Self-similar Characteristics Research Articles

Unsupervised Ground Roll Attenuation via Implicit Neural Representations

Coherent noise attenuation presents a significant challenge compared to incoherent noise, particularly concerning ground roll in land seismic data. Traditional methods encounter limitations with the substantial overlap of ground roll and reflections, resulting in a compromise between signal distortion and residual noise. Recent deep learning strategies, while promising, predominantly rely on supervised learning, necessitating extensive paired training#xD;data, which is frequently scarce in real-world scenarios. Unsupervised approaches often struggle with convergence issues or excessive parameter tuning. We introduce an unsupervised deep learning framework for separating reflections from ground roll to address these hurdles. Leveraging the inherent low-frequency bias of implicit neural representations (INR), our method prioritizes extracting self-similarity features during training. For seismic data, the network learns self-similarity flattened events before those with deep dips and other incoherent noise. To enhance the self-similarity of reflections, we first apply normal moveout (NMO) correction to flatten reflections and then use the network to extract these flattened reflections from the NMO-corrected data. Moreover, to ensure convergence, we integrate a horizontal derivative regularization term into the loss function, penalizing horizontal variations. This regularization prevents the extraction of unflattened events through extended training, ensuring convergence with high fidelity of flattened reflections. It additionally streamlines parameter tuning, yielding stable outputs and obviating the need for early stopping. We validate our method using synthetic and real land data examples, comparing it with traditional f-k filters with real data and demonstrating its superiority in noise attenuation and signal preservation.

Unsupervised cervical cell instance segmentation method integrating cellular characteristics.

Cell instance segmentation is a key technology for cervical cancer auxiliary diagnosis systems. However, pixel-level annotation is time-consuming and labor-intensive, making it difficult to obtain a large amount of annotated data. This results in the model not being fully trained. In response to these problems, this paper proposes an unsupervised cervical cell instance segmentation method that integrates cell characteristics. Cervical cells have a clear corresponding structure between the nucleus and cytoplasm. This method fully takes this feature into account by building a dual-flow framework to locate the nucleus and cytoplasm and generate high-quality pseudo-labels. In the nucleus segmentation stage, the position and range of the nucleus are determined using the standard cell-restricted nucleus segmentation method. In the cytoplasm segmentation stage, a multi-angle collaborative segmentation method is used to achieve the positioning of the cytoplasm. First, taking advantage of the self-similarity characteristics of pixel blocks in cells, a cytoplasmic segmentation method based on self-similarity map iteration is proposed. The pixel blocks are mapped from the perspective of local details, and the iterative segmentation is repeated. Secondly, using low-level features such as cell color and shape, a self-supervised heatmap-aware cytoplasm segmentation method is proposed to obtain the activation map of the cytoplasm from the perspective of global attention. The two methods are fused to determine cytoplasmic regions, and combined with nuclear locations, high-quality pseudo-labels are generated. These pseudo-labels are used to train the model cyclically, and the loss strategy is used to encourage the model to discover new object masks, thereby obtaining a segmentation model with better performance. Experimental results show that this method achieves good results in cytoplasm segmentation. On the three datasets of ISBI, MS_CellSeg, and Cx22, 54.32%, 44.64%, and 66.52% AJI were obtained, respectively, which is better than other typical unsupervised methods selected in this article.

Dynamics of droplet adsorption by liquid film on a grooved surface

Understanding the dynamics of droplet adsorption by liquid film on a grooved surface is of great significance for the possible manipulation of dropwise condensation on the grooved surface. In this study, an improved phase-field lattice Boltzmann model is proposed to describe the process of droplet adsorption from the ridge to the liquid film within the channel. The results indicate that the leading edge of the droplet undergoes two accelerations during the adsorption process, obeying the power law of and , respectively. The adsorption process between droplets with different sizes and the liquid film exhibits self-similarity characteristics including the same first peak velocity, the similar droplet displacement-time curve and the equal dimensionless spreading length of . Decreasing the contact angle of the droplet from to accelerates the displacement of the leading edge and extends the spreading length. These findings may help reveal the mechanics of droplet adsorption by the liquid film on the grooved surface and thus manipulate the condensation behavior for the heat transfer enhancement.

