Exponential Function Research Articles

Sugarcane leaf return and mixing significantly reduce slope runoff and soil loss

AbstractImproper management of sugarcane cultivation may cause severe soil erosion, especially in lateritic red soil hilly areas. Crop straw return to the field can effectively improve the soil structure, but there is a lack of evaluation studies of the soil and water conservation benefits of sugarcane leaf mixing and return to the field, and the underlying regulatory mechanism has rarely been described. Thus, we conducted a series of simulated rainfall experiments to investigate the impact of returning different mixed sugarcane leaf weights (0, 3, 6, 9, 12 and 15 t/ha) to the field on erodible lateritic red soil slopes that support sugarcane production under various slopes (5°, 10°, 15° and 20°) in different rainfall events (60 and 120 mm/h). The results indicated that returning sugarcane leaves into farmland could effectively regulate the process of runoff and sediment production on lateritic red soil slopes, and the optimal mixing amount was 9 t/ha. Under a low rainfall intensity, the erosion process was mainly affected by the slope, and the benefits of applying the sugarcane leaf mixing treatment to the slope to reduce runoff and sediment could reach 13.37–53.04% and 23.86–77.55%, respectively. However, under a high rainfall intensity, the sugarcane leaf mixing amount was the main influencing factor, the benefits for reducing runoff and sediment could reach 4.64–38.72% and 30.87–93.14%, respectively. The sugarcane leaf mixing amount exhibited a linear relationship with the Reynolds number (R2 > 0.63), whereas the runoff velocity (R2 > 0.96), Froude number (R2 > 0.94) and drag coefficient (R2 > 0.85) exhibited well‐fitting exponential function relationship with it. This study provides a reference for future endeavours regarding the inhibition mechanisms of sugarcane leaves mixed and returned to the field for decreasing slope erosion.

A new version of trial equation method for a complex nonlinear system arising in optical fibers

In this study, the dissipation problem of nonlinear pulse in mono mode optical fibers which is governed by the Fokas system (FS) is considered. The solutions of this system have an important role in comprehending the different wave structures in physical settings. Therefore, a new version of the trial equation method (NVTEM) is employed to present the new exact wave solutions of the FS. The advantage of the NVTEM is to use different root possibilities of a polynomial which shape the solutions of the related model. Primarily this system is converted to a nonlinear ordinary differential equation (NODE) via the traveling wave transform to apply the proposed method. Various exact wave solutions to the FS are obtained such as rational function, exponential function, hyperbolic function, and Jacobi elliptic function solutions. Thus, we have revealed solutions featly which are unlike the wave solutions previously found by other analytical methods. The present results depict the formation and development of such waves and their interactions. The exhibition of the solutions is given by 3D plots together with the corresponding 2D plots. The outcomes have shown that the proposed technique is abundant in achieving different wave solutions of many nonlinear differential equations in the field of optics.

Evaluating habitat-specific interference in automated radio telemetry systems: implications for animal movement studies

Automated radio telemetry systems have become a popular and invaluable tool in tracking the activity and movement of wild animals. However, many environmental conditions can hinder accuracy when tracking with this technology. For instance, study sites may contain multiple habitat types, each habitat uniquely affecting the signal strength received from tagged species. To investigate the influence of a structurally diverse study site on an automated radio telemetry system, we conducted this project at a restored and managed pine barren habitat that consisted of a mix of mature pitch pine, treated pitch pine, scrub oak, and hardwood forests. This site, Montague Plains Wildlife Management Area, Montague, Massachusetts, is also a known breeding ground for Eastern whip-poor-will (Antrostomus vociferus). To measure the relationship of radio signal strength with distance across each habitat, we used radio telemetry equipment manufactured by Cellular Tracking Technologies. We produced negative exponential decay functions measuring radio signal strength over distance and tested for differences among habitat types on radio signal strength (RSS). We found that decay function parameters significantly differed by habitat type, prompting us to investigate if accounting for these differences improved location estimate accuracy. To test this, we estimated known locations using trilateration methods with and without habitat calibration. Comparing these tests indicates that habitat-specific adjustments significantly improved location accuracy. Lastly, we visualized estimated RSS-based locations of 1 week of whip-poor-will data and compared them to GPS data generated from the same individual. Previous studies have accounted for types of environmental interference (like elevation) in the field but have avoided incorporating habitat-specific factors by working with node networks covering a relatively small area, but in this study, we examined the potential to scale up for larger areas and in more complex habitats.

