the lower ionosphere requires a reasonably accurate theoretical description of the underlying physical processes. For such a highly collisional plasma environment as the E-region ionosphere, kinetic theory represents the most accurate theoretical description of wave processes. For the analytical treatment, however, collisional kinetic theory is extremely complicated and succeeds only in a limited number of physical problems. To date, most research has applied oversimplified fluid models that lack a number of critical kinetic aspects, so the coefficients in the corresponding fluid equations are often accurate only to an order of magnitude.MethodsThis paper presents a derivation for the highly collisional, partially magnetized case relevant to E-region conditions, using methods of the collisional kinetic theory with a new set of analytic approximations.ResultsThis derivation provides a more accurate reduction of the ion and, especially, electron kinetic equations to the corresponding 5-moment fluid equations. It results in a more accurate fluid model set of equations appropriate for most E-region problems.DiscussionThe results of this paper could be used for a routine practical analysis when working with actual data. The improved equations can also serve as a basis for more accurate plasma fluid computer simulations.

Study on the influence of submergence depth on the hydrodynamic and wave load characteristics of semi-submersible structures induced by a solitary wave

The submergence depth directly affects the safety of semi-submersible marine structures due to that the submergence depth significantly impacts on the hydrodynamic characteristics and wave loads of structures excited by extreme wave. This paper studies the influence of submergence depth on the hydrodynamic and wave load characteristics of semi-submersible structures by establishing a numerical model of the interaction between solitary waves and semi-submersible structures based on the SPH model and Rayleigh theory. Furthermore, equations for transmission coefficient, reflection coefficient, and wave load are fitted. The calculated wave heights of solitary wave propagation test case are in good agreement with the theoretical values. The maximum relative error of the wave peak is 8.4%. The calculated wave loads of submerged horizontal plates test case has a consistent trend with the experimental data. The maximum relative error of wave load peak and valley is 54% (absolute error 0.37 N). Furthermore, the interaction between solitary waves and structures with different submergence depths is investigated by using the meshless numerical model. It is found that the reflection coefficient first increases and then decreases with increasing submergence depth, and reaching a maximum value of 0.39 at the submergence depth equal to 0.0 m. On the contrary, the transmission coefficient decreases first and then increases with the increase of submergence depth. The minimum value of transmission coefficient is 0.36 with the submergence depth of 0.3 m. As the submergence depth increased, the horizontal wave load peak of the structure gradually increases, and the maximum value of 0.13 is obtained at the submergence depth of 0.7 m. The peak of vertical wave load rapidly increases with the increase of submergence depth and then gradually decreases while the trough gradually decreases with increasing submergence depth.

Travelling Solitary Wave Solutions to Non-Gaussian χ-Wick-Type Stochastic Burgers’ Equation with Variable Coefficients

In this work, we obtain non-Gaussian (NG) stochastic solutions to χ-Wick-type stochastic (χ-Wk-TS) Burgers’ equations with variable coefficients. An Exp-function method, the connection between white noise theory and hypercomplex systems (HCSs), the χ-Wick product (χ-Wk-product) and an χ-Hermite transform (χ-Hr-transform) are proposed. We provide a new set of non-Gaussian solitary wave solutions (NG-SWSs) to Burgers’ equations with variable coefficients. NG white noise functional solutions (NG-WNFSs) to χ-Wk-TS Burgers’ equations with variable coefficients are shown. The symmetry coefficients of partial differential equations and the symmetrical properties of SPDEs are critical in determining the best solution.

