Exponential Relationship Research Articles

Aridity regulates the impacts of multiple dimensional plant diversity on soil properties in the drylands of northern China

Relationships between plant diversity and soil properties are important for restoring ecosystem function to adapt climate change in drylands. Taxonomic, functional and phylogenetic diversity are widely used for understanding community assembly and the responses of plant communities to environmental change. However, one dimension of diversity index is difficult to reflect the multiple dimensional plant diversity, and their effects on soil properties (i.e., moisture, nutrients, and texture characteristics) along aridity gradient in drylands are limitedly understood. In this study, we proposed a holistic biodiversity (HB) index to integrate all the characteristics of plant diversity, and investigated the relationships between plant diversity and soil properties across 41 sites along aridity gradient (from hyperarid to arid and semiarid levels) in drylands of northern China. The results showed that the taxonomic diversity and phylogenetic diversity increased significantly while most of functional diversity indices did not differ significantly along the aridity gradient. The functional diversity was more important than taxonomic and phylogenetic diversity to plant communities, and the importance of taxonomic and phylogenetic diversity varied greatly and inversely along the aridity gradient. The HB index could much better reflect the positive or negative exponential relationships with soil properties compared to the single diversity index. Further, the aridity weakened the positive effects of plant diversity on several soil properties (including soil water content, soil organic carbon and soil total nitrogen), and indirectly strengthened the accumulation of soil total phosphorus, as well as intensified the soil coarsening by limiting the negative effects of plant diversity on soil sand content. Our findings suggest that the holistic biodiversity index can represent the overall traits of plant diversity in drylands, and guide a further step to understand the role of plant diversity in plant-soil relationships of dryland ecosystems.

A Novel Method for Estimating the Undrained Shear Strength of Marine Soil Based on CPTU Tests

The undrained shear strength is an essential parameter in the foundation design of marine structures. Due to the complex marine environment and technical limitations, it is difficult and costly to obtain offshore samples. Piezocone penetration tests (CPTU) are relatively low-cost compared to drilling and sampling methods. Therefore, based on the soil behavior type index (Ic) derived from CPTU results, a model for estimating cone factors (Nkt, Nke) is proposed to improve the accuracy of estimation of undrained shear strength. The result shows that the soil behavior type index (Ic) and cone factors take on a negatively correlated exponential relation. Incorporating a cone factor that varies with the soil behavior type index (Ic) significantly enhances the accuracy of undrained shear strength predictions compared to the conventional method of using a constant cone factor. This approach reduces the root mean square error (RMSE) for Nkt (Nke) from 0.124 (0.126) MPa to 0.056 (0.06) MPa, and the mean absolute error (MAE) from 0.0154 (0.016) MPa to 0.0032 (0.0036) MPa. The method was validated at an additional location and the predictions were in high agreement with the results of the consolidated quick direct shear test. The developed method can serve as an effective tool used in the design of foundations of marine structures.

Enhanced humidity sensing performance of a triple-electrode ionization sensor utilizing carbon nanotubes

This paper introduces a novel ionization humidity sensor featuring a carbon nanotube triple-electrode design, aimed at achieving sensitivities of 381.67 %RH−1 in nitrogen and 11.83 %RH−1 in air, a detection ranges from 25.8 % RH to 100 % RH in nitrogen and 30 % RH to 100 % RH in air, and response times of 11 s and recovery times of 5 s. The sensor leverages the exponential relationship between collecting current and relative humidity, enhanced by the exceptional adsorption properties of CNTs, particularly their large surface area which allows for efficient water molecule attraction, to offer superior performance across diverse detection environments. Two structural configurations are proposed to optimize the sensor’s efficiency: one integrating carbon nanotubes directly onto the cathode and another utilizing a silicon strip as a substrate for CNT growth. The design’s effectiveness is further validated through simulations that calculate electron distribution, positive ion concentration, and collected current, highlighting the sensor’s potential for high-precision humidity detection in real-world applications.

