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Search Results (459)

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Keywords = power-law relationship

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18 pages, 6915 KiB  
Article
Strength Mobilisation in Karlsruhe Fine Sand
by Jinghong Liu, Yi Pik Cheng and Min Deng
Geotechnics 2025, 5(3), 52; https://doi.org/10.3390/geotechnics5030052 - 4 Aug 2025
Abstract
The strength mobilisation framework was adopted for the first time to describe the stress–strain responses for three different types of sands, including a total of 30 published drained triaxial tests—25 for Karlsruhe Fine Sand, 2 for Ottawa sands and 3 for Fontainebleau sand, [...] Read more.
The strength mobilisation framework was adopted for the first time to describe the stress–strain responses for three different types of sands, including a total of 30 published drained triaxial tests—25 for Karlsruhe Fine Sand, 2 for Ottawa sands and 3 for Fontainebleau sand, under confining pressures ranging from 50 to 400 kPa. The peak shear strength τpeak obtained from drained triaxial shearing of these sands was used to normalise shear stress. Shear strains normalised at peak strength γpeak and at half peak of shear strength γM=2 were taken as the normalised reference strains, and the results were compared. Power–law functions were then derived when the mobilised strength was between 0.2τpeak and 0.8τpeak. Exponents of the power–law functions of these sands were found to be lower than in the published undrained shearing data of clays. Using γM=2 as the reference strain shows a slightly better power–law correlation than using γpeak. Linear relationships between the reference strains and variables, such as relative density, relative dilatancy index, and dilatancy, are identified. Full article
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15 pages, 3175 KiB  
Article
Creep Deformation Mechanisms of Gas-Bearing Coal in Deep Mining Environments: Experimental Characterization and Constitutive Modeling
by Xiaolei Sun, Xueqiu He, Liming Qiu, Qiang Liu, Limin Qie and Qian Sun
Processes 2025, 13(8), 2466; https://doi.org/10.3390/pr13082466 - 4 Aug 2025
Abstract
The impact mechanism of long-term creep in gas-containing coal on coal and gas outbursts has not been fully elucidated and remains insufficiently understood for the purpose of disaster engineering control. This investigation conducted triaxial creep experiments on raw coal specimens under controlled confining [...] Read more.
The impact mechanism of long-term creep in gas-containing coal on coal and gas outbursts has not been fully elucidated and remains insufficiently understood for the purpose of disaster engineering control. This investigation conducted triaxial creep experiments on raw coal specimens under controlled confining pressures, axial stresses, and gas pressures. Through systematic analysis of coal’s physical responses across different loading conditions, we developed and validated a novel creep damage constitutive model for gas-saturated coal through laboratory data calibration. The key findings reveal three characteristic creep regimes: (1) a decelerating phase dominates under low stress conditions, (2) progressive transitions to combined decelerating–steady-state creep with increasing stress, and (3) triphasic decelerating–steady–accelerating behavior at critical stress levels. Comparative analysis shows that gas-free specimens exhibit lower cumulative strain than the 0.5 MPa gas-saturated counterparts, with gas presence accelerating creep progression and reducing the time to failure. Measured creep rates demonstrate stress-dependent behavior: primary creep progresses at 0.002–0.011%/min, decaying exponentially to secondary creep rates below 0.001%/min. Steady-state creep rates follow a power law relationship when subject to deviatoric stress (R2 = 0.96). Through the integration of Burgers viscoelastic model with the effective stress principle for porous media, we propose an enhanced constitutive model, incorporating gas adsorption-induced dilatational stresses. This advancement provides a theoretical foundation for predicting time-dependent deformation in deep coal reservoirs and informs monitoring strategies concerning gas-bearing strata stability. This study contributes to the theoretical understanding and engineering monitoring of creep behavior in deep coal rocks. Full article
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31 pages, 7371 KiB  
Article
Manufacturing and Mechanical Behaviour of Scalmalloy® Lattice Structures: Experimental Validation and Model
by Ilaria Lagalante, Diego Manfredi, Sergio Balestrieri, Vito Mocella, Andrea El Hassanin, Giuseppe Coppola, Mariangela Lombardi and Paolo Fino
Materials 2025, 18(15), 3479; https://doi.org/10.3390/ma18153479 - 24 Jul 2025
Viewed by 420
Abstract
This study investigates the influence of process parameters on the fabrication and mechanical performance of Scalmalloy® lattice structures produced via laser powder bed fusion (PBF-LB) and their mechanical responses at different cell size. A full-factorial design of experiments was employed to evaluate [...] Read more.