Symmetry-based closed-form solutions and conserved quantities of the new (2+1)-dimensional Bogoyavlensky-Konopelchenko equation in fluid mechanics

In this investigation, we explore the mathematical intricacies of the novel (2+1)-dimensional Bogoyavlensky-Konopelchenko equation, a model with practical applications in elucidating the dynamics of internal waves within deep water. The equation’s significance spans various scientific domains, including plasma physics, nonlinear optics, and fluid dynamics. Employing a comprehensive analytical approach, specifically Lie symmetry analysis, we aim to unravel the underlying complexities of this equation and obtain new analytical solutions. To further scrutinize the equation, we apply various methods, namely Kudryashov’s method, the (G′/G)-expansion method, the simplest equation technique, and the power series method, all of which have not been applied to the equation before. Through these techniques, we successfully derive solutions in diverse functional forms, encompassing rational, trigonometric, exponential, hyperbolic, and Jacobi elliptic functions. To enhance comprehension, we present our findings visually using three-dimensional and two-dimensional plots density plots via the Mathematica tool. These graphical representations effectively communicate the intricate characteristics and nuances inherent in the solutions. Our visual representations reveal a spectrum of patterns, including periodic, singular periodic, kink-shaped structures. Additionally, our investigation extends to the determination of conserved quantities associated with the new (2+1)-dimensional Bogoyavlensky-Konopelchenko equation. This involves the application of the multiplier method and Ibragimov’s theorem, two potent techniques for identifying and understanding the conservation laws governing the model.

INFLUENCE OF ELECTROMAGNETIC TREATMENT ON HYDRAULIC CHARACTERISTICS OF HOT PIPELINES DURING NEWTONIAN AND NON-NEWTONIAN PETROLEUM SYSTEMS TRANSPORTATION

This work examines the influence of radio-frequency (RF) electromagnetic (EM) influence on the hydraulic characteristics of hot pipelines for the transport of petroleum Newtonian and non-Newtonian systems.Newtonian and non-Newtonian petroleum and their rheological properties before and after RF EM exposure, as well as the hydraulic characteristics of hot petroleum pipelines for pumping selected petroleum, were selected as objects of study.As a result: a methodology for petroleum processing has been developed that corresponds to industrial practice in the operation of petroleum pipelines; empirical dependences of petroleum viscosity on temperature were obtained in the form of piecewise exponential functions. The influence of RF EM exposure on the thixotropic properties of petroleum and the values of ultimate shear stresses was assessed. A decrease or complete disappearance of hysteresis loops after RF EM exposure to petroleum and a decrease in the maximum shear stress for non-Newtonian petroleum were revealed.By using the software developed by the authors, «Hydraulic calculation of isothermal and non-isothermal petroleum pipelines (GRINT)», the processes of pipeline transport of petroleum treated with EM fields were modeled, taking into account the obtained empirical dependencies. An assessment of the influence of RF EM exposure on the hydraulic characteristics of «hot» pipelines was carried out. It has been established that after RF EM exposure to petroleum, the zone of stable operation of a «hot» petroleum pipeline increases and the required pressure for pumping the same volume of petroleum decreases.