Echo characteristics of pulsed lasers in non-uniform smoke environments

This work establishes a pulsed laser backscattering echo signal model based on an improved semi-analytical Monte Carlo method. The developed model is applied in non-uniform smoke environments to mitigate the smoke interference of laser fuzes for ground proximity detection. The model considers variations of the photon step size according to the concentration of the smoke environment, and the computational speed is accelerated by implementing an improved semi-analytical reception method. The proposed echo signal model is employed to investigate the effects of smoke-related parameters and laser detection system parameters on the backscattering echo waveform of smoke. Finally, the model is validated based on experiments. The results show that the intensity of the smoke backscattering echo and the emission pulse width approximately conform to a logarithmic relationship. Specifically, the echo intensity is positively correlated with the emission pulse width, and the ratio of the time between the rising edge and the falling edge of the echo signal is positively correlated with the pulse width. Meanwhile, the intensity of the smoke backscattering echo and the distance between the transmitter and receiver approximately adopt an exponential relationship. Herein, we describe the characteristics of a laser backscattering echo in a non-uniform smoke environment. The results can guide future research regarding laser fuze detection methods and strategies relevant for ground targets in smoke environments.

INVESTIGATION OF THE EFFECT OF GEOMETRIC IRREGULARITIES ON CAPACITY OF TRAFFIC CIRCLES BY USING PARTIAL LEAST SQUARE REGRESSION METHOD

This paper examined the impact of geometric irregularities on the intersection capacity at traffic circles. A new empirical capacity relation was proposed to predict the capacity of the traffic circle as a function of geometric elements, exit and circulating flows. Within this scope, firstly, the relationship between the vehicles entering from the minor approach and the circulating flow from the turning movement in the traffic circle was examined based on the K-Means cluster analysis method. The analysis was created in accordance with an exponential relationship between entry and circulating flow. Secondly, two clusters were selected by the partial least squares regression method to improve the model's effectiveness. Lastly, to validate the model, "leave-one-out" cross validation was used to select the components that maximize the model's predictive ability. The results show that geometric parameters of a traffic circle create different effects on capacity, especially in different circulating flow conditions.

Microstructure and damage characteristics of cement mortar with different aggregate sizes after cooling based on nuclear magnetic resonance technology

This article studies the effects of cooling methods and aggregate sizes (particle size: 0.63–1.25 mm, 1.25–2.5 mm, 2.5–5.0 mm, 5.0–10.0 mm) on the microscopic properties and damage characteristics of cement mortar specimens. After heating the specimens to 400 °C, air cooling (cooling in air as a whole, A), water cooling (cooling in water as a whole, W), and semi-water cooling (half in air and the other half in water, AW) cooling methods are applied. The T2 spectrum, magnetic resonance imaging (MRI), permeability and P-wave velocity of the specimens were tested by low-field nuclear magnetic resonance (NMR), pulse pore permeability tester and digital acoustic wave instrument, respectively. The effect of cooling method and aggregate size on pore size distribution and fractal characteristics, permeability and tortuosity, P wave and damage degree of cement mortar specimens were studied. The relationship between MRI pixel value and damage degree was deeply explored. The results show that the average permeability and MRI pixel value increase after high temperature, and the pore tortuosity decreases. The mass loss rate, the increase of the most probable pore size and the increase of the pore volume are negatively correlated with the aggregate size, and the permeability ratio, the decrease of the tortuosity and the damage degree are positively correlated with the aggregate size. At the same time, the influence of cooling method on mass loss rate, porosity and permeability from large to small is: A, AW, W, while the decrease rate of pore tortuosity from large to small is: AW, W, A. The most probable pore size and pore volume change most obviously after high temperature treatment of W and AW. In addition, with the increase of aggregate size, the fractal dimension increases under air cooling, and the U-shaped change with W2.5 particle size as the threshold decreases first and then increases under semi-water cooling. Finally, there is a good exponential relationship between the average ratio of MRI pixel values and the damage degree, and the damage degree of the sample can be obtained by the average ratio of MRI pixel values.

