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Keywords = nonlinear growth models

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23 pages, 10868 KiB  
Article
Quantitative Analysis and Nonlinear Response of Vegetation Dynamic to Driving Factors in Arid and Semi-Arid Regions of China
by Shihao Liu, Dazhi Yang, Xuyang Zhang and Fangtian Liu
Land 2025, 14(8), 1575; https://doi.org/10.3390/land14081575 (registering DOI) - 1 Aug 2025
Abstract
Vegetation dynamics are complexly influenced by multiple factors such as climate, human activities, and topography. In recent years, the frequency, intensity, and diversity of human activities have increased, placing substantial pressure on the growth of vegetation. Arid and semi-arid regions are particularly sensitive [...] Read more.
Vegetation dynamics are complexly influenced by multiple factors such as climate, human activities, and topography. In recent years, the frequency, intensity, and diversity of human activities have increased, placing substantial pressure on the growth of vegetation. Arid and semi-arid regions are particularly sensitive to climate change, and climate change and large-scale ecological restoration have led to significant changes in the dynamic of dryland vegetation. However, few studies have explored the nonlinear relationships between these factors and vegetation dynamic. In this study, we integrated trend analysis (using the Mann–Kendall test and Theil–Sen estimation) and machine learning algorithms (XGBoost-SHAP model) based on long time-series remote sensing data from 2001 to 2020 to quantify the nonlinear response patterns and threshold effects of bioclimatic variables, topographic features, soil attributes, and anthropogenic factors on vegetation dynamic. The results revealed the following key findings: (1) The kNDVI in the study area showed an overall significant increasing trend (p < 0.01) during the observation period, of which 26.7% of the area showed a significant increase. (2) The water content index (Bio 23, 19.6%), the change in land use (15.2%), multi-year average precipitation (pre, 15.0%), population density (13.2%), and rainfall seasonality (Bio 15, 10.9%) were the key factors driving the dynamic change of vegetation, with the combined contribution of natural factors amounting to 64.3%. (3) Among the topographic factors, altitude had a more significant effect on vegetation dynamics, with higher altitude regions less likely to experience vegetation greening. Both natural and anthropogenic factors exhibited nonlinear responses and interactive effects, contributing to the observed dynamic trends. This study provides valuable insights into the driving mechanisms behind the condition of vegetation in arid and semi-arid regions of China and, by extension, in other arid regions globally. Full article
(This article belongs to the Section Land Use, Impact Assessment and Sustainability)
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24 pages, 1408 KiB  
Systematic Review
Fear Detection Using Electroencephalogram and Artificial Intelligence: A Systematic Review
by Bladimir Serna, Ricardo Salazar, Gustavo A. Alonso-Silverio, Rosario Baltazar, Elías Ventura-Molina and Antonio Alarcón-Paredes
Brain Sci. 2025, 15(8), 815; https://doi.org/10.3390/brainsci15080815 - 29 Jul 2025
Viewed by 266
Abstract
Background/Objectives: Fear detection through EEG signals has gained increasing attention due to its applications in affective computing, mental health monitoring, and intelligent safety systems. This systematic review aimed to identify the most effective methods, algorithms, and configurations reported in the literature for detecting [...] Read more.