Study on Ultra-Long-Distance Transportable Concentration Gradient of Coal Gangue Slurry with Different Gradations

Coal gangue, the primary solid waste generated during the coal mining process, is typically disposed of on the surface, where it gradually accumulates to form gangue piles that significantly contaminate the surrounding environment. Filling technology has been widely employed for the safe and efficient disposal of coal gangue due to its sustainability, safety, and efficiency. However, there is still a lack of theoretical research on the concentration of gangue slurry in long-distance filling pipeline transportation. Therefore, a calculation model of the ultra-long-distance transportable concentration of coal gangue slurry with different grades was constructed based on the static anti-segregation performance and Bingham model. In addition, the relevant parameters of the calculation model of the ultra-long-distance transportable concentration of coal gangue slurry in this mine were determined using the 8 km pipeline transport of coal gangue slurry in one mine as the technical background. It was subsequently demonstrated that the yield stress, plastic viscosity, and mass concentration of the various grades of gangue slurry in this mine exhibit an increasing exponential function, while the slurry density and mass concentration exhibit an increasing linear function, and the mass concentration and actual flow rate correspond to a quadratic polynomial increment. Finally, the minimum and maximum concentrations for different grades of gangue slurry that can be transported over long distances in this mine were determined. This work provides theoretical and practical guidance on how to select the concentration of gangue slurry for long-distance pipeline transport.

Investigating wave solutions and impact of nonlinearity: Comprehensive study of the KP-BBM model with bifurcation analysis.

In this paper, we investigate the (2+1)-dimensional Kadomtsev-Petviashvili-Benjamin-Bona Mahony equation using two effective methods: the unified scheme and the advanced auxiliary equation scheme, aiming to derive precise wave solutions. These solutions are expressed as combinations of trigonometric, rational, hyperbolic, and exponential functions. Visual representations, including three-dimensional (3D) and two-dimensional (2D) combined charts, are provided for some of these solutions. The influence of the nonlinear parameter p on the wave type is thoroughly examined through diverse figures, illustrating the profound impact of nonlinearity. Additionally, we briefly investigate the Hamiltonian function and the stability of the model using a planar dynamical system approach. This involves examining trajectories, isoclines, and nullclines to illustrate stable solution paths for the wave variables. Numerical results demonstrate that these methods are reliable, straightforward, and potent tools for analyzing various nonlinear evolution equations found in physics, applied mathematics, and engineering.

Fault Structure Reconstruction From Magnetic Anomalies Using an Improved Backtracking Search Optimization Algorithm

AbstractFault structure reconstruction is an important aspect of magnetic prospecting as it contributes to understanding tectonic history, hazard assessment, and infrastructure planning. Metaheuristics have proven useful in estimating fault structure parameters from geophysical anomalies. Recently, a modified version of the Backtracking Search Optimization Algorithm (BSA), named mBSA, has been proposed that combines mutation steps of BSA and Differential Evolution (DE) algorithms to achieve a better balance between exploration and exploitation. Here, we present imBSA as an efficient approach that builds on the improvements of mBSA. It uses an adaptive amplitude control factor in the mutation step derived from a normally distributed random number obtained via an exponential function. The performances of these approaches were tested on some widely used benchmark functions such as Rosenbrock, Rastrigin, Griewank, and Himmelblau. Synthetic magnetic fault anomalies were evaluated with and without noise, as well as three real anomalies from the Dehri (India), Perth Basin, and Lachlan Fold Belt (Australia). Prior to the optimizations, the solvability of the model parameters was examined using some error topography images. The obtained solutions in the synthetic cases were evaluated using principal component analysis. In addition, a novel visualization option for high‐dimensional optimization problems was introduced. The experiments showed that imBSA has a faster convergence rate and better optimization statistics compared to BSA and mBSA. Therefore, it is believed to be an efficient and good alternative tool to widely used metaheuristics such as Particle Swarm Optimization and DE in explaining geophysical anomalies and optimization problems in other geoscientific disciplines.