This study investigates the influence of process parameters on the fabrication and mechanical performance of Scalmalloy® lattice structures produced via laser powder bed fusion (PBF-LB) and their mechanical responses at different cell size. A full-factorial design of experiments was employed to evaluate the effect of scan speed, hatch distance, and downskin power on internal porosity and dimensional accuracy. Regression models revealed significant relationships, with optimised parameters identified at a scan speed of 700 mm/s, hatch distance of 0.13 mm, and downskin power of 80 W. Mechanical characterisation through tensile tests of bulk samples and compression tests of lattice structures highlighted the strengthening effects of the heat treatment. Experimental data on quasi-elastic gradient and yield strength were compared to predictions from the Ashby–Gibson model, revealing a partial agreement but noticeable deviations attributed to cell geometry and manufacturing defects. The scaling laws observed differed from the classical model, particularly in the yield strength exponent, indicating the need for empirical models tailored to metallic lattices. This work provides key insights into the optimisation of PBF-LB parameters for Scalmalloy® and underlines the complex interplay between process parameters, structural design, and mechanical behaviour. Full article
(This article belongs to the Special Issue Recent Advances in Advanced Laser Processing Technologies)
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24 pages, 4085 KiB  
Article
A Joint Optimization Method for Power and Array of Multi-Point Sources System
by Zhihao Cai, Shiqi Xing, Xinyuan Su, Junpeng Wang, Weize Meng and Ziwen Xiao
Remote Sens. 2025, 17(14), 2445; https://doi.org/10.3390/rs17142445 - 14 Jul 2025
Viewed by 257
Abstract
In a multi-point source system, increasing the jamming power can expand the distribution area of the equivalent radiation center, but significantly increases the system exposure risk. Therefore, in order to achieve an optimal balance between the two, this paper proposes a joint optimization [...] Read more.
In a multi-point source system, increasing the jamming power can expand the distribution area of the equivalent radiation center, but significantly increases the system exposure risk. Therefore, in order to achieve an optimal balance between the two, this paper proposes a joint optimization method for jamming power and an array of multi-point source systems. First, based on determining the spatial geometric relationship between the triplet antenna and the target, the distribution law of the equivalent radiation center of the triplet antenna under the condition of the target echo is derived. Second, by introducing the angle factor, the jamming power and equivalent radiation center distribution area are combined to construct the joint optimization model of jamming power and array in omnidirectional and non-omnidirectional situations. Third, based on the non-dominated sorting whale optimization algorithm (NSWOA), an adaptive inertia weight based on the cosine function and logistic chaotic map is introduced to obtain the optimal arrangement. The experimental results show that in the omnidirectional case, when the average jamming-to-signal ratio is 13.83 dB, the equilateral triangle array can achieve the goal of protecting the target while avoiding the exposure of the triplet antenna position. In the non-omnidirectional case, when the average jamming-to-signal ratio is 13.90 dB, the equilateral triangle array can achieve the optimal balance between the jamming power and the area of the distribution area of the equivalent radiation center, and control the distribution of the equivalent radiation center to strictly meet the preset angular domain constraints. Furthermore, the optimal JSR value was reduced by an average of 1.14 dB compared with that of the conventional selection scheme. Full article
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12 pages, 843 KiB  
Article
Thermalization in Asymmetric Harmonic Chains
by Weicheng Fu, Sihan Feng, Yong Zhang and Hong Zhao
Entropy 2025, 27(7), 741; https://doi.org/10.3390/e27070741 - 11 Jul 2025
Viewed by 281
Abstract
The symmetry of the interparticle interaction potential (IIP) plays a critical role in determining the thermodynamic and transport properties of solids. This study investigates the isolated effect of IIP asymmetry on thermalization. Asymmetry and nonlinearity are typically intertwined. To isolate the effect of [...] Read more.