Dynamic Analysis and Equivalent Modeling for a Four-Axle Vehicle

This paper focuses on a comprehensive study of a four-axle vehicle, including dynamics analysis, equivalent modeling methods, and their comparison. Firstly, a linear two-degree lateral dynamic model is established, which has four drive axles and two steer axles. Secondly, the mathematical transfer function expressions for the yaw rate and the centroid sideslip angle were derived on the basis of the model. The steady-state parameters, such as yaw rate gain Gγss, centroid sideslip angle gain Gβss, stability factor Kn, equivalent axial distance ln, and equivalent centroid sideslip angle coefficient Kn’ were obtained by using the transfer functions. Then, the steady-state and transient characteristics are roundly discussed, including steady-state parameters, system root trajectory, frequency domain, and time domain. Some recommendations for the four-axle vehicle’s parameter design are also given. Finally, for a more simple and efficient analysis of response characteristics of four-axle vehicles and even n (n > 4) axle vehicles, the equivalent model is developed for the four-axle vehicle, and comprehensive analyses are presented with four equalization methods, which are based on the inner heart of the approximation triangle, the outer heart of the approximation triangle, the center of gravity of the approximation triangle and the compensation point. Following a thorough analysis of the four, it is determined that the inner approximation triangle solution approach is most suited for four-axle vehicles.

Recovery of a coefficient in a diffusion equation from large time data*

Abstract This paper considers the determination of a spatially varying coefficient in a parabolic equation from time trace data. There are many uniqueness theorems known for such problems but the reconstruction step is severally ill-posed: essentially the problem comes down to trying to reconstruct an analytic function from values on a strip. However, we look at an even more restricted data where the measurements are not made on the whole time axis but only for large values adding further to the ill-conditioning situation. In addition, we do not assume the initial state is known. Uniqueness is restored by making changes to the boundary condition, in particular, to the impedance parameter, for each of a series of measurements. We show that an implementation of the above paradigm leads to both uniqueness and an effective reconstruction algorithm. Extension is also made to the case of fractional model and to replacing the parabolic equation with a damped wave equation.

A Multi-Scale Thermal-Mechanical Numerical Method for Mini-Channel Heat Exchanger Subjected to Fluid Pressure Loads

Abstract This study proposes a novel multi-scale numerical method for thermal-mechanical analysis of mini-channel heat exchangers (MCHEs) under internal fluid pressure and temperature loads. The method comprises a macro-scale model for global analysis and a meso-scale model for detailed submodel analysis, specifically focusing on the internal fluid pressure effects within the MCHEs. The macroscopic model divides the MCHE into cover plate and homogenized regions subjected to pressure and temperature loads. To incorporate internal pressures into the homogenized MCHE model, mathematical equations are formulated to convert internal fluid pressures into equivalent strain loads. Additionally, a novel equivalent thermal expansion method is introduced, integrating internal fluid pressure loads by prescribing equivalent thermal expansion coefficients alongside spatially-varying nodal temperature fields within the MCHE. The meso-scale models with detailed channel patterns are assigned to specific portions of the homogenized region. The integration of the mesoscale model into the macroscopic framework is achieved through the application of the submodel method. Comparisons between the equivalent and actual MCHE models show that the proposed equivalent method can provide accurate predictions for thermal-mechanical deformations and stresses, and significantly reduce the computational expenses.

Investigation on the cyclic buckling and plastic overstrength characteristics of steel shear links utilizing corrugated panels

This paper established and validated the finite element model (FEM) for novel steel shear links utilizing corrugated panels (CSSL), analyzed the stress and strain distributions of CSSL, and summarized the buckling characteristics and determination criteria for CSSL. Utilizing the FEM, the influence of CSSL configuration parameters on its buckling deformation capacity and plastic overstrength characteristics were analyzed. The analysis results indicated that: the decrease in the corrugated panel's sub-panel slenderness a/tw could significantly improve the buckling deformation capacity of CSSL, but had little influence on pre-buckling plastic overstrength characteristics; the decrease in sub-panel aspect ratio h/a and web aspect ratio e/h, as well as the increase in web corrugation angle θ was beneficial for the buckling deformation capacity of CSSL, but might decrease the plastic overstrength characteristics; the decrease in the equivalent links length coefficient eVp/Mp and the increase in structural steel strain-hardening value α had a slight influence on the buckling deformation capacity, but could significantly improve the plastic overstrength characteristics. Based on the analysis result, a theoretical prediction approach for the buckling deformation capacity and plastic overstrength characteristics was proposed, and the load-deformation skeleton curve model was also established, which was validated to exhibit good accuracy with compassion to experimental and finite element analysis results.