Background/Objectives: Fear detection through EEG signals has gained increasing attention due to its applications in affective computing, mental health monitoring, and intelligent safety systems. This systematic review aimed to identify the most effective methods, algorithms, and configurations reported in the literature for detecting fear from EEG signals using artificial intelligence (AI). Methods: Following the PRISMA 2020 methodology, a structured search was conducted using the string (“fear detection” AND “artificial intelligence” OR “machine learning” AND NOT “fnirs OR mri OR ct OR pet OR image”). After applying inclusion and exclusion criteria, 11 relevant studies were selected. Results: The review examined key methodological aspects such as algorithms (e.g., SVM, CNN, Decision Trees), EEG devices (Emotiv, Biosemi), experimental paradigms (videos, interactive games), dominant brainwave bands (beta, gamma, alpha), and electrode placement. Non-linear models, particularly when combined with immersive stimulation, achieved the highest classification accuracy (up to 92%). Beta and gamma frequencies were consistently associated with fear states, while frontotemporal electrode positioning and proprietary datasets further enhanced model performance. Conclusions: EEG-based fear detection using AI demonstrates high potential and rapid growth, offering significant interdisciplinary applications in healthcare, safety systems, and affective computing. Full article
(This article belongs to the Special Issue Neuropeptides, Behavior and Psychiatric Disorders)
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33 pages, 709 KiB  
Article
Integrated Generation and Transmission Expansion Planning Through Mixed-Integer Nonlinear Programming in Dynamic Load Scenarios
by Edison W. Intriago Ponce and Alexander Aguila Téllez
Energies 2025, 18(15), 4027; https://doi.org/10.3390/en18154027 - 29 Jul 2025
Viewed by 196
Abstract
A deterministic Mixed-Integer Nonlinear Programming (MINLP) model for the Integrated Generation and Transmission Expansion Planning (IGTEP) problem is presented. The proposed framework is distinguished by its foundation on the complete AC power flow formulation, which is solved to global optimality using BARON, a [...] Read more.
A deterministic Mixed-Integer Nonlinear Programming (MINLP) model for the Integrated Generation and Transmission Expansion Planning (IGTEP) problem is presented. The proposed framework is distinguished by its foundation on the complete AC power flow formulation, which is solved to global optimality using BARON, a deterministic MINLP solver, which ensures the identification of truly optimal expansion strategies, overcoming the limitations of heuristic approaches that may converge to local optima. This approach is employed to establish a definitive, high-fidelity economic and technical benchmark, addressing the limitations of commonly used DC approximations and metaheuristic methods that often fail to capture the nonlinearities and interdependencies inherent in power system planning. The co-optimization model is formulated to simultaneously minimize the total annualized costs, which include investment in new generation and transmission assets, the operating costs of the entire generator fleet, and the cost of unsupplied energy. The model’s effectiveness is demonstrated on the IEEE 14-bus system under various dynamic load growth scenarios and planning horizons. A key finding is the model’s ability to identify the most economic expansion pathway; for shorter horizons, the optimal solution prioritizes strategic transmission reinforcements to unlock existing generation capacity, thereby deferring capital-intensive generation investments. However, over longer horizons with higher demand growth, the model correctly identifies the necessity for combined investments in both significant new generation capacity and further network expansion. These results underscore the value of an integrated, AC-based approach, demonstrating its capacity to reveal non-intuitive, economically superior expansion strategies that would be missed by decoupled or simplified models. The framework thus provides a crucial, high-fidelity benchmark for the validation of more scalable planning tools. Full article
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24 pages, 1264 KiB  
Article
Internal Mechanism and Empirical Analysis of Digital Economy’s Impact on Agricultural New Quality Productive Forces: Evidence from China
by Yongsheng Xu, Ying Zhang, Siqing Wang, Mingzheng Zhao, Guifang Li, Yu Kang and Cuiping Zhao
Sustainability 2025, 17(15), 6844; https://doi.org/10.3390/su17156844 - 28 Jul 2025
Viewed by 383
Abstract
Agricultural new quality productive forces (ANQPFs) signify the progressive trajectory of modern agriculture. However, their development encounters significant challenges in many nations. The digital economy, characterized by its strong innovative capacity, offers continuous impetus for advancing agricultural new quality productive forces (ANQPFs). Based [...] Read more.