The symmetry of the interparticle interaction potential (IIP) plays a critical role in determining the thermodynamic and transport properties of solids. This study investigates the isolated effect of IIP asymmetry on thermalization. Asymmetry and nonlinearity are typically intertwined. To isolate the effect of asymmetry, we introduce a one-dimensional asymmetric harmonic (AH) model whose IIP possesses asymmetry but no nonlinearity, evidenced by energy-independent vibrational frequencies. Extensive numerical simulations confirm a power-law relationship between thermalization time (Teq) and perturbation strength for the AH chain, revealing an exponent larger than the previously observed inverse-square law in the thermodynamic limit. Upon adding symmetric quartic nonlinearity into the AH model, we systematically study thermalization under combined asymmetry and nonlinearity. Matthiessen’s rule provides a good estimate of Teq in this case. Our results demonstrate that asymmetry plays a distinct role in enhancing higher-order effects and governing relaxation dynamics. Full article
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16 pages, 2149 KiB  
Article
ZR Relationships for Different Precipitation Types and Events from Parsivel Disdrometer Data in Warsaw, Poland
by Mariusz Paweł Barszcz and Ewa Kaznowska
Remote Sens. 2025, 17(13), 2271; https://doi.org/10.3390/rs17132271 - 2 Jul 2025
Viewed by 229
Abstract
In this study, the relationship between radar reflectivity and rain rate (Z–R) was investigated. The analysis was conducted using data collected by the OTT Parsivel1 disdrometer during the periods 2012–2014 and 2019–2025 in Warsaw, Poland. As a first step, the [...] Read more.
In this study, the relationship between radar reflectivity and rain rate (Z–R) was investigated. The analysis was conducted using data collected by the OTT Parsivel1 disdrometer during the periods 2012–2014 and 2019–2025 in Warsaw, Poland. As a first step, the parameters a and b of the power-law Z–R relationship were estimated separately for three precipitation types: rain, sleet (rain with snow), and snow. Subsequently, observational data from all 12 months of the annual cycle were used to derive Z–R relationships for 118 individual precipitation events. To date, only a few studies of this kind have been conducted in Poland. In the analysis limited to rain events, the estimated parameters (a = 265, b = 1.48) showed relatively minor deviations from the classical Z–R function for convective rainfall, Z = 300R1.4. However, the parameter a deviated more noticeably from the Z = 200R1.6 relationship proposed by Marshall and Palmer, which is commonly used to convert radar reflectivity into rainfall estimates, including in the Polish POLRAD radar system. The dataset used in this study included rainfall events of varying types, both stratiform and convective, which contributed to the averaging of Z–R parameters. The values for the parameter a in the Z–R relationship estimated for the other two categories of precipitation types, sleet and snow, were significantly higher than those determined for rain events alone. The a values calculated for individual events demonstrated considerable variability, ranging from 80 to 751, while the b values presented a more predictable range, from 1.10 to 1.77. The highest parameter a values were observed during the summer months: June, July, and August. The variability in the Z–R relationship for individual events assessed in this study indicates the need for further research under diverse meteorological conditions, particularly for stratiform and convective precipitation. Full article
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13 pages, 3164 KiB  
Article
The Steady-State and Dynamic Characteristics of a Humidity-Sensitive Air Inlet: Modeling Based on Measurements
by Maciej Mijakowski and Piotr Narowski
Energies 2025, 18(13), 3444; https://doi.org/10.3390/en18133444 - 30 Jun 2025
Viewed by 208
Abstract
This paper presents the airflow characteristics of humidity-sensitive air inlet. This type of air inlets and exhausts are often part of demand control ventilation, especially in dwellings where humidity is an important indicator of ventilation needs. Humidity-controlled ventilation is one of the simplest [...] Read more.
This paper presents the airflow characteristics of humidity-sensitive air inlet. This type of air inlets and exhausts are often part of demand control ventilation, especially in dwellings where humidity is an important indicator of ventilation needs. Humidity-controlled ventilation is one of the simplest implementations of smart ventilation, even in the case of a natural ventilation system. This type of solution leads to decreased energy consumption and increases the indoor air quality. A description of airflow characteristics is crucial for resolving these issues. The presented characteristics are based on the measurements of the indoor/outdoor relative humidity, airflow, and pressure drop across the air inlet. The characteristics are described based on a general power law flow model (V = C·∆pn), which is the most suitable, for example, for the CONTAM multizone indoor air quality and ventilation analysis computer program. The characteristics include relationships between the indoor and outdoor relative humidity, hysteresis, and dynamic changes in indoor relative humidity. The simplified and complex formulas are presented. The accuracy of the airflow calculation based on these formulas is discussed. Full article
(This article belongs to the Section G: Energy and Buildings)
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22 pages, 6603 KiB  
Article
Vibration Characterization of Ship Propulsion System Including Stern-Bearing Installation Errors
by Jianhua Zhou, Shidong Fan, Hanhua Zhu, Yulei Zhu, Hailong Weng, Junlang Yuan and Taiwei Yang
J. Mar. Sci. Eng. 2025, 13(7), 1241; https://doi.org/10.3390/jmse13071241 - 27 Jun 2025
Viewed by 368
Abstract
During the operation and service of a ship, its power system will affect the stability, reliability, and safety of the ship’s power system and the ship’s vitality if there are typical problems, such as unstable operation and vibration of the shaft system. If [...] Read more.