The Mass Density of Mg ii Absorbers from the Australian Dark Energy Survey

We present an all-southern sky survey for Mg ii λλ2796, 2803 doublet absorbers in 951 z < 4 active galactic nucleus/quasar spectra from the Australian Dark Energy Survey. The spectral resolution ranges from R = 1400 to 1700 over the wavelengths 3700–8800 Å. The survey has a 5σ detection completeness of 50% and above for rest-frame equivalent widths W r (2796) ≥ 0.3 Å. We studied 656 Mg ii absorption systems over the redshift range 0.33 ≤ z ≤ 2.19 with equivalent widths 0.3 ≤ W r (2796) ≤ 3.45 Å. The equivalent width distribution is well fit by an exponential function with W * = 0.76 ± 0.04 Å, and the redshift path density exhibits very little evolution. Overall, our findings are consistent with the large, predominantly northern sky, surveys of Mg ii absorbers. We developed and implemented a Monte Carlo model informed by a high-resolution Mg ii survey for determining the Mg ii mass density, ΩMg II . We found ΩMg II ∼ 5 × 10−7 with no evidence of evolution over a ∼7 Gyr time span following Cosmic Noon. Incorporating measurements covering 2.0 ≤ z ≤ 6.4 from the literature, we extended our insights into Mg ii mass density evolution from the end of reionization well past the Cosmic Noon epoch. The presented Monte Carlo model has potential for advancing our knowledge of the evolution of mass densities of metal ions common to quasar absorption line studies, as it exploits the efficiency of large low-resolution surveys while requiring only small samples from expensive high-resolution surveys.

Optimization of pulmonary artery mechanical testing

Pulmonary arterial hypertension (PAH) is an incurable disease with mortality within 3 years in 28-55% of high-risk patients. The progression of PAH has been known to be associated with increased vascular stiffness and vascular remodeling. Recent studies have suggested that increased stiffness may in fact be a driver for some of the metabolic abnormalities observed during PAH. To gain more insights into this relationship, we need to quantify the differences in mechanical properties of healthy and hypertensive pulmonary arteries. The stress-strain relationship is the gold standard for the ex-vivo stiffness measurement of arteries. This is obtained by obtaining force vs. distension data by tensile testing and using sample dimensions, i.e. length, lumen diameter, and wall thickness, to calculate engineering stress and strain. While this approach is well-optimized for large muscular arteries, it has not been used to test pulmonary arteries as their thin walls and low basal tone make it challenging to make precise measurements of sample wall thickness and lumen diameter. Thus, the goals of this study were to: 1) establish a reliable protocol for rat pulmonary artery tensile testing and 2) quantify the differences in stiffness between hypertensive and healthy pulmonary arteries. First, a methodology to improve the fidelity of determining the lumen diameter and wall thickness was developed. Using this approach, we observed that the modulus was negatively correlated with the length of the vessel segment tested. This suggests that vessel length should be standardized to perform reliable comparisons between groups. Next, we performed tensile tensing on both control and hypertensive pulmonary arteries, after standardizing vessel segment lengths. We initially modeled this tensile testing data using a one-term exponential equation and we observed that intact hypertensive arteries were ~2.7 times stiffer than control arteries at low strain (strain = 0.8). Whereas at high strain (strain = 2.8) intact and decellularized hypertensive arteries were 20 and 29 times stiffer than control arteries respectively. To better capture the viscoelastic properties of both, the cellular and ECM components of the vessels we also fit the tensile testing data using a two-term exponential equation. Using this two-term exponential model, we observed that hypertensive vessels were 2.2 times stiffer than the controls at normal hoop stress (20 kPa), and at the hypertensive hoop stress (66 kPa) the diseased vessels showed less variability in stiffness as compared to the controls. These findings and the methods developed in this study will be helpful in conducting and analyzing experiments to investigate the relationship between changes in biomechanical signals and the progression of PAH. R01HL151530 (KS), R01HL126514 (LS). This is the full abstract presented at the American Physiology Summit 2024 meeting and is only available in HTML format. There are no additional versions or additional content available for this abstract. Physiology was not involved in the peer review process.