Agricultural new quality productive forces (ANQPFs) signify the progressive trajectory of modern agriculture. However, their development encounters significant challenges in many nations. The digital economy, characterized by its strong innovative capacity, offers continuous impetus for advancing agricultural new quality productive forces (ANQPFs). Based on panel data from 30 Chinese provinces (2014–2023), this study employs a two-way fixed-effects model, mediation and threshold effect analyses, and a spatial Durbin model to comprehensively assess the influence of the digital economy (DE) on agricultural new quality productive forces (ANQPFs). The findings reveal that (1) the digital economy (DE) significantly enhances the advancement of agricultural new quality productive forces (ANQPFs); (2) while its positive effect is pronounced in eastern, central, and western China, the impact is weaker in the northeastern region; (3) rural financial development (RFD) acts as a mediator in the relationship between digital economy (DE) growth and agricultural new quality productive forces (ANQPFs); (4) the digital economy (DE)’s contribution to agricultural new quality productive forces (ANQPFs) demonstrates non-linear trends; and (5) spatially, while the digital economy (DE) boosts the local agricultural new quality productive forces (ANQPFs), it exerts a negative spillover effect on neighboring areas. This research offers fresh empirical insights into the determinants of agricultural new quality productive forces (ANQPFs) and suggests policy measures to support agricultural modernization. Full article
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22 pages, 1156 KiB  
Article
An Attribute-Based Proxy Re-Encryption Scheme Supporting Revocable Access Control
by Gangzheng Zhao, Weijie Tan and Changgen Peng
Electronics 2025, 14(15), 2988; https://doi.org/10.3390/electronics14152988 - 26 Jul 2025
Viewed by 226
Abstract
In the deep integration process between digital infrastructure and new economic forms, structural imbalance between the evolution rate of cloud storage technology and the growth rate of data-sharing demands has caused systemic security vulnerabilities such as blurred data sovereignty boundaries and nonlinear surges [...] Read more.
In the deep integration process between digital infrastructure and new economic forms, structural imbalance between the evolution rate of cloud storage technology and the growth rate of data-sharing demands has caused systemic security vulnerabilities such as blurred data sovereignty boundaries and nonlinear surges in privacy leakage risks. Existing academic research indicates current proxy re-encryption schemes remain insufficient for cloud access control scenarios characterized by diversified user requirements and personalized permission management, thus failing to fulfill the security needs of emerging computing paradigms. To resolve these issues, a revocable attribute-based proxy re-encryption scheme supporting policy-hiding is proposed. Data owners encrypt data and upload it to the blockchain while concealing attribute values within attribute-based encryption access policies, effectively preventing sensitive information leaks and achieving fine-grained secure data sharing. Simultaneously, proxy re-encryption technology enables verifiable outsourcing of complex computations. Furthermore, the SM3 (SM3 Cryptographic Hash Algorithm) hash function is embedded in user private key generation, and key updates are executed using fresh random factors to revoke malicious users. Ultimately, the scheme proves indistinguishability under chosen-plaintext attacks for specific access structures in the standard model. Experimental simulations confirm that compared with existing schemes, this solution delivers higher execution efficiency in both encryption/decryption and revocation phases. Full article
(This article belongs to the Topic Recent Advances in Security, Privacy, and Trust)
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16 pages, 1145 KiB  
Article
A Hybrid Transformer–Mamba Model for Multivariate Metro Energy Consumption Forecasting
by Liheng Long, Zhiyao Chen, Junqian Wu, Qing Fu, Zirui Zhang, Fan Feng and Ronghui Zhang
Electronics 2025, 14(15), 2986; https://doi.org/10.3390/electronics14152986 - 26 Jul 2025
Viewed by 291
Abstract
With the rapid growth of urban populations and the expansion of metro networks, accurate energy consumption prediction has become a critical task for optimizing metro operations and supporting low-carbon city development. Traditional statistical and machine learning methods often struggle to model the complex, [...] Read more.