During the operation and service of a ship, its power system will affect the stability, reliability, and safety of the ship’s power system and the ship’s vitality if there are typical problems, such as unstable operation and vibration of the shaft system. If the tail bearing is not properly installed, it will lead to increased vibration at its support during operation, which will cause the propulsion system components to come loose and even produce destructive accidents. This paper combines the theory of multi-degree-of-freedom system dynamics to study the propulsion system vibration modeling technology based on the bearing–mounting error, analyze the mapping law between the bearing–mounting error and the shaft system vibration, construct a shaft system vibration model with the bearing–mounting error included, and analyze the influence of the bearing vertical mounting error and lateral mounting error on the vibration performance of the shaft system. This paper establishes the equations of motion of the shaft system with bearing–mounting errors and analyzes the relationship between the bearing vertical mounting errors and lateral mounting errors and the amplitude, speed, and acceleration of the paddle shaft system. The analyzed results show that the vibration response of the shaft system gradually increases with the increase in the bearing–mounting error. With the increase in the bearing vertical mounting error, the increase in vibration amplitude and the transient response of vibration acceleration in the vertical direction is larger than that in the horizontal direction, and the sensitivity of the transient response of vibration acceleration in the vertical direction to the bearing vertical mounting error is larger than that in the horizontal direction. With the increase in the bearing lateral mounting error, the increase in the vibration acceleration transient response value of the paddle shaft system in the horizontal direction is larger than that in the vertical direction, and the sensitivity of the vibration amplitude and vibration acceleration transient response to the bearing lateral mounting error in the horizontal direction is larger than that in the vertical direction. The bearing vertical installation error has a greater effect on the vibration of the paddle shaft system in the vertical direction than in the horizontal direction, and the bearing lateral installation error has a greater effect on the vibration of the paddle shaft system in the horizontal direction than in the vertical direction. The results of this paper can provide a theoretical basis and technical reference for the installation and calibration of ship propulsion system. Full article
(This article belongs to the Special Issue Safety and Reliability of Ship and Ocean Engineering Structures)
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14 pages, 1723 KiB  
Article
The Social Network of the Holy Land
by Christian Canu Højgaard
Religions 2025, 16(7), 843; https://doi.org/10.3390/rel16070843 - 25 Jun 2025
Viewed by 374
Abstract
The so-called Holiness Code (Leviticus 17–26) describes the land (אֶרֶץ) almost as a human being. In biblical scholarship on this law-text, the land has often been explained as an independent agent and more powerful than even the human beings that are present in [...] Read more.
The so-called Holiness Code (Leviticus 17–26) describes the land (אֶרֶץ) almost as a human being. In biblical scholarship on this law-text, the land has often been explained as an independent agent and more powerful than even the human beings that are present in the text. This paper will use social network analysis to test these conclusions and provide a more detailed account of the role of the land. The paper sets out to develop a social network model of the Holiness Code by including all interactions among human/divine participants and physical space. The paper then explores how human/divine participants relate to space, and it is shown that the participant roles are closely connected to access to space. Afterwards, the social role of the land is scrutinized by exploring each of its relationships, and by conducting a cluster analysis to understand the structural properties of the network. It is shown that the land is not as central and agentive as is usually thought but, rather, that the land plays a secondary role as a vulnerable character in need of protection. The paper is concluded by reflections on the potential of social network analysis for understanding character roles in literature. Full article
(This article belongs to the Special Issue Computational Approaches to Ancient Jewish and Christian Texts)
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15 pages, 1957 KiB  
Article
General Solutions for Magnetohydrodynamic Unidirectional Motions of a Class of Fluids with Power-Law Dependence of Viscosity on Pressure Through a Planar Channel
by Constantin Fetecau and Dumitru Vieru
Mathematics 2025, 13(11), 1800; https://doi.org/10.3390/math13111800 - 28 May 2025
Viewed by 227
Abstract
An analytical study is conducted on unsteady, one-directional magnetohydrodynamic (MHD) flows of electrically conducting, incompressible, and viscous fluids, where the viscosity varies with pressure following a power-law relationship. The flow takes place within a planar channel and is driven by the lower plate, [...] Read more.