Stone inscription image segmentation based on Stacked-UNets and GANs

To overcome the challenges posed in effectively extracting stone inscriptions characterized by highly self-similarity between the foreground and background, a character image segmentation framework is proposed that integrates Stacked-UNets and Generative Adversarial Networks (GANs). Initially, a convolutional rule tailored for self-similar feature extraction is introduced to enhance the image detail segmentation. Subsequently, in improving the stacked units, multi-scale character masks with Spatial Transformer Network (STN) are added to guide the character segmentation. Finally, with two GANs and datasets, the character recognition and generation capabilities of the Stacked-UNets are trained, and further constructing its character segmentation and restoration abilities. Ultimately, the edge segmentation performance was enhanced, both in extracting characters from stone inscriptions with self-similar blocks and in effectively recovering partially incomplete characters. Compared to state-of-the-art methods, the Stacked-UNets demonstrates improvements of 6.41%, 7.39%, 8.43%, 8.11%, 4.13%, and 2.58% across six indicators, respectively.

Robust unsupervised 5D seismic data reconstruction on regular and irregular grids

Seismic data reconstruction has become a central focus in seismic data processing, addressing challenges posed by sparse sampling due to physical and budgetary constraints. The advent of 5D acquisition methodologies marks a significant advancement in the quality and completeness of seismic data sets. Most traditional 5D reconstruction methods commonly use the fast Fourier transform (FFT), requiring regular grids and preliminary 4D binning before 5D interpolation. Discrete Fourier transform and nonequidistant FFT can honor the original irregular coordinates. However, when using exact locations, these methods become computationally expensive. We introduce an unsupervised deep-learning methodology to learn a continuous function across the sampling points in seismic data, facilitating reconstruction on regular and irregular grids. The network comprises a multilayer perceptron with linear layers and element-wise periodic activation functions. It excels at mapping the input coordinates to the corresponding seismic data amplitudes without relying on external training sets. The network’s intrinsic low-frequency bias is crucial in prioritizing acquiring self-similar features over high-frequency and incoherent ones during training. This characteristic mitigates incoherent noise in seismic data, such as random and erratic components. To assess the robustness of the unsupervised reconstruction technique, we conduct comprehensive evaluations using synthetic data examples sampled regularly and irregularly, as well as field-data examples with and without binning. The findings demonstrate the efficacy of our deep-learning framework in achieving resilient and accurate seismic data reconstruction across diverse sampling scenarios.

Parametric study of free turbulent slurry jet: influence of particle size and particle concentration on the flow dynamics and thermal behavior of high-speed slurry jet

A detailed computational investigation was conducted to explore the dynamics of high-speed free slurry jets, with a focus on how variations in abrasive size and concentration affect their behavior. The study yielded several significant observations: Firstly, it was observed that slurry jets containing larger particles exhibited notably higher average velocities, attributed to their inherent self-similar characteristics. Specifically, at the far field of the jet, slurry jets with larger particle sizes demonstrated a 15% increase in velocity compared to those with smaller particles. Additionally, an analysis of turbulent intensity revealed that beyond a certain axial distance (x/D = 10), turbulence levels progressively increased. However, intriguingly, for slurry jets with a high concentration (Co = 15%), there was a notable decrease (28%) in turbulent intensity compared to water jets, indicating a complex interplay between particle size and concentration. Secondly, the study found that as the concentration of particles in the slurry jet increased, there was a corresponding rise in the bulk temperature of the jet. This phenomenon was primarily attributed to the heightened thermal conductivity resulting from the increased density of particles in the water. Furthermore, an examination of the Nusselt number revealed interesting trends. While the Nusselt number exhibited a peak near the nozzle exit, indicative of enhanced heat transfer in this region, it showed a decremental trend along the axial direction of the jet, attributable to jet divergence. In summary, the computational analysis provided valuable insights into the behavior of high-speed slurry jets, highlighting the intricate relationships between abrasive size, concentration, velocity distribution, and thermal characteristics. These findings contribute to a deeper understanding of slurry jet dynamics and have significant implications for various industrial applications.