An event-based distributed least square linear equation solver employing network flow

In this article, we study a distributed, second-order, event-triggered network flow for solving linear algebraic equations described by the form z=Hy in the sense of least squares. An undirected graph is utilized to describe the distributed computation network. In the network, each node broadcasts its dynamic states to its neighbors in an asynchronous fashion, and updates the flow at the isolated event times. We construct a specific trigger function to determine the event times, in which an exponential decay function is introduced as a comparison term. We show that if the linear algebraic equation has a unique least squares solution, all nodes states converge to this unique solution exponentially fast, when the applied network is connected and the decay rate of the comparison term satisfies certain bounds determined jointly by the topology and the linear equations information. We obtain a strictly positive lower bound on the time interval between consecutive events for time t∈[0,∞), and therefore the event-triggered system does not exhibit Zeno behavior. We provide numerical examples to verify the effectiveness of the proposed event-based network flow. In addition, we illustrate the importance of the strictly positive inter-event time interval, in comparison with the case that the inter-event time interval may converge to zero when time t goes to infinity.

Dynamic Analysis, Image Encryption Application and FPGA Implementation of a Discrete Memristor-Coupled Neural Network

This paper presents a novel discrete memristor model that incorporates exponential and absolute value functions. A discrete coupled memristor neural network model is constructed based on this memristor design. The periodic and chaotic regions of the discrete neural network model are determined using bifurcation and Lyapunov exponent spectrum. Furthermore, by varying the initial values of the discrete memristive neural network, we observe the coexistence of chaos and periodic attractors, as well as periodic attractors. Additionally, an application to color image encryption based on the discrete system model is given. Security analysis is conducted in the aspects of key space, histogram analysis, correlation analysis, sensitivity analysis, Peak Signal-to-Noise Ratio (PSNR), and information entropy analysis. The analysis results show that the algorithm has a key space size of [Formula: see text], and the information entropy of baboon graph is 7.9993, which is very close to the ideal value of 8. It shows that the image encryption algorithm is feasible and effective. Finally, the implementation of the discrete memristive neural network model is realized using Field Programmable Gate Array (FPGA). The experimental implementation is conducted using the Verilog language on the Vivado 2018.3 platform, and the obtained results align with the numerical simulation results obtained through MATLAB.

Predicting permeability coefficient in soil-rock mixtures using parameters from the negative exponential continuous grading equation

Soil-rock mixtures (SRMs) are widely utilized for embankment filling of highways in mountainous areas. The permeability characteristics of SRMs must be investigated as mountain highways are often exposed to strands of rainwater subjected to extreme rainfall. For the same species of SRM, its permeability is determined by its pore distribution and grading characteristics, which can be considered as an expression of particle grading and pore parameters. The predictive model of the SRMs permeability coefficient encompassing gradation coefficients and porosity was proposed based on the negative exponential continuous gradation equation and the Kozeny–Carman model. The applicability of the prediction model was verified based on the existing literature and performing SRMs seepage tests. The findings indicated that the permeability coefficient formula for SRMs established on the particle grading parameters and porosity was reasonable. Nevertheless, its current applicability is limited to the prediction of permeability coefficients for continuously graded SRMs. Consequently, further investigation is required to assess the suitability of the model for intermittently graded SRMs.

Analysis of basalt fiber reinforcement on static shear properties of Beibu Gulf sea sand

Basalt fibers are a reinforcing material with excellent mechanical properties and durability. In contrast, although Beibu Gulf sea sand is widely in engineering, it exhibits low strength and poor stability, which can be improved by adding basalt fibers. In this study, the effects of fiber content, fiber length, and effective confining pressure on the static shear strength of fiber-reinforced sea sand were investigated using a triaxial shear test. The maximum improvement on the static shear characteristics and deformation resistance of sea sand were achieved for a fiber content and length of 0.8% and 12 mm, respectively. The cohesion and internal friction angle of sea sand were improved and the secant modulus and strain before and after basalt fiber reinforcement showed a nonlinear attenuation tendency. The reinforcement effect coefficient R and the basalt fiber content under different dosages were in accordance with the law of the Gaussian function. The value of R conformed to a linear growth and exponential function law under different fiber lengths and effective confining pressures, respectively. This study provides a solid theoretical basis for the sustainable utilization of sea sand resources and fiber reinforcement for road and coastal protection engineering in the Beibu Gulf region.