An analytical study is conducted on unsteady, one-directional magnetohydrodynamic (MHD) flows of electrically conducting, incompressible, and viscous fluids, where the viscosity varies with pressure following a power-law relationship. The flow takes place within a planar channel and is driven by the lower plate, which moves along its own plane with an arbitrary, time-dependent speed. The effects of gravitational acceleration are also considered. General exact formulas are derived for both the dimensionless velocity of the fluid and the resulting non-zero shear stress. Moreover, these are the only general solutions for the MHD motions of the fluids considered, and they can produce precise solutions for any motion of this type for respective fluids. The proposed analytical method leads to simple forms of analytical solutions and can be useful in the study of other cases of fluids with viscosity depending on pressure. As an example, solutions related to the modified Stokes’ second problem are presented and confirmed through graphical validation. These solutions also help highlight the impact of the magnetic field on fluid dynamics and determine the time needed for the system to achieve a steady state. Graphical representations indicate that a steady state is reached more quickly and the fluid moves more slowly when a magnetic field is applied. Full article
(This article belongs to the Special Issue Advances and Applications in Computational Fluid Dynamics)
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20 pages, 3863 KiB  
Article
Analysis of Wind–Wave Relationship in Taiwan Waters
by Kai-Ho Cheng, Chih-Hsun Chang, Yi-Chung Yang, Yu-Hao Tseng, Chung-Ru Ho, Tai-Wen Hsu and Dong-Jiing Doong
J. Mar. Sci. Eng. 2025, 13(6), 1047; https://doi.org/10.3390/jmse13061047 - 26 May 2025
Viewed by 851
Abstract
The relationship between wind and waves has been extensively studied over time. However, understanding the local wind and wave relationship remains crucial for advancing renewable energy development and optimizing ocean management strategies. This study used wind and wave data collected by the ten [...] Read more.
The relationship between wind and waves has been extensively studied over time. However, understanding the local wind and wave relationship remains crucial for advancing renewable energy development and optimizing ocean management strategies. This study used wind and wave data collected by the ten weather buoys in the waters surrounding Taiwan to analyze regional sea states. The relationship between wind speed and significant wave height (SWH) was examined using regression analysis. Additionally, machine learning techniques were employed to assess the relative importance of features contributing to SWH growth. The regression analysis revealed that SWH in the waters surrounding Taiwan was not fully developed, with notable discrepancies observed between the waters east and west of Taiwan. According to the power law formula describing the relationship between wind speed and SWH, the eastern waters exhibited a larger prefactor coupled with a smaller scaling exponent, while the western waters manifested a converse parametric configuration. Through an evaluation of four machine learning algorithms, it was determined that wind speed is the most influential factor driving these regional differences, especially in the waters west of Taiwan. Beyond wind speed, air pressure or temperature emerged as the secondary feature factor governing wind–wave interactions in the waters east of Taiwan. Full article
(This article belongs to the Special Issue Ocean Observations)
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22 pages, 5676 KiB  
Article
Research on Rheological Behavior and Strength Characteristics of Cement-Based Grouting Materials
by Xuewei Liu, Hao Qu, Bin Liu, Yuan Zhou, Jinlan Li, Wei Deng and Weilong Tao
Buildings 2025, 15(11), 1796; https://doi.org/10.3390/buildings15111796 - 23 May 2025
Viewed by 393
Abstract
The mechanical properties of grouting materials and their cured grouts significantly impact the reinforcement effectiveness in deep coal mine roadways. This study employed shear rheology tests of slurry, structural tests, NMR (nuclear magnetic resonance), and uniaxial compression tests to comparatively analyze the mechanical [...] Read more.