SHM data compression and reconstruction based on IGWO-OMP algorithm

The long-term operating structural health monitoring (SHM) system generates massive monitoring data, whose transmission and storage are challenging tasks. To address this issue, this study proposed an improved grey wolf optimizer-orthogonal matching pursuit (IGWO-OMP) algorithm for SHM data compression and reconstruction. The effectiveness of the proposed algorithm was validated using four SHM datasets including ultrasonic guided wave (UGW), acceleration, and audio signals. Firstly, the optimization results of IGWO were compared with those of other classical algorithms to verify its superiority in reconstruction accuracy. Secondly, the reconstruction accuracy under various compression factors was investigated and the optimal compression factor was determined. Finally, the relationship between reconstruction accuracy and signal sparsity as well as the performance of IGWO-OMP in dealing with noise-containing signals were discussed. The results demonstrate the generalizability and excellent noise robustness of IGWO-OMP in SHM data compression and reconstruction. Compared with other optimization algorithms, IGWO exhibits the best global optimal solution searching ability and obtains the reconstructed signal closest to the original one. Comprehensively considering the compressed signal length, reconstruction accuracy and computational efficiency, the optimal compression factor is suggested to be 0.2. In IGWO-OMP, the signal reconstruction accuracy is related to its sparsity, the variation of the CCD index for the reconstructed signal with relative sparsity follows an exponential growth relationship.

Investigating the dynamics of water–sand mixing inrush in viscous sand layers: insights from laboratory experiments

The geological hazard of water–sand inrush is a matter of concern for infrastructure construction and resource exploration activities in China, due to the complex interplay between groundwater dynamics and the stability properties of sand particles. This phenomenon is characterized by its intensity, hazardous nature, and unpredictable behavior. Following comprehensive analysis, this study identifies the critical factors influencing water–sand inrush processes as fissure width, water stress (waterhead height), in-situ sand ground stress within the sand stratum, and clay content. To investigate these factors experimentally, a custom-designed hydraulically coupled water–sand inrush test apparatus was used. The apparatus was equipped with a cylinder to apply ground stress, a pneumatic diaphragm pump to regulate water stress, and a bottom opening in the sand layer. Tests were conducted to investigate the dynamic response of water–sand inrush events under various combinations of factor levels. The findings revealed that the critical value for inrush is only present in the fissure width, which was observed to be 3 mm for the tested sand material. Unlike fissure width, the other factors do not have definitive critical values but instead modulate the intensity of the inrush process without determining its occurrence. The ‘inrush rate’ serves as a measure of the severity of water–sand inrush disasters and shows a linear increase with both increasing groundwater stress and fissure width, a negative exponential function relationship between the inrush rate and the clay content. Notably, ground stress does not exert a significant influence on the intensity of the inrush process itself. Under constant conditions, the inrush rate remains relatively constant across different levels of sand ground stress, for instance, in the experiments, the inrush rate was measured at 1.606 kg/s when the water stress was 0.1 MPa and the fissure width was 5 mm. Grey relation analysis was used to examine the sensitivity of each factor’s influence on the inrush rate. The results showed that water stress has the greatest impact on the intensity of water–sand inrush, followed by ground or soil stress, clay content, and the width of the fissures in the sand layer.

Mesoscale fracture simulation of recycled aggregate concrete under uniaxial compression based on cohesive zone model

It is important to clarify the uniaxial compressive mechanical properties and fracture mechanism of recycled aggregate concrete (RAC) from a mesoscale perspective for its further application in engineering. In this study, the cohesive zone model (CZM) based on the Benzeggagh–Kenane (B–K) criterion was used to simulate the RAC's complex fracture behavior. Meanwhile, the effects of cohesive element parameters and mechanical properties of mesoscale components on macroscopic mechanical properties and damage modes of RAC were investigated. The results show that the CZM based on the B–K criterion can be used to characterize the whole fracture process of RAC. The RAC's compressive strength has an exponential relationship with the shear strengths of the mortars as well as the ITZs and is quadratically related to the logarithm of cohesive element stiffness. The RAC's damage morphology is more sensitive to the change of element stiffness, Mode II fracture energy and hybrid fracture energy ratio.

Analysis of pore-fracture structure evolution and permeability in tar-rich coal under high-temperature pyrolysis using μCT technology

To study the internal evolution characteristics of tar-rich coal under high-temperature pyrolysis and improve pyrolysis efficiency, three-dimensional reconstruction and analysis of tar-rich coal from northern Shaanxi after high-temperature pyrolysis were conducted using μCT technology. The evolutionary development of pore and fracture structure at different temperatures and the relationship between pore-fractures and permeability was studied and discussed. The results show that when tar-rich coal from 300 to 600 °C, it mainly undergoes two stages: in the first stage, the internal substance structure of the coal mainly undergoes thermal cracking, forming large fracture bands; in the second stage, the coal undergoes intense pyrolysis reactions, resulting in primarily circular or elliptical large pore structures within the coal, with a reduction in the number of fractures. Furthermore, a strong exponential relationship is exhibited between the porosity and permeability of tar-rich coal, and a predictive equation is provided. When the temperature exceeds 500 °C, the coupled effect of pores and fractures contributes more than 20% to permeability, and its impact cannot be ignored.