With the rapid growth of urban populations and the expansion of metro networks, accurate energy consumption prediction has become a critical task for optimizing metro operations and supporting low-carbon city development. Traditional statistical and machine learning methods often struggle to model the complex, nonlinear, and time-varying nature of metro energy data. To address these challenges, this paper proposes MTMM, a novel hybrid model that integrates the multi-head attention mechanism of the Transformer with the efficient, state-space-based Mamba architecture. The Transformer effectively captures long-range temporal dependencies, while Mamba enhances inference speed and reduces complexity. Additionally, the model incorporates multivariate energy features, leveraging the correlations among different energy consumption types to improve predictive performance. Experimental results on real-world data from the Guangzhou Metro demonstrate that MTMM significantly outperforms existing methods in terms of both MAE and MSE. The model also shows strong generalization ability across different prediction lengths and time step configurations, offering a promising solution for intelligent energy management in metro systems. Full article
(This article belongs to the Special Issue AI Applications for Smart Grid)
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20 pages, 392 KiB  
Article
Digital Economy and Chinese-Style Modernization: Unveiling Nonlinear Threshold Effects and Inclusive Policy Frameworks for Global Sustainable Development
by Tao Qi, Wenhui Liu and Xiao Chang
Economies 2025, 13(8), 215; https://doi.org/10.3390/economies13080215 - 25 Jul 2025
Viewed by 317
Abstract
This study focuses on the impact of China’s digital economy on sustainable modernization from 2011 to 2021, using provincial panel data for empirical analysis. By applying threshold and mediation models, we find that the digital economy promotes modernization through industrial upgrading (with a [...] Read more.
This study focuses on the impact of China’s digital economy on sustainable modernization from 2011 to 2021, using provincial panel data for empirical analysis. By applying threshold and mediation models, we find that the digital economy promotes modernization through industrial upgrading (with a mediating effect of 38%) and trade openness (coefficient = 0.234). The research reveals “U-shaped” nonlinear threshold effects at specific levels of digital development (2.218), market efficiency (9.212), and technological progress (12.224). Eastern provinces benefit significantly (coefficient ranging from 0.12 to 0.15 ***), while western regions initially experience some inhibition (coefficient = −0.08 *). Industrial digitalization (coefficient = 0.13 ***) and innovation ecosystems (coefficient = 0.09 ***) play crucial roles in driving eco-efficiency and equity, in line with Sustainable Development Goals 9 and 13. Meanwhile, the impacts of infrastructure (coefficient = 0.07) and industrialization (coefficient = 0.085) are delayed. Economic modernization improves (coefficient = 0.37 ***), yet social modernization declines (coefficient = −0.12 *). This study not only enriches economic theory but also extends the environmental Kuznets curve to the digital economy domain. We propose tiered policy recommendations, including the construction of green digital infrastructure, carbon pricing, and rural digital transformation, which are applicable to China and offer valuable references for emerging economies aiming to achieve inclusive low-carbon growth in the digital era. Future research could further explore the differentiated mechanisms of various digital technologies in the modernization process across different regions and how to optimize policy combinations to better balance digital innovation with sustainable development goals. Full article
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16 pages, 1655 KiB  
Article
FO-DEMST: Optimized Multi-Scale Transformer with Dual-Encoder Architecture for Feeding Amount Prediction in Sea Bass Aquaculture
by Hongpo Wang, Qihui Zhang, Hong Zhou, Yunchen Tian, Yongcheng Jiang and Jianing Quan
J. Sens. Actuator Netw. 2025, 14(4), 77; https://doi.org/10.3390/jsan14040077 - 22 Jul 2025
Viewed by 229
Abstract
Traditional methods for predicting feeding amounts rely on historical data and experience but fail to account for non-linear fish growth and the influence of water quality and meteorological factors. This study presents a novel approach for sea bass feeding prediction based on Spearman [...] Read more.
Traditional methods for predicting feeding amounts rely on historical data and experience but fail to account for non-linear fish growth and the influence of water quality and meteorological factors. This study presents a novel approach for sea bass feeding prediction based on Spearman + RF feature optimization and multi-scale feature fusion using a transformer model. A logistic growth curve model is used to analyze sea bass growth and establish the relationship between biomass and feeding amount. Spearman correlation analysis and random forest optimize the feature set for improved prediction accuracy. A dual-encoder structure incorporates historical feeding data and biomass along with water quality and meteorological information. Multi-scale feature fusion addresses time-scale inconsistencies between input variables The results showed that the MSE and MAE of the improved transformer model for sea bass feeding prediction were 0.42 and 0.31, respectively, which decreased by 43% in MSE and 33% in MAE compared to the traditional transformer model. Full article
(This article belongs to the Special Issue Remote Sensing and IoT Application for Smart Agriculture)
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27 pages, 4136 KiB  
Article
Quantum-Enhanced Attention Neural Networks for PM2.5 Concentration Prediction
by Tichen Huang, Yuyan Jiang, Rumeijiang Gan and Fuyu Wang
Modelling 2025, 6(3), 69; https://doi.org/10.3390/modelling6030069 - 21 Jul 2025
Viewed by 224
Abstract
As industrialization and economic growth accelerate, PM2.5 pollution has become a critical environmental concern. Predicting PM2.5 concentration is challenging due to its nonlinear and complex temporal dynamics, limiting the accuracy and robustness of traditional machine learning models. To enhance prediction accuracy, [...] Read more.