Non-Stationary ETAS Model: How It Works for External Forcing

Abstract The stationary epidemic-type aftershock sequence (ETAS) model is based on the important empirical laws in aftershock statistics with a self-similar feature, and is therefore useful for the statistical analysis of many common earthquake occurrence series. However, because earthquake catalogs become richer, the non-stationarity arising from geophysical heterogeneity becomes more pronounced. This article discusses the utility of a model that assumes time dependence of the first two ETAS parameters, which are sensitive to the short-term prediction. The inversion analyses of the non-stationary ETAS model in this article show heuristic results for swarm earthquakes and complex mainshock–aftershock-type seismicity. The case studies demonstrate how these parameters change quantitatively in swarm seismicity associated with slow slips, increases in pore-fluid pressure such as magma and hydrothermal fluids, stress changes associated with an earthquake motion, and interseismic-induced effects due to geological properties.

Pavement Crack Detection Using Fractal Dimension and Semi-Supervised Learning

Pavement cracks are crucial indicators for assessing the structural health of asphalt roads. Existing automated crack detection models depend on large quantities of precisely annotated crack sample data. The irregular morphology of cracks makes manual annotation time-consuming and costly, thereby posing challenges to the practical application of these models. This study proposes a pavement crack image detection method integrating fractal dimension analysis and semi-supervised learning. It identifies the self-similarity characteristics within the crack regions by analyzing pavement crack images and using fractal dimensions to preliminarily determine the candidate crack regions. The Crack Similarity Learning Network (CrackSL-Net) is then employed to learn the semantic similarity of crack image regions. Semi-supervised learning facilitates automatic crack detection by combining a small amount of labeled data with a large volume of unlabeled image data. Comparative experiments are conducted on two public pavement crack datasets against the HED, U-Net, and RCF models to comprehensively evaluate the performance of the proposed method. The results indicate that, with a 50% annotation ratio, the proposed method achieves high-precision crack detection, with an intersection over union (IoU) exceeding 0.84, which is close to that of U-Net. Visual analysis of the detection results confirms the method’s effectiveness in identifying cracks in complex environments.

DOT-SLAM: A Stereo Visual Simultaneous Localization and Mapping (SLAM) System with Dynamic Object Tracking Based on Graph Optimization.

Most visual simultaneous localization and mapping (SLAM) systems are based on the assumption of a static environment in autonomous vehicles. However, when dynamic objects, particularly vehicles, occupy a large portion of the image, the localization accuracy of the system decreases significantly. To mitigate this challenge, this paper unveils DOT-SLAM, a novel stereo visual SLAM system that integrates dynamic object tracking through graph optimization. By integrating dynamic object pose estimation into the SLAM system, the system can effectively utilize both foreground and background points for ego vehicle localization and obtain a static feature points map. To rectify the inaccuracies in depth estimation from stereo disparity directly on the foreground points of dynamic objects due to their self-similarity characteristics, a coarse-to-fine depth estimation method based on camera-road plane geometry is presented. This method uses rough depth to guide fine stereo matching, thereby obtaining the 3 dimensions (3D)spatial positions of feature points on dynamic objects. Subsequently, by establishing constraints on the dynamic object's pose using the road plane and non-holonomic constraints (NHCs) of the vehicle, reducing the initial pose uncertainty of dynamic objects leads to more accurate dynamic object initialization. Finally, by considering foreground points, background points, the local road plane, the ego vehicle pose, and dynamic object poses as optimization nodes, through the establishment and joint optimization of a nonlinear model based on graph optimization, accurate six degrees of freedom (DoFs) pose estimations are obtained for both the ego vehicle and dynamic objects. Experimental validation on the KITTI-360 dataset demonstrates that DOT-SLAM effectively utilizes features from the background and dynamic objects in the environment, resulting in more accurate vehicle trajectory estimation and a static environment map. Results obtained from a real-world dataset test reinforce the effectiveness.

Fluctuation in cortical excitation/inhibition modulates capability of attention across time scales ranging from hours to seconds.

Sustained attention, as the basis of general cognitive ability, naturally varies across different time scales, spanning from hours, e.g. from wakefulness to drowsiness state, to seconds, e.g. trial-by-trail fluctuation in a task session. Whether there is a unified mechanism underneath such trans-scale variability remains unclear. Here we show that fluctuation of cortical excitation/inhibition (E/I) is a strong modulator to sustained attention in humans across time scales. First, we observed the ability to attend varied across different brain states (wakefulness, postprandial somnolence, sleep deprived), as well as within any single state with larger swings. Second, regardless of the time scale involved, we found highly attentive state was always linked to more balanced cortical E/I characterized by electroencephalography (EEG) features, while deviations from the balanced state led to temporal decline in attention, suggesting the fluctuation of cortical E/I as a common mechanism underneath trans-scale attentional variability. Furthermore, we found the variations of both sustained attention and cortical E/I indices exhibited fractal structure in the temporal domain, exhibiting features of self-similarity. Taken together, these results demonstrate that sustained attention naturally varies across different time scales in a more complex way than previously appreciated, with the cortical E/I as a shared neurophysiological modulator.