The mechanical properties of grouting materials and their cured grouts significantly impact the reinforcement effectiveness in deep coal mine roadways. This study employed shear rheology tests of slurry, structural tests, NMR (nuclear magnetic resonance), and uniaxial compression tests to comparatively analyze the mechanical characteristics of a composite cement-based grouting material (HGC), ordinary Portland cement (OPC), and sulfated aluminum cement (SAC) slurry and their cured grouts. The HGC (High-performance Grouting Composite) slurry is formulated with 15.75% sulfated aluminum cement (SAC), 54.25% ordinary Portland cement (OPC), 10% fly ash, and 20% mineral powder, achieving a water/cement ratio of 0.26. The results indicate that HGC slurry more closely follows power-law flow characteristics, while OPC and SAC slurries fit better with the Bingham model. The structural recovery time for HGC slurry after high-strain disturbances is 52 s, significantly lower than the 312 s for OPC and 121 s for SAC, indicating that HGC can quickly produce hydration products that re-bond the flocculated structure. NMR T2 spectra show that HGC cured grouts have the lowest porosity, predominantly featuring inter-nanopores, whereas OPC and SAC have more super-nanopores. Uniaxial compression tests show that the uniaxial compressive strength of HGC, SAC, and OPC samples at various curing ages gradually decreases. Compared to traditional cementitious materials, HGC exhibits a rapid increase in uniaxial compressive strength within the first seven days, with an increase rate of approximately 77.97%. Finally, the relationship between micropore distribution and strength is analyzed, and the micro-mechanisms underlying the strength differences of different grouting materials are discussed. This study aids in developing a comparative analysis system of mechanical properties for deep surrounding rock grouting materials, providing a reference for selecting grouting materials for various engineering fractured rock masses. Full article
(This article belongs to the Special Issue Trends and Prospects in Cementitious Material)
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23 pages, 9305 KiB  
Article
Structure and Regeneration Differentiation of Coniferous Stand Groups in Representative Altay Montane Forests: Demographic Evidence from Dominant Boreal Conifers
by Haiyan Zhang, Yang Yu, Lingxiao Sun, Chunlan Li, Jing He, Ireneusz Malik, Malgorzata Wistuba and Ruide Yu
Forests 2025, 16(6), 885; https://doi.org/10.3390/f16060885 - 23 May 2025
Viewed by 454
Abstract
With the intensification of global climate change and human activities, coniferous species as the main components of natural forests in the Altay Mountains are facing the challenges of aging and regeneration. This study systematically analyzed structural heterogeneity and regeneration of three coniferous stand [...] Read more.
With the intensification of global climate change and human activities, coniferous species as the main components of natural forests in the Altay Mountains are facing the challenges of aging and regeneration. This study systematically analyzed structural heterogeneity and regeneration of three coniferous stand groups, Larix sibirica Ledeb. stand group, Abies sibirica Ledeb.-Picea obovata Ledeb.-Larix sibirica mixed stand group, and Picea obovata stand group, respectively, across western, central, and eastern forest areas of the Altay Mountains in Northwest China based on field surveys in 2023. Methodologically, we integrated Kruskal–Wallis/Dunn’s post hoc tests, nonlinear power-law modeling (diameter at breast height (DBH)–age relationships, validated via R2, root mean square error (RMSE), and F-tests), static life tables (age class mortality and survival curves), and dynamic indices. Key findings revealed structural divergence: the L. sibirica stand group exhibited dominance of large-diameter trees (>30 cm DBH) with sparse seedlings/saplings and limited regeneration; the mixed stand group was dominated by small DBH individuals (<10 cm), showing young age structures and vigorous regeneration; while the P. obovata stand group displayed uniform DBH/height distributions and slow regeneration capacity. Radial growth rates differed significantly—highest in the mixed stand group (average of 0.315 cm/a), intermediate in the P. obovata stand group (0.216 cm/a), and lowest in the L. sibirica stand group (0.180 cm/a). Age–density trends varied among stand groups: unimodal in the L. sibirica and P. obovata stand groups while declining in the mixed stand group. All stand groups followed a Deevey-II survival curve (constant mortality across ages). The mixed stand group showed the highest growth potential but maximum disturbance risk, the L. sibirica stand group exhibited complex variation with lowest risk probability, while the P. obovata stand group had weaker adaptive capacity. These results underscore the need for differentiated management: promoting L. sibirica regeneration via gap-based interventions, enhancing disturbance resistance in the mixed stand group through structural diversification, and prioritizing P. obovata conservation to maintain ecosystem stability. This multi-method framework bridges stand-scale heterogeneity with demographic mechanisms, offering actionable insights for climate-resilient forestry. Full article
(This article belongs to the Section Forest Ecology and Management)
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12 pages, 14016 KiB  
Article
Peculiarities of the Creep Behavior of 15Kh2NMFAA Vessel Steel at High Temperatures
by Egor Terentyev, Artem Marchenkov, Vladimir Loktionov, Anastasia Pankina, Georgy Sviridov, Ksenia Borodavkina, Danila Chuprin and Nikita Lavrik
Metals 2025, 15(6), 571; https://doi.org/10.3390/met15060571 - 22 May 2025
Viewed by 340
Abstract
The creep properties of 15Kh2NMFAA nuclear WWER (water–water energetic reactor) vessel steel in the range of 500–1200 °C temperatures, which may appear during severe nuclear reactor accidents, were investigated. The present paper attempts to analyze the creep curves obtained from tensile testing at [...] Read more.