Which is greater: eπ or πe? An unorthodox physical solution to a classic puzzle

The question of the title is a famous mathematical puzzle and can be addressed by several approaches. In this contribution, we present an alternative solution based on the second law of thermodynamics. The method can be extended to derive a more general result involving the exponential function.

Energy partitioning among compressional and shear waves in three-dimensional attenuating elastic media.

In strongly scattering elastic media without attenuation and dispersion, the wavefield is dominated by shear waves, and in three dimensions, the ratio of the S to P energy is given by ES/EP=2(vP/vS)3. This study investigates how this ratio is influenced by attenuation. Both the case of the ringdown mode, where the energy evolves from initial values, and the case of energy equilibrium, where the attenuation is balanced by energy injection sources, are treated. It is shown that in ringdown mode, the energy ratio ES/EP satisfies a Ricatti equation in time: hence, the energy ratio is not an exponential function of time. It is also shown that the long-time energy ratio differs from the value in non-attenuating media when the attenuation coefficients for P and S waves are different. In the case of energy equilibrium, the energy ratio only is equal to the value in non-attenuating media when (1) the time scale of P- and S-wave equilibration is much smaller than the attenuation time or (2) the energy injection rate for each wave type is balanced by the dissipation for that wave type. The latter situation happens when the wavefield is excited by thermal fluctuations in thermal equilibrium.

Modeling attenuation of photosynthetically active radiation across the optical gradient in the Laurentian Great Lakes with application to Lake Erie

Representation of subsurface photosynthetically active radiation (PAR) in biophysical models of the Laurentian Great Lakes (LGL) is imperative to their utility as tools for research and management. Here we consolidated measured vertical profiles of subsurface PAR with concurrent water quality (WQ) data from four LGL. We estimated the diffuse attenuation coefficient of PAR (Kd(PAR)) by fitting an exponential function to measured PAR over depth, and evaluated 68 regressions predicting Kd(PAR) as a function of water quality variables (Kd-WQ regressions). We compare four of the top cross-lake calibrated regressions against two published regressions trained on western Lake Erie (WLE) data. Then, as a case study, we demonstrate the utility of our cross-lake calibrated Kd-WQ regressions with a simplified biophysical model of Lake Erie consisting of the Finite Volume Community Ocean Model with submodules for simulating suspended sediment and dissolved organic carbon (FVCOM-SS-DOC). Twenty-five Kd-WQ regressions were identified as candidates for use in biophysical models based on their skill determined via cross-validation. WLE-trained Kd-WQ regressions were less able to simulate Kd(PAR) and PAR in more transparent waters compared to cross-lake calibrated Kd-WQ regressions, which translated to considerable differences in primary production estimates for the central and eastern basins when using WQ data simulated by FVCOM-SS-DOC. A cross-lake calibrated Kd-WQ regression was installed into FVCOM-SS-DOC, which then simulated spatial patterns of suspended sediments and Kd(PAR). These calibrated Kd-WQ regressions can be used in a variety of biophysical models across optically-distinct waters of the LGL to support adaptive management of nutrient inputs and fisheries.