Modeling two-dimensional ice shape based on fractal interpolation

The ice accretion data obtained from ice wind tunnel tests reveal a multiscale structure and rough surface. In the follow-up aerodynamic evaluation of icing airfoils, simplified two-dimensional ice shapes are generally used as substitutes, but this simplification changes the aerodynamic effects of the original ice shape. Therefore, finding a simple and effective two-dimensional ice shape simulation method is urgent. Due to the self-similarity characteristics of ice shape surfaces, fractal interpolation is proposed for ice shape simulation. First, the geometric characteristics of the ice shapes are analyzed to determine interpolation points, and an iterative function system is constructed for interpolation simulation. Considering the influence of various characteristics of ice shapes on aerodynamics, interpolation parameters are limited to simulating more realistic ice shapes. High-order numerical simulation methods were utilized to numerically simulate and analyze the aerodynamic characteristics of icing airfoil while also verifying the feasibility of fractal interpolation for simulating ice shapes. The analysis revealed that this method could effectively simulate ice profiles of various feature scales with minimal ice shape data. These simulated shapes closely resemble real ice formations and maintain the original aerodynamic characteristics of the icing airfoil. This method can be used to improve the computational accuracy of ice accretion codes and provide improvement strategies for complex ice shape prediction; thus, this method has great application prospects in engineering.

Identification of Interwell Interference Based on Hydrogeochemical Characteristics of Produced Water from Coalbed Methane Wells: A Case Study in the Southern Qinshui Basin, China

Summary Interwell interference is the superposition effect of coalbed methane (CBM) reservoir pressure. This study aims to provide a new direction for the quantitative analysis of interwell interference from the hydrogeochemical characteristics of produced water from CBM wells. A total of 24 produced water samples collected from the Panhe (PH) group, Shizhuangnan (SZN)-1 group, and SZN-2 group in Qinshui Basin were selected for the comparative analysis. The water type of all water samples is characterized by Na-HCO3, with Na+ being the main total dissolved solids (TDS) provider. The self-similar major ionic characteristics of the PH and SZN-2 groups are prone to the occurrence of interwell interference. The δD and δ18O show that the main source of produced water is atmospheric circulating water. The similar isotope characteristics of produced water in the PH and SZN-2 groups represent that there is remarkable interwell interference. Sr, As, Cu, Ga, Li, Rb, Sn, Mo, and V are selected as indicator elements. In the cluster analysis, all CBM wells form a single cluster in the PH and SZN-2 groups in the first three iterations, indicating interwell interference. According to the established fuzzy discriminative model, interwell interference is divided into two types—strong interwell interference and weak interwell interference. Most CBM wells in the PH and SZN-2 groups show strong interwell interference. This study can provide theoretical foundations for the dynamic pressure regulation and well pattern infilling of CBM wells.

Spatial optical soliton cluster solutions in strongly nonlocal nonlinear media

A (2+1)-dimensional variable coefficient nonlinear Schrödinger equation (NLSE) is described under strongly nonlocal nonlinear media. The soliton cluster solutions are obtained by using the improved self-similar reduction and F-expansion method. The regulation of nonlinear coefficients on the dynamics of spatial optical solitons and the self-similar propagation characteristics of the optical soliton clusters are investigated. It is observed that dark solitons transmitted in nonlinear media show two different spatial distributions. It is also found that the peak intensity of the soliton cluster only fluctuates in a small range during the propagation process, but the soliton cluster after harmonic potential modulation has some loss during the propagation process. But the loss is not as dramatic as when bright solitons are modulated. A new kind of soliton cluster is formed after the modulation of dark solitons, which has great practical significance such as application in logic gates, all-optical devices.