A superhydrophobic coating prepared by carbonated fly ash: Properties and mechanism

In this paper, carbonated fly ash (CFA) was prepared by aqueous carbonation of fly ash (FA) and carbide slag (CS) with CO2. It was bonded with room-temperature vulcanized rubber (RTV) to fabricate a superhydrophobic coating. The wettability, self-cleaning property, surface lyophobicity and water absorption of cement mortar coated with CFA/RTV coating were investigated. Then, the morphology and roughness of CFA, and quantity of nano CaCO3 product were characterized. Meanwhile, the effects of carbonation conditions (CS content, temperature, pH) on the performance of CFA/RTV coating were evaluated. The results showed that CaCO3 produced on CFA surface increased with CS content increasing. Although hydrophobicity was increased as CS content was up to 10 %, it decreased when CS content was more than 10 %. Temperature increased from 20 °C to 60 °C barely affected CaCO3 amount, surface roughness, wettability and water absorption of CFA/RTV coating. CFA/RTV coating carbonated at pH 7 formed the most CaCO3, and had the highest surface roughness, hydrophobicity and resistance to water absorption of coating. The carbonation condition of 10 % CS content, 20 °C carbonization temperature and pH 7 was optimal to obtain the largest contact angle (CA) of 161.2° and surface roughness of 478 nm. The mechanism of hydrophobicity (contact angle and sliding angle) for CFA/RTV coating was strongly associated with surface roughness in an exponential relationship. Moreover, the trend of resistance to water absorption was consistent with hydrophobicity of the coating. The developed superhydrophobic CFA/RTV coating had remarkable properties of self-cleaning, surface lyophobicity and resistance to water absorption.

Ultrasonic velocity anisotropy of Jurassic shales with different lithofacies

Abstract Given the growing importance of organic-rich shale as unconventional reservoirs, a thorough understanding of the elastic and anisotropic behavior of shales is of great concern. However, for lacustrine shales, the complex lithofacies assemblage with geological deposition makes it challenging. Four lithofacies (argillaceous, mixed, siliceous, and calcareous) are recognized for 40 lacustrine shale samples from Jurassic formation in Sichuan Basin on the basis of their mineral compositions. We perform ultrasonic velocity measurements on 40 pairs of shale plugs at varied confining pressures, attempting to uncover the controls on the anisotropic properties of different lithofacies. The experimental results reveal that the total porosity, clay, and organic matter would positively contribute to velocity anisotropy of Jurassic shales. Combined with microstructure and pressure-dependent velocity analysis, the preferred orientations of platy clay particles and lenticular kerogen, the development of clay pores along clay fabric, and the sub-parallel micro-cracks induced by hydrocarbon expulsion are treated to be the controlling mechanisms. We add the total porosity, clay content, and kerogen volume together, intending to distinguish the elastic and anisotropic properties of four lithofacies. Generally, argillaceous shales, the dominant lithofacies in Jurassic formation, could be characterized by the highest clay and total organic content (TOC), the lowest bedding-normal velocities, and the strongest velocity anisotropy. Finally, with the laboratory data, two rock-physics-driven exponential relationships are proposed to predict the P- and S-wave velocity anisotropy with the bedding-normal velocities.

Flexibility evaluation of psammophytes using Young’s modulus based on 3D numerical simulation

Flexible psammophytes play an important role in controlling soil wind erosion and desertification, owing to their characteristics. Although flexibility of psammophytes has been considered in previous studies, the interaction between flexible psammophytes and the surrounding airflow field still remained unclear. In this study, we used the Young’s modulus to describe plant flexibility and conducted a 3D computational fluid dynamics simulation using a standard k-ε model and a fluid–structure interaction model. Taking Caragana korshinskii (Caragana), a typical psammophyte, as the research object, we constructed 3D geometric models with different diameters to simulate the airflow field around the flexible psammophytes. By comparing with the simulation results of rigid plants and simulation results of flexible plants at different wind speeds, we could verify the rationality of the simulation method. Based on the simulation results, the maximum swing amplitude of the model and the Young’s modulus were found to have a negative correlation, presenting an exponential functional relationship with good fitting. The relationship between the actual Young’s modulus of the plant branches and that of different diameter models in the numerical simulation was also established. This study is expected to improve our basic understanding of the interaction between flexible psammophytes and the surrounding airflow field, and provide some qualitative reference for the numerical simulation of the airflow field around flexible psammophytes.