As industrialization and economic growth accelerate, PM2.5 pollution has become a critical environmental concern. Predicting PM2.5 concentration is challenging due to its nonlinear and complex temporal dynamics, limiting the accuracy and robustness of traditional machine learning models. To enhance prediction accuracy, this study focuses on Ma’anshan City, China and proposes a novel hybrid model (QMEWOA-QCAM-BiTCN-BiLSTM) based on an “optimization first, prediction later” approach. Feature selection using Pearson correlation and RFECV reduces model complexity, while the Whale Optimization Algorithm (WOA) optimizes model parameters. To address the local optima and premature convergence issues of WOA, we introduce a quantum-enhanced multi-strategy improved WOA (QMEWOA) for global optimization. A Quantum Causal Attention Mechanism (QCAM) is incorporated, leveraging Quantum State Mapping (QSM) for higher-order feature extraction. The experimental results show that our model achieves a MedAE of 1.997, MAE of 3.173, MAPE of 10.56%, and RMSE of 5.218, outperforming comparison models. Furthermore, generalization experiments confirm its superior performance across diverse datasets, demonstrating its robustness and effectiveness in PM2.5 concentration prediction. Full article
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20 pages, 8592 KiB  
Article
Spatial Differentiation in the Contribution of Innovation Influencing Factors: An Empirical Study in Nanjing from the Perspective of Nonlinear Relationships
by Chengyu Wang, Renchao Luo and Lingchao Zhou
Buildings 2025, 15(14), 2565; https://doi.org/10.3390/buildings15142565 - 21 Jul 2025
Viewed by 252
Abstract
The agglomeration characteristics of innovation spaces reflect the intrinsic mechanisms of regional resource integration and collaborative innovation. Investigating the contributions of influencing factors to innovation space agglomeration and their spatial differentiation has significant implications for improving urban innovation quality. Taking the Nanjing central [...] Read more.
The agglomeration characteristics of innovation spaces reflect the intrinsic mechanisms of regional resource integration and collaborative innovation. Investigating the contributions of influencing factors to innovation space agglomeration and their spatial differentiation has significant implications for improving urban innovation quality. Taking the Nanjing central urban area as a case study, this research applied gradient boosting regression trees (GBRT) and multiscale geographically weighted regression (MGWR) models to explore the contributions of influencing factors to innovation space agglomeration and its spatial differentiation. Findings demonstrated that (1) Innovation platforms and patents emerged as the most significant driving factors, collectively accounting for 54.8% of the relative contributions; (2) The contributions of influencing factors to innovation space agglomeration exhibited marked nonlinear characteristics, specifically categorized into five distinct patterns: Sustained Growth Pattern, Growth-Stabilization Pattern, Growth-Decline Pattern, Global Stabilization Pattern, and Global Decline Pattern. The inflection thresholds of marginal effects across factors ranged from approximately 12% to 55% (e.g., 40% for metro stations, 13% for integrated commercial hubs); (3) Each influence factor’s contribution mechanism showed pronounced spatial heterogeneity across different regions. Based on these discoveries, governments should optimize innovation resource allocation according to regional characteristics and enhance spatial quality to promote efficient resource integration and transformation. This research provides a novel perspective for understanding innovation space agglomeration mechanisms and offers actionable references for urban policymakers to implement context-specific innovation economic development strategies. Full article
(This article belongs to the Section Architectural Design, Urban Science, and Real Estate)
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23 pages, 406 KiB  
Article
Periodically Kicked Rotator with Power-Law Memory: Exact Solution and Discrete Maps
by Vasily E. Tarasov
Fractal Fract. 2025, 9(7), 472; https://doi.org/10.3390/fractalfract9070472 - 21 Jul 2025
Viewed by 378
Abstract
This article discusses the transformation of a continuous-time model of the fractional system into a discrete-time model of the fractional system. For the continuous-time model, the exact solution of the nonlinear equation with fractional derivatives (FDs) that has the form of the damped [...] Read more.