Sound Speed Prediction Equations for Seafloor Sediments in Offshore Area Southeast of Hainan Island

In this study, single- and double-parameter empirical equations were produced, and the influences of physical properties on sound speed were assessed, based on the measured data of seafloor sediments obtained in an area near southeastern Hainan Island. The correlation coefficients of the single-parameter empirical equations were found to be greater than 0.65, while those of the double-parameter empirical equations were found to be greater than 0.72, indicating that the double-parameter empirical equations have an advantage in predicting sound speed. According to the sensitivity analysis, mean grain size is the best predictor for sediment sound speed. Furthermore, the empirical equations constructed in this study are a significant addition to sound speed prediction equations and have important application potential in predicting sound speed in the studied area near southeastern Hainan Island.

Frequency-dependent nonlinear AVO inversion for fluid mobility in viscoelastic media

Reservoir fluid mobility is defined as the ratio of rock permeability to fluid viscosity, which is an important attribute to guide the prediction of high-quality oil and gas reservoirs. Frequency-dependent amplitude variation with offset (AVO) inversion, based on viscoelastic theory, is a useful tool for fluid identification. In conventional pre-stack inversion, linear approximations are usually used to calculate the reflection coefficients, while nonlinear inversions are only occasionally carried out. However, the nonlinear equation for the reflection coefficient, derived from the exact Zoeppritz equation, has higher accuracy and fewer assumptions than the linear approximations. Therefore, we derive a nonlinear frequency-dependent reflection coefficient equation of the PP-wave in terms of P-wave velocity reflectivity, S-wave velocity reflectivity and fluid mobility, based on the relationship among fluid mobility, incident angle, and seismic wave frequency. We consider viscoelastic media and frequency-dependent responses to improve the authenticity of the reflection coefficients. Additionally, we develop a split-step inversion method for fluid mobility based on the Artificial Neural Network Inversion (ANNI) algorithm. Synthetic and field data examples demonstrate that the proposed split-step inversion method outperforms traditional inversion methods that rely on approximate equations for predicting underground reservoirs, improving the stability of fluid mobility parameter inversion.

PICL: Physics informed contrastive learning for partial differential equations

Neural operators have recently grown in popularity as Partial Differential Equation (PDE) surrogate models. Learning solution functionals, rather than functions, has proven to be a powerful approach to calculate fast, accurate solutions to complex PDEs. While much work has been performed evaluating neural operator performance on a wide variety of surrogate modeling tasks, these works normally evaluate performance on a single equation at a time. In this work, we develop a novel contrastive pretraining framework utilizing generalized contrastive loss that improves neural operator generalization across multiple governing equations simultaneously. Governing equation coefficients are used to measure ground-truth similarity between systems. A combination of physics-informed system evolution and latent-space model output is anchored to input data and used in our distance function. We find that physics-informed contrastive pretraining improves accuracy for the Fourier neural operator in fixed-future and autoregressive rollout tasks for the 1D and 2D heat, Burgers’, and linear advection equations.

Diffusion Behavior and Kinetics for the Vapor Phase Infiltration of Trimethylaluminum in Poly(ethylene oxide): An In Situ Quartz Crystal Microgravimetry Study.

Vapor phase infiltration (VPI) facilitates the incorporation of inorganic components into organic polymers, emerging as an effective technique for fabricating organic-inorganic hybrid materials. However, the complexity of diffusion behavior during the VPI process presents challenges in studying diffusion kinetics, particularly for highly reactive precursor-polymer systems such as trimethylaluminum (TMA) and poly(ethylene oxide) (PEO). In this study, we investigate the VPI process of TMA in PEO using in situ quartz crystal microgravimetry (QCM), which enables measurement of diffusion behavior and kinetics with high precision due to its high temporal resolution. Our results indicate that the VPI process consists of two main regions: a rapid diffusion process, corresponding to the initial penetration of the precursor into the film, followed by a slower relaxation process, attributed to the ongoing chemical reaction. The equivalent diffusion coefficient (De) was estimated to be on the order of 10-9 cm2/s and decreased with increasing aluminum content. Using energy application as a proof-of-concept, when optimized, VPI-modified PEO films were successfully utilized as solid polymer electrolytes (SPEs) for lithium metal batteries (LMBs), showcasing superior performance in mitigating lithium dendrite growth. This study offers valuable insights into the VPI process for PEO-TMA systems and provides guidance for optimizing VPI conditions to enhance the performance of advanced materials.