The creep properties of 15Kh2NMFAA nuclear WWER (water–water energetic reactor) vessel steel in the range of 500–1200 °C temperatures, which may appear during severe nuclear reactor accidents, were investigated. The present paper attempts to analyze the creep curves obtained from tensile testing at high temperatures using the Larson–Miller parametric technique. The power law rate and material coefficient of Norton’s equation with the Monkman–Grant relationship coefficient were found for each test temperature. It is shown that in accordance with the Monkman–Grant relationship coefficient values, changing the creep type from dislocation glide to high temperature dislocation climb occurs in the temperature range of 600–700 °C, which leads to a slope change in the Larson–Miller parameter plot and the conversion of steel creep behavior. It is also shown that in the range of A1A3 temperatures, a stepwise change in creep characteristics occurs, which is associated with phase transformations. In addition, the constancy of the product of the time to rupture τr and the minimum creep rate ϵ˙min in the ranges of 600–700 °C and A3—1200 °C was noted. The proposed approach improves the accuracy of time to rupture estimation of 15Kh2NMFAA steel by at least one order of magnitude. Based on the research results, the calculated dependence of the steel’s long-term strength limit on temperature was obtained for several time bases, allowing us to increase the accuracy of material survivability prediction in the case of a severe accident at a nuclear reactor. Full article
(This article belongs to the Special Issue Advances in Creep Behavior of Metallic Materials)
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29 pages, 67369 KiB  
Article
Fractal–Fractional Synergy in Geo-Energy Systems: A Multiscale Framework for Stress Field Characterization and Fracture Network Evolution Modeling
by Qiqiang Ren, Tianhao Gao, Rongtao Jiang, Jin Wang, Mengping Li, Jianwei Feng and He Du
Fractal Fract. 2025, 9(5), 322; https://doi.org/10.3390/fractalfract9050322 - 19 May 2025
Viewed by 713
Abstract
This research introduces an innovative fractal–fractional synergy framework for multiscale analysis of stress field dynamics in geo-energy systems. By integrating fractional calculus with multiscale fractal dimension analysis, we develop a coupled approach examining stress redistribution patterns across different geological scales. The methodology combines [...] Read more.
This research introduces an innovative fractal–fractional synergy framework for multiscale analysis of stress field dynamics in geo-energy systems. By integrating fractional calculus with multiscale fractal dimension analysis, we develop a coupled approach examining stress redistribution patterns across different geological scales. The methodology combines fractal characterization of rock mechanical parameters with fractional-order stress gradient modeling, validated through integrated analysis of core testing, well logging, and seismic inversion data. Our fractal–fractional operators enable simultaneous characterization of stress memory effects and scale-invariant fracture propagation patterns. Key insights reveal the following: (1) Non-monotonic variations in rock mechanical properties (fractal dimension D = 2.31–2.67) correlate with oil–water ratio changes, exhibiting fractional-order transitional behavior. (2) Critical stress thresholds (12.19–25 MPa) for fracture activation follow fractional power-law relationships with fracture orientation deviations. (3) Fracture network evolution demonstrates dual-scale dynamics—microscale tip propagation governed by fractional stress singularities (order α = 0.63–0.78) and macroscale expansion obeying fractal growth patterns (Hurst exponent H = 0.71 ± 0.05). (4) Multiscale modeling reveals anisotropic development with fractal dimension increasing by 18–22% during multi-well fracturing operations. The fractal–fractional formalism successfully resolves the stress-shadow paradox while quantifying water channeling risks through fractional connectivity metrics. This work establishes a novel paradigm for coupled geomechanical–fluid dynamics analysis in complex reservoir systems. Full article
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