PEMFC sealing modeling relating to fractal characteristics of gasket-BPP interface based on micro-contact

The interface leaking of the gasket-BPP sealing structure affects the efficiency, safety, and reliability of PEMFCs. Aiming to reveal the basic cause of interface leaking and predict the leakage rate, the contact behavior at the micro-scale had been researched by FEM with the fractal multi-scale method, which could eliminate the negative influence of a single observation scale on the gasket-BPP rough interface modeling. Furthermore, in order to relate the contacting behavior at the micro-scale to the leakage rate at the macro-scale of PEMFCs, the mapping model had been established to analyze the sealing performance of the entire interface through the self-affine and self-similar characteristics of the fractal multi-scale contacting model of the gasket-BPP. Not only macroscopic properties of gasket rubber materials are considered in this model, but also microscopic morphologies are taken in to investigate the interface leakage rate, which had not been studied in traditional macroscopic research. By comparing the compression curves and interface leakage rates of the flange sealing device in testing and calculating approaches, the accuracy and reliability of the mapping model had been verified, leading to the analysis and the prediction of the PEMFC interface leakage rate rapidly.

Analysis of TBM tunneling performance based on mass fractal dimension of rock chips

The size of the rock chips and its particle size distribution can fully reflect the rock-breaking efficiency of the TBM, but the index that can comprehensively characterize the particle size distribution of rock chips has not yet been found to quantitatively evaluate the TBM tunneling efficiency. Based on the fractal theory, this study uses the mass fractal dimension to quantitatively analyze the particle size distribution of rock chips, and explores its relationship with TBM tunneling performance index. Field sieving tests were carried out on rock chips from two tunnel projects. According to the sieving test results, the mass fractal dimension of the rock chips is calculated as well as the correlation between it and common TBM performance evaluation indexes, average tunneling thrust is discussed. The research results show that the mass distribution of TBM rock chips has significant fractal and self-similar characteristics, the higher the content of large-size rock chips, the lower the content of small-size rock chips, the smaller the fractal dimension value. Simultaneously, under the same surrounding rock conditions, the mass fractal dimension of rock chips is positively correlated with the logarithm of specific energy and negatively correlated with the logarithm of coarseness index, which indicates that the smaller the fractal dimension, the higher the efficiency of rock breaking. It is demonstrated that the interval of TBM thrust force corresponding to smaller specific energy, larger coarseness index and smaller fractal dimension is the same, which can be determined as the optimal thrust interval.

A New Approach to Multiroot Vectorial Problems: Highly Efficient Parallel Computing Schemes

In this article, we construct an efficient family of simultaneous methods for finding all the distinct as well as multiple roots of polynomial equations. Convergence analysis proves that the order of convergence of newly constructed family of simultaneous methods is seventeen. Fractal-based simultaneous iterative algorithms are thoroughly examined. Using self-similar features, fractal-based simultaneous schemes can converge to solutions faster, saving computational time and resources necessary for solving nonlinear equations. Fractals analysis illustrates the newly developed method’s global convergence behavior when compared to single root-finding procedures for solving fractional order polynomials that arise in complex engineering applications. Some real problems from various branches of engineering along with some higher degree polynomials are considered as test examples to show the global convergence property of simultaneous methods, performance and efficiency of the proposed family of methods. Further computational efficiencies, CPU time and residual graphs are also drawn to validate the efficiency, robustness of the newly introduced family of methods as compared to the existing methods in the literature.

Short-Term Wind Turbine Blade Icing Wind Power Prediction Based on PCA-fLsm

To enhance the economic viability of wind energy in cold regions and ensure the safe operational management of wind farms, this paper proposes a short-term wind turbine blade icing wind power prediction method that combines principal component analysis (PCA) and fractional Lévy stable motion (fLsm). By applying supervisory control and data acquisition (SCADA) data from wind turbines experiencing icing in a mountainous area of Yunnan Province, China, the model comprehensively considers long-range dependence (LRD) and self-similar features. Adopting a combined pattern of previous-day predictions and actual measurement data, the model predicts the power under near-icing conditions, thereby enhancing the credibility and accuracy of icing forecasts. After validation and comparison with other prediction models (fBm, CNN-Attention-GRU, XGBoost), the model demonstrates a remarkable advantage in accuracy, achieving an accuracy rate and F1 score of 96.86% and 97.13%, respectively. This study proves the feasibility and wide applicability of the proposed model, providing robust data support for reducing wind turbine efficiency losses and minimizing operational risks.