This article discusses the transformation of a continuous-time model of the fractional system into a discrete-time model of the fractional system. For the continuous-time model, the exact solution of the nonlinear equation with fractional derivatives (FDs) that has the form of the damped rotator type with power non-locality in time is obtained.This equation with two FDs and periodic kicks is solved in the general case for the arbitrary orders of FDs without any approximations. A three-stage method for solving a nonlinear equation with two FDs and deriving discrete maps with memory (DMMs) is proposed. The exact solutions of the nonlinear equation with two FDs are obtained for arbitrary values of the orders of these derivatives. In this article, the orders of two FDs are not related to each other, unlike in previous works. The exact solution of nonlinear equation with two FDs of different orders and periodic kicks are proposed. Using this exact solution, we derive DMMs that describe a kicked damped rotator with power-law non-localities in time. For the discrete-time model, these damped DMMs are described by the exact solution of nonlinear equations with FDs at discrete time points as the functions of all past discrete moments of time. An example of the application, the exact solution and DMMs are proposed for the economic growth model with two-parameter power-law memory and price kicks. It should be emphasized that the manuscript proposes exact analytical solutions to nonlinear equations with FDs, which are derived without any approximations. Therefore, it does not require any numerical proofs, justifications, or numerical validation. The proposed method gives exact analytical solutions, where approximations are not used at all. Full article
32 pages, 1236 KiB  
Article
How Does Urban Compactness Affect Green Total Factor Productivity? An Empirical Study of Urban Agglomerations in Southwest China
by Tao Chen, Yike Zhang, Jiahe Wang, Binbin Wu and Yaoning Yang
Sustainability 2025, 17(14), 6612; https://doi.org/10.3390/su17146612 - 19 Jul 2025
Viewed by 368
Abstract
With the development of urban scale and economic growth, the challenges posed by limited resources and insufficient environmental carrying capacity become increasingly severe, making the sustainable improvement of production efficiency an urgent requirement. Based on panel data for cities in the Dianzhong Urban [...] Read more.
With the development of urban scale and economic growth, the challenges posed by limited resources and insufficient environmental carrying capacity become increasingly severe, making the sustainable improvement of production efficiency an urgent requirement. Based on panel data for cities in the Dianzhong Urban Agglomeration and the Chengdu–Chongqing Economic Circle in Southwest China (2012–2021), this study elucidates the positive effect of urban compactness on green total factor productivity (GTFP). By constructing a composite index to measure urban compactness and employing an SBM model to quantify GTFP, we find that a 1% increase in urban compactness leads to a 0.65% increase in GTFP. A mediating-effect analysis reveals that green technological innovation serves as a significant mediator, with a mediating effect value of 0.363. Heterogeneity analysis uncovers differing mechanisms of influence: urban compactness exerts a positive effect in regions with higher levels of economic development, while its impact is not significant in regions with lower economic development, indicating that the effect of compactness varies with economic context; the impact of urban compactness on GTFP is statistically insignificant in regions with higher tertiary sector shares (p > 0.1), whereas it exhibits a highly significant positive effect in regions with lower tertiary sector presence (β = 1.49, p < 0.01). These results collectively demonstrate that the influence of urban compactness on GTFP varies significantly with industrial structure composition. Threshold-effect analysis further shows that there is a threshold in the proportion of industrial output value, beyond which the influence of compactness on GTFP becomes even stronger. Our research quantitatively explores both linear and nonlinear relationships between urban compactness and GTFP, clarifying the linkage between urban spatial dynamics and green production efficiency, and provides empirical evidence and scholarly support for urban planning and economic development. Full article
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17 pages, 7633 KiB  
Article
Mechanical Behavior Characteristics of Sandstone and Constitutive Models of Energy Damage Under Different Strain Rates
by Wuyan Xu and Cun Zhang
Appl. Sci. 2025, 15(14), 7954; https://doi.org/10.3390/app15147954 - 17 Jul 2025
Viewed by 206
Abstract
To explore the influence of mine roof on the damage and failure of sandstone surrounding rock under different pressure rates, mechanical experiments with different strain rates were carried out on sandstone rock samples. The strength, deformation, failure, energy and damage characteristics of rock [...] Read more.