Methods for estimating entropy and analyzing sectoral development of the economy

Aim. To substantiate the method of estimating the entropy of the sectoral structure of the economy and on this basis to develop methods of analyzing its sectoral development.Objectives. To define the essence of sectoral entropy of socio-economic systems; to consider the approaches to its assessment and the relationship between the entropy of industries and average per capita gross domestic product (GDP) with the structure of value added of industries of the economy.Methods. To achieve the set goals, the general scientific methods of analysis, synthesis, comparison, generalization, as well as methods of statistical data processing were applied.Results. The expediency of using a probabilistic approach to the estimation of entropy of homogeneous economic structures, which with their development changes according to the exponential law, is substantiated. The position that it is reasonable to estimate the entropy of a homogeneous structure by the averaged sum of entropies of its elements has been argued. The boundary values of the entropy of a homogeneous structure are established. The exponential relationship between the entropy of industries and average GDP per capita and the structure of value added of industries, industry entropy and the share of net taxes on production and imports in the GDP structure has been determined.Conclusions. The identified features of sectoral development of the economy constitute a theoretical and methodological basis, which allows us to establish the significance of influencing factors. This is necessary for sectoral regulation of the economy.

Critical radius prediction for small radius curved section of two-lane secondary highways based on speed characteristics

Small radius curved sections of two-lane secondary highways have low technical indicators, complex alignments, and frequent accidents. In order to improve the safety of traffic operation, the article investigates the curved sections of two-lane secondary highways with different radii and obtains the travelling speeds of different vehicle types at different section locations. By studying the trajectory characteristics and speed characteristics of vehicles travelling in curves, the velocity difference ratio, which responds to the continuity of driving speed, was defined. Then, based on this, this paper investigates the vehicle motion law of small radius curved road sections. The results show that the speed change of large cars in small radius curves is similar to a “U" shape, while the speed change of small cars is similar to a “V" shape. The speed adjustments of the larger cars occur mainly within the range of gentle curves, whereas the speed changes of the smaller cars are large throughout the range of curves. There is a significant exponential function relationship between curve radius and 85 % percentile speed, from which the curve radius threshold can be predicted. This provides a basis for engineering construction of curved road sections and optimization of curve design indicators, which greatly improves the traffic safety level of curved road sections.

Threshold pressure gradient in fractured reservoirs: Experimental simulation and mathematical modeling

Aiming to solve the problems of unclear fluid flow laws and controlling factors in fractured reservoirs, as well as the lack of a mathematical model of threshold pressure gradient (TPG) considering fracture structural parameters, research on the structural characterization of fractured reservoirs, physical simulation of fluid flow, and TPG prediction models has been carried out. Physical simulations demonstrate that fluid flow in fractured reservoirs under stress is nonlinear and exhibits TPG. The TPG displays a significant positive exponential relationship with confining pressure and water saturation. As the confining pressure or water saturation increases, the effective opening of fractures decreases. The TPG will increase dramatically when the fracture opening decreases to the critical thickness for the rapid increase in TPG. On the basis of the fluid flow law study, the TPG fractal prediction model is further developed based on fractal dimension of fracture length distribution (Df), fractal dimension of tortuosity (DT), water saturation (Sw), maximum fracture width (wmax), limit shear stress (η0), and sample characteristic length (L0). The results predicted by the model show good agreement with physical simulations (with average relative error of 7.56%). Experimental simulation and mathematical modeling of TPG in fractured reservoirs can reveal the fluid flow mechanism and improve the accurate evaluation of production capacity during different development processes.