Enhancing luminescence performance via adjusting the doping concentration and boron aluminum ratio in Dy3+ -activated barium-boroaluminosilicate glasses for laser and W-LED applications

A series of barium-boroaluminosilicate [30SiO2-11Al2O3-44B2O3-5BaO-(10-x)K2O-xDy2O3 (with x = 0.25, 0.5, 0.75, 1.0, 1.25, 1.5 mol%)] glasses doped with Dy3+ ions were prepared by the high temperature (melt quenching) method. In the glass matrix, the relationship among structure, luminescence properties, and B/Al ratio was analyzed; also studied are the physical properties of glass and influence of Dy3+ concentration on the luminescence properties. Differential Scanning Calorimeter (DSC) results have shown the glass matrix exhibiting good thermal stability and high resistance to crystallization. FTIR and Raman spectra have confirmed the presence of stretching and bending vibrations of [BO3], [AlO4] and [SiO4] structural units in the prepared glass. The observed UV–Vis–NIR spectra have indicated that the existence of thirteen bands corresponding to the transition Dy3+ ions from 6H15/2 level to different excited levels; the transmittance curves obtained have shown the transmittance up to 91 %. Increase in Dy3+ concentration is found to decrease the optical band gap; the calculated Judd-Oflet parameter is found to follow the trend Ω2＞Ω4＞Ω6. Photoluminescence studies have shown three emission peaks which could be associated to the transitions: 4F9/2 → 6H15/2 (blue light), 4F9/2 → 6H13/2 (yellow light), and 4F9/2 → 6H11/2 (red light); the maximum intensity obtained for the glass with x = 0.75 mol%, with spacing between Dy3+ ions being 1.9137 Å; and the decay curve could be fitted with double exponential function. The CIE results have revealed that the chromaticity coordinates are closer to that of standard white light, and the color temperature located in the region of cold white light.

National variability in soil organic carbon stock predictions: Impact of bulk density pedotransfer functions

Accurate soil organic carbon storage (SOCS) estimation is crucial for sustaining ecosystem health and mitigating climate change impacts. This study investigated the accuracy and variability of SOCS predictions, focusing on the role of pedotransfer functions (PTFs) in estimating soil bulk density (BD). Utilizing a comprehensive dataset from the Korean Rural Development Administration (RDA database), which includes 516 soil horizons, we evaluated 36 widely-used BD PTFs, well-established formulas that estimate BD by considering soil properties, including soil organic carbon (SOC), soil organic matter (OM), sand, gravel, silt, and clay. These PTFs demonstrated varying levels of precision, with root mean squared errors (RMSE) ranging from 0.177 to 0.377 Mg m−3 and coefficients of determination (R2) from 0.176 to 0.658; hence, the PTFs have been classified into excellent, moderate, and poor-performing groups for predicting BD. Further, a novel PTF based on an exponential function of SOC was developed, showing superior predictive power (R2 = 0.73) compared to existing PTFs, using an independent validation dataset. Our findings reveal significant differences in SOCS predictions and observations among the PTFs, with a p-value <0.05. The highest concentrations of SOCS were noted in forest soils, considerably above the national average, highlighting the importance of tailored soil management practices to enhance carbon sequestration. These findings are crucial for refining PTF precision to improve the accuracy of national SOCS estimates, supporting effective land management and climate change mitigation strategies.

A prediction model for residual shear strength of liquefiable soil based on lateral spreading cases

The residual shear strength of liquefiable soil plays an important role in evaluating the displacement magnitude of lateral spreading when applying the Newmark sliding block method. Currently, the empirical model is a mainstream alternative method for estimating the residual shear strength. In this study, a database of well-documented lateral spreading cases is used to establish an exponential function for residual shear strength evaluation correlated with the vertical effective stress and normalized standard penetration test blow counts for liquefied soil. A comparative analysis with two other empirical models is conducted, and the lateral spreading of the Wildlife Site during the Superstition Hills earthquake in 1987 is estimated using the Newmark sliding block method. The model exhibits good performance for soil residual shear strength estimation in cases of liquefaction-induced lateral spreading. The average estimated value of the residual shear strength may be appropriate for deterministic analyses in engineering practice.