Quantification of three-dimensional added turbulence intensity for the horizontal-axis wind turbine considering the wake anisotropy

The accurate evaluation of wake turbulence intensity (TI) is of great significance for the layout optimization of wind farms and research on control strategies. However, the existing engineering wake models still have many shortcomings in evaluating the TI in the wake of horizontal-axis wind turbines (HAWTs), especially in the near wake region. In response to this, this article proposed an analytical model based on the double-Gaussian ellipse function that can describe the three-dimensional added TI distribution in the entire wake region. Firstly, the anisotropy of wake expansion is taken into account in both the horizontal and vertical directions, assuming that the added TI distribution downstream of the HAWT is a double-Gaussian elliptical shape. Secondly, taking into account the self-similarity characteristics of flow TI, the maximum added TI and its position in the entire wake region are evaluated. In addition, considering the influence of the ground effect, the vertical turbulence distribution was corrected. Finally, the proposed added turbulence model was validated and relative error analysis was conducted using large eddy simulation (LES) data, wind field measurement data, and wind tunnel experimental data. The results show that the model had good prediction accuracy in the entire wake region, and its prediction performance was significantly improved compared to traditional models, especially in the near wake region, with the lowest even relative error of 3.66%. This model has significant advantages such as low computational cost, wide applicability, and high accuracy. It can reduce energy losses in wind farms, improve wind energy utilization efficiency, and has great potential for widespread application in large-scale wind farms.

Mittag–Leffler kernel operator on prey-predator model interfusing intra-specific competition and prey fear factor

In the present research, a prey-predator system that classifies predator species into premature and veteran species was proposed. Mathematical models of the system of species that include the impact of panic and a variety of functional reactions to the species have been recently reviewed. The consequence of fear is a reduction factor in the fundamental reproduction of the prey species. Relying on the prior research, we propose a mathematical predator-prey model employing the concept of fractional order system that contains two crucial components: intra-specific competition under mature predator density and fear, which affects the progeny of the prey community. Incorporating self-similarity characteristics is the significance of adopting a fractional order system. Following that, using memory kernel, we have interpret this model into the perspective of Caputo, that is, Atangana_Baleanu_Caputo (A_B_C) kind of fractional order derivatives. Singularity and non-locality are two of the main properties of fractional operators that make it simpler to figure out the natural behaviour of complicated systems. Details regarding the unique solution to the established model's derivation are provided. The dichotomy operator investigates the stability of the system under Hyper-Ulam`s stability method. The numerical interpolation to the suggested model generates the best precise approximate result. Through computer simulations, a thorough investigation on the predator species exhibiting intra-specific factor and prey species exhibiting fear factor is investigated. Using Adam's semi-analytical technique, we were able to derive the numerical estimates and determine the solution. The purpose to employ the Adams-Moulton approach is that it will provide more implicitly accurate results. Extensive numerical experiments are carried out using MATLAB software in order to portray the dynamical behaviour of the system. These observations lead us to the conclusion that total population expansion in the environment would be managed by the successful adoption of the fear factor in prey and the intra-species rivalry in predators.

Dynamic compressive properties and self-similarity characteristics of deep coral reef limestone subjected to high loading rates

Coral reef limestone is a kind of porous anisotropic geo-material. Understanding its dynamic mechanical properties subjected to high loading rates is of great significance to the blasting excavation and military attack defense of the reef underground space. In this paper, the Split Hopkinson Pressure Bar tests were carried out on the specimens of deep coral reef limestone in the South China Sea, and the difference of dynamic response between deep reef limestone and shallow calcified coral skeleton was revealed. The results show that the pore structure affects the dynamic deformation response of coral reef limestone, which makes the strain rate of the specimen independent of other mechanical parameters. However, the high loading rate overcomes the influence of the primary pore structure on the strength, so that the dynamic compressive strength and the degree of breakage are linearly related to the stress rate. In addition, under high loading rate, the coral framework limestone is mainly damaged by tension, which is significantly different from the calcified coral skeleton along the coral growth line. At the same strain rate, the fractal dimension of the dry specimen is greater than that of the saturated one, and the self-similarity characteristics of the specimen fragments that reach the crushing level at higher strain rate are poor. The viscous effect of water hinders the propagation of cracks in the coral framework limestone, but free water reduces the surface energy of the crystal boundary. These two kinds of mechanisms compete with each other, and the key factors controlling the competition mechanism are water content and loading rate.