To explore the influence of mine roof on the damage and failure of sandstone surrounding rock under different pressure rates, mechanical experiments with different strain rates were carried out on sandstone rock samples. The strength, deformation, failure, energy and damage characteristics of rock samples with different strain rates were also discussed. The research results show that with the increases in the strain rate, peak stress, and elastic modulus show a monotonically increasing trend, while the peak strain decreases in the reverse direction. At a low strain rate, the proportion of the mass fraction of complete rock blocks in the rock sample is relatively high, and the shape integrity is good, while rock samples with a high strain rate retain more small-sized fragmented rock blocks. This indicates that under high-rate loading, the bifurcation phenomenon of secondary cracks is obvious. The rock samples undergo a failure form dominated by small-sized fragments, with severe damage to the rock samples and significant fractal characteristics of the fragments. At the initial stage of loading, the primary fractures close, and the rock samples mainly dissipate energy in the forms of frictional slip and mineral fragmentation. In the middle stage of loading, the residual fractures are compacted, and the dissipative strain energy keeps increasing continuously. In the later stage of loading, secondary cracks accelerate their expansion, and elastic strain energy is released sharply, eventually leading to brittle failure of the rock sample. Under a low strain rate, secondary cracks slowly expand along the clay–quartz interface and cause intergranular failure of the rock sample. However, a high strain rate inhibits the stress relaxation of the clay, forces the energy to transfer to the quartz crystal, promotes the penetration of secondary cracks through the quartz crystal, and triggers transgranular failure. A constitutive model based on energy damage was further constructed, which can accurately characterize the nonlinear hardening characteristics and strength-deformation laws of rock samples with different strain rates. The evolution process of its energy damage can be divided into the unchanged stage, the slow growth stage, and the accelerated growth stage. The characteristics of this stage reveal the sudden change mechanism from the dissipation of elastic strain energy of rock samples to the unstable propagation of secondary cracks, clarify the cumulative influence of strain rate on damage, and provide a theoretical basis for the dynamic assessment of surrounding rock damage and disaster early warning when the mine roof comes under pressure. Full article
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28 pages, 10262 KiB  
Article
Driving Forces and Future Scenario Simulation of Urban Agglomeration Expansion in China: A Case Study of the Pearl River Delta Urban Agglomeration
by Zeduo Zou, Xiuyan Zhao, Shuyuan Liu and Chunshan Zhou
Remote Sens. 2025, 17(14), 2455; https://doi.org/10.3390/rs17142455 - 15 Jul 2025
Viewed by 548
Abstract
The remote sensing monitoring of land use changes and future scenario simulation hold crucial significance for accurately characterizing urban expansion patterns, optimizing urban land use configurations, and thereby promoting coordinated regional development. Through the integration of multi-source data, this study systematically analyzes the [...] Read more.