Photoacoustic trace-analysis of breath isoprene and acetone via interband- and Quantum Cascade Lasers

This research presents two laser-based photoacoustic approaches for analyzing exhaled breath isoprene and acetone. The integration of a PTR-ToF-MS as a reference device ensured the reliability and accuracy of the photoacoustic systems that is based on an ICL for isoprene and a QCL for acetone detection. The calibration yielded limits of detection of 26.9 ppbV and 1.7 ppbV, respectively, and corresponding normalized noise equivalent absorption coefficients (NNEAs) of 5.0E-9 Wcm−1Hz−0.5 and 4.9E-9 Wcm−1Hz−0.5. Laboratory as well as real breath sample measurements from alveolar breath revealed a robust system performance, with only one outlier within the static isoprene measurements. However, discrepancies emerged under dynamic breath sampling conditions, emphasizing the need for further optimization. Especially by knowing the dynamic nature and endogenous origin of exhaled isoprene our findings highlight the potential of breath analysis for non-invasive physio-metabolic and pathophysiological monitoring towards point-of-care devices.

Spatiotemporal dynamics and driving factors of ecosystem services value in Lanzhou City, China

Aligned with the imperatives of national ecological civilization construction, the systematic investigation into the intricate interplay between shifts in land utilization and the assessment of ecosystem services plays a pivotal and indispensable role in advancing ecological civilization. This endeavor holds significant implications. It aids in optimizing the ecological landscape at the regional level and fosters harmonious coexistence between humanity and the natural world. The study utilizes land-use remote sensing interpretation data from three time periods (2000, 2010, and 2020) and employs various methodologies, including equivalent factor coefficient correction, sensitivity analysis, and spatial autocorrelation. The objective is to uncover the spatiotemporal dynamics of land-use changes and Ecosystem Service Value (ESV) in Lanzhou City. Furthermore, geographic detectors are applied to explore the driving factors influencing ESV spatial heterogeneity and their interactions. The research findings indicate the following: (1) From 2000 to 2020, grassland and cropland were the predominant land-use types in Lanzhou City, with cropland and urban land experiencing the most active changes. (2) ESV in Lanzhou City increased from 179.37 billion RMB in 2000 to 193.86 billion RMB in 2020, reflecting an ESV total growth rate of 8.07% and a gradual improvement in the ecological environment. Spatially, ESV exhibits a “west high, east low” distribution pattern, with the center shifting towards the northwest and southeast, gradually reducing spatial imbalance. (3) Analysis of ESV spatial autocorrelation reveals that high-high clusters are predominantly found within the Tulu Gou National Forest Park and the Xinglong Mountain National Natural Reserve, while low-low clusters are primarily concentrated in the central urban area of Lanzhou City. Over the period from 2000 to 2020, the spatial clustering effect of ESV within the study area has progressively intensified. 4)NDVI, precipitation, and GDP emerge as pivotal factors influencing spatial differentiation within Lanzhou City, with natural and societal elements exerting interactive effects on ESV spatial disparities. The research results integrate environmental considerations into the decision-making process, offering valuable insights for formulating targeted ecological protection policies in Lanzhou City. This study embodies concrete measures taken by Lanzhou City in practicing China’s concept of “green water and green mountains are golden silver mountains,” providing a theoretical basis for the harmonious and sustainable development of the ecological economy.

Oscillation of 3 rd order non-canonical delay differential equations of limited neutral coefficient

Oscillation of 3 rd order non-canonical delay differential equations of limited neutral coefficient