Investigating parameters and ultimate load-bearing performance of novel anchor-box type cable–girder anchoring structure for large-span cable-stayed bridges

This study combined experimental research and finite element numerical simulations to investigate the ultimate bearing performance of a novel anchor-box-type cable–girder anchorage structure for large-span cable-stayed bridges. The stress distribution and deformation in the structure was assessed under varying loads, and the effects of the construction parameters on peak stress in key load-bearing welds were analyzed. The proposed design exhibits a safety margin of 3.2. The simulated and experimental stress distributions agree well with experimental data, although deformation and load-bearing capacity results are non-conservative. The maximum stress in the main load-bearing welds exhibits an exponential relationship with construction parameters.

Effect of waste oyster shell powder on the micro- and macroproperties and sustainable performance of cement-based materials

A large amount of oyster shell waste is generated globally every year. Proper disposal of discarded oyster shells is crucial for reducing environmental pollution and achieving sustainable development. The aim of this paper was to study the feasibility of using waste oyster shells as a cementitious material to replace cement. The effects of waste oyster shell powder (OSP) with different water–binder ratios (w/b = 0.5, w/b = 0.2) and different substitution rates (10 %, 20 %) on the properties of cement-based materials were studied. The experimental results are as follows: The addition of oyster shell powder reduces the compressive strength, ultrasonic pulse velocity (UPV), surface electrical resistivity and cumulative heat of hydration of the mortar, but the strength loss is smaller for a water-to-binder ratio of 0.2 than for a water-to-binder ratio of 0.5. A good linear relationship between the compressive strength and UPV was also found. A good exponential relationship exists between the surface electrical resistivity and compressive strength. The heat of hydration results show that when the water–binder ratio is 0.5, replacing cement with waste OSP promotes aluminate phase hydration and advances the acceleration period. Finally, the carbon emissions of the mortar were normalized according to the compressive strength, and using OSP instead of cement at a low water–binder ratio was more conducive to reducing CO2 emissions.

Transferability of Buckingham Parameters for Short-Range Repulsion between Topological Atoms.

The repulsive part of the Buckingham potential, with parameters A and B, can be used to model deformation energies and steric energies. Both are calculated using the interacting quantum atom energy decomposition scheme where the latter is obtained from the former by a charge-transfer-based energy correction. These energies relate to short-range interactions, specifically the deformation of electron density and steric hindrance, respectively, when topological atoms approach each other. In this work, we calculate and fit the energies of carbonyl carbon, carbonyl oxygen, and, where possible, amine nitrogen atoms to the repulsive part of the Buckingham potential for 26 molecules. We find that while the steric energies of all atom pairs studied display exponential behavior with respect to distance, some deformation energy data do not. The obtained parameters are shown to be transferable by calculating root-mean-square errors of fitted potentials with respect to energy data of the same atom in, as far as possible, all other molecules from our data set. We observed that 36% and 10% of these errors were smaller than 4 kJ mol-1 for steric and deformation energy, respectively. Thus, we find that steric energy parameters are more transferable than deformation energy parameters. Finally, we speculate about the physical meaning of the A and B parameters and the implications of the strong exponential and exponential-linear piecewise relationships that we observe between them.

Understanding the effect of cathodic reaction on corrosion-enhanced erosion in sand-entraining electrolyte

In this study, the pure erosion behaviour of pure iron and its erosion-corrosion behaviour under different anodic polarization currents were investigated in various cathodic reactions (oxygen reduction, hydrogen ion reduction, and water reduction) using a cylindrical stirring system. The corrosion-enhanced erosion (C-E) rates were determined for each condition. The results revealed that pure iron displayed similar pure erosion behaviour across all three cathodic reactions. When the cathodic reactions involve hydrogen ion reduction or water reduction, the erosion-corrosion of pure iron manifested as uniform damage, with the reduction in hardness being the main cause of the C-E in this case. Conversely, in the case of oxygen reduction reaction as the cathodic reaction, the erosion-corrosion presented as pitting damage, with the reduction in hardness resulting from localized concentration of anodic current and the formation of easily worn protruding flaky iron structures at the edges of the pits as the main mechanism of the C-E. Moreover, linear and exponential relationships were found between the C-E rate and the anodic current density for uniform damage and pitting damage, respectively. Finally, the concept of surface equivalent hardness was proposed, along with the establishment of a mathematical model for surface equivalent hardness based on the relationships between the C-E rate and the anodic current density. Utilizing the surface equivalent hardness enables the evaluation of the erosion rate on material surfaces considering the coupled effect.