The remote sensing monitoring of land use changes and future scenario simulation hold crucial significance for accurately characterizing urban expansion patterns, optimizing urban land use configurations, and thereby promoting coordinated regional development. Through the integration of multi-source data, this study systematically analyzes the spatiotemporal trajectories and driving forces of land use changes in the Pearl River Delta urban agglomeration (PRD) from 1990 to 2020 and further simulates the spatial patterns of urban land use under diverse development scenarios from 2025 to 2035. The results indicate the following: (1) During 1990–2020, urban expansion in the Pearl River Delta urban agglomeration exhibited a “stepwise growth” pattern, with an annual expansion rate of 3.7%. Regional land use remained dominated by forest (accounting for over 50%), while construction land surged from 6.5% to 21.8% of total land cover. The gravity center trajectory shifted southeastward. Concurrently, cropland fragmentation has intensified, accompanied by deteriorating connectivity of ecological lands. (2) Urban expansion in the PRD arises from synergistic interactions between natural and socioeconomic drivers. The Geographically and Temporally Weighted Regression (GTWR) model revealed that natural constraints—elevation (regression coefficients ranging −0.35 to −0.05) and river network density (−0.47 to −0.15)—exhibited significant spatial heterogeneity. Socioeconomic drivers dominated by year-end paved road area (0.26–0.28) and foreign direct investment (0.03–0.11) emerged as core expansion catalysts. Geographic detector analysis demonstrated pronounced interaction effects: all factor pairs exhibited either two-factor enhancement or nonlinear enhancement effects, with interaction explanatory power surpassing individual factors. (3) Validation of the Patch-generating Land Use Simulation (PLUS) model showed high reliability (Kappa coefficient = 0.9205, overall accuracy = 95.9%). Under the Natural Development Scenario, construction land would exceed the ecological security baseline, causing 408.60 km2 of ecological space loss; Under the Ecological Protection Scenario, mandatory control boundaries could reduce cropland and forest loss by 3.04%, albeit with unused land development intensity rising to 24.09%; Under the Economic Development Scenario, cross-city contiguous development zones along the Pearl River Estuary would emerge, with land development intensity peaking in Guangzhou–Foshan and Shenzhen–Dongguan border areas. This study deciphers the spatiotemporal dynamics, driving mechanisms, and scenario outcomes of urban agglomeration expansion, providing critical insights for formulating regionally differentiated policies. Full article
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21 pages, 10296 KiB  
Article
Spatiotemporal Mechanical Effects of Framework–Slope Systems Under Frost Heave Conditions
by Wendong Li, Xiaoqiang Hou, Jixian Ren and Chaoyang Wu
Appl. Sci. 2025, 15(14), 7877; https://doi.org/10.3390/app15147877 - 15 Jul 2025
Viewed by 263
Abstract
To investigate the slope instability caused by differential frost heaving mechanisms from the slope crest to the toe during frost heave processes, this study takes a typical silty clay slope in Xinjiang, China, as the research object. Through indoor triaxial consolidated undrained shear [...] Read more.
To investigate the slope instability caused by differential frost heaving mechanisms from the slope crest to the toe during frost heave processes, this study takes a typical silty clay slope in Xinjiang, China, as the research object. Through indoor triaxial consolidated undrained shear tests, eight sets of natural and frost-heaved specimens were prepared under confining pressure conditions ranging from 100 to 400 kPa. The geotechnical parameters of the soil in both natural and frost-heaved states were obtained, and a spatiotemporal thermo-hydro-mechanical coupled numerical model was established to reveal the dynamic evolution law of anchor rod axial forces and the frost heave response mechanism between the frame and slope soil. The analytical results indicate that (1) the frost heave process is influenced by slope boundaries, resulting in distinct spatial variations in the temperature field response across the slope surface—namely pronounced responses at the crest and toe but a weaker response in the mid-slope. (2) Under the coupled drive of the water potential gradient and gravitational potential gradient, the ice content in the toe area increases significantly, and the horizontal frost heave force exhibits exponential growth, reaching its peak value of 92 kPa at the toe in February. (3) During soil freezing, the reverse stress field generated by soil arching shows consistent temporal variation trends with the temperature field. Along the height of the soil arch, the intensity of the reverse frost heave force field displays a nonlinear distribution characteristic of initial strengthening followed by attenuation. (4) By analyzing the changes in anchor rod axial forces during frost heaving, it was found that axial forces during the frost heave period are approximately 1.3 times those under natural conditions, confirming the frost heave period as the most critical condition for frame anchor design. Furthermore, through comparative analysis with 12 months of on-site anchor rod axial force monitoring data, the reliability and accuracy of the numerical simulation model were validated. These research outcomes provide a theoretical basis for the design of frame anchor support systems in seasonally frozen regions. Full article
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