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18 pages, 5587 KiB  
Article
The Determinants of Commercial Land Leases in the Non-Central Districts of a Large City in China: Data Analysis from the Government–Market Perspective
by Jing Cheng
Mathematics 2025, 13(10), 1595; https://doi.org/10.3390/math13101595 - 13 May 2025
Viewed by 152
Abstract
Based on the data of the non-central districts in Shanghai, this paper investigates the determinants of the commercial land leases of district governments from the government–market perspective and how these determinants affect the price and area of commercial land leasing. A kernel density [...] Read more.
Based on the data of the non-central districts in Shanghai, this paper investigates the determinants of the commercial land leases of district governments from the government–market perspective and how these determinants affect the price and area of commercial land leasing. A kernel density analysis is used to analyze the agglomeration degree and density distribution of commercial land leasing. The variables are considered as the factors impacting commercial land leases based on a literature review and land development in Shanghai. The mathematical models used for multiple linear regression for the leased price and area of the influencing factors of commercial land leases from the perspective of the government and market are proposed. The results show that Shanghai’s multi-center development strategy aims to optimize the city’s commercial layout by developing the key areas of non-central districts. The construction area and plot ratio of land; the distances from the land to the city center, district center, airports, the nearest middle schools, the nearest park, and the nearest industrial zone; and the quantity of subway stations and highways affect commercial land leases. Policies are proposed to improve commercial land lease efficiency, make more suitable land planning strategies, and optimize urban spatial structures. Full article
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17 pages, 4574 KiB  
Article
A Multi-Source Object-Oriented Framework for Extracting Aquaculture Ponds: A Case Study from the Chaohu Lake Basin, China
by Lingyan Qi, Zhengxin Wang, Liuyi Dai, Fengwen Wu, Han Yin, Kejia Zhang, Mingzhu Guo, Liangtao Ye and Shanshan Zhang
Water 2025, 17(9), 1406; https://doi.org/10.3390/w17091406 - 7 May 2025
Viewed by 262
Abstract
Quantifying the extent and distribution of aquaculture ponds has become the key to management in the aquaculture industry, thereby contributing to the sustainable development of the region. However, accurate extraction of individual aquaculture pond boundaries from mesoscale remote sensing images remains a significant [...] Read more.
Quantifying the extent and distribution of aquaculture ponds has become the key to management in the aquaculture industry, thereby contributing to the sustainable development of the region. However, accurate extraction of individual aquaculture pond boundaries from mesoscale remote sensing images remains a significant challenge. In this work, we developed the Multi-source Object-oriented Framework for extracting Aquaculture ponds (MOFA) to address mapping challenges in the Chaohu Lake basin, China. The MOFA combined Sentinel-1 synthetic aperture radar (SAR) with Sentinel-2 data, applying an object-oriented approach with adaptive threshold segmentation for robust and automated aquaculture pond delineation. Our performance evaluation results showed that the overall accuracy is as high as 90.75%. The MOFA is thus capable of distinguishing seasonal water bodies, lakes, reservoirs, and rivers from individual (non-centralized, contiguous) aquaculture ponds. Our results showed that the central and south sections of the Chaohu Lake basin are characterized by denser aquaculture pond distributions, relative to those in the western basin. The total area of aquaculture ponds across the entire basin decreased from 19,297.86 hm2 in 2016 to 18,262.77 hm2 in 2023, which is likely attributed to local policy adjustments, resource optimization, shifting market demands, or natural environmental changes. The abandonment and unregulated expansion of aquaculture ponds threaten sustainable development. Local governments must implement adaptive governance strategies to balance ecological preservation with economic growth. Overall, the MOFA can quickly and accurately extract and map aquaculture ponds, and further support the scientific planning of sustainable aquaculture development. Full article
(This article belongs to the Special Issue Wetland Water Quality Monitoring and Assessment)
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10 pages, 1146 KiB  
Article
The Effectiveness of Collaborative Centralized Information Systems in Project Management: A Pilot Demonstration of a Multifunctional Building in Africa
by Fábio Oliveira Santos and Nuno Lacerda Lopes
Buildings 2025, 15(6), 860; https://doi.org/10.3390/buildings15060860 - 10 Mar 2025
Viewed by 796
Abstract
In the current context of transformation within the Architecture, Engineering, and Construction (AEC) sector, and the growing adoption of interdisciplinary collaboration processes such as Integrated Project Delivery (IPD) and Building Information Modeling (BIM), information management systems are crucial to ensure both the security [...] Read more.
In the current context of transformation within the Architecture, Engineering, and Construction (AEC) sector, and the growing adoption of interdisciplinary collaboration processes such as Integrated Project Delivery (IPD) and Building Information Modeling (BIM), information management systems are crucial to ensure both the security and reliability of data, and its effective distribution among project stakeholders. Collaborative centralized information systems have emerged as powerful tools for communication and data exchange. However, establishing efficient and flexible methodologies for managing this information remains a significant challenge. This study aims to demonstrate the effectiveness of collaborative centralized information systems in project information management through a real-world example. The research focuses on analyzing a pilot project developed by our organization using the Bimcollab digital collaborative platform. The methodology adopted includes the following: (i) descriptive characterization of the project; (ii) selection of a defined timeframe; (iii) description and characterization of the information management systems; and (iv) comparative analysis between non-centralized and centralized information management systems. The case study examines the Detail Design phase of a project for a pharmaceutical industry complex comprising six buildings, with a total area of approximately 18,000 m2. From October to December 2022, a non-centralized information system was used, followed by the implementation of a centralized information system from January to March 2023. Key indicators, such as the number of occurrences, average number of recipients involved, response times, and resolution rates, were analyzed. The results showed that the complete resolution rate improved from 51% under the non-centralized system to 85% with the centralized system, representing a 34% increase. The pilot project underscores the benefits of centralized collaborative information systems, particularly in reducing response times and increasing resolution rates among stakeholders. These benefits are expected to apply across various functional programs, including residential construction, contributing to optimizing both project design and construction practices. While derived from a single case study, the findings highlight the need for further research involving multiple cases and phases of the project lifecycle to validate the generalizability of these outcomes. Full article
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24 pages, 15920 KiB  
Article
Optimizing the Equality of Healthcare Services in Wuhan, China, Using a New Multimodal Two-Step Floating Catchment Area Model in Conjunction with the Hierarchical Maximal Accessibility Equality Model
by Pengfei Lu, Xiang Li, Lina Wang, Zhengbin Zhang, Danfei Zhang, Wenya Zhang and Yaru Li
ISPRS Int. J. Geo-Inf. 2025, 14(2), 93; https://doi.org/10.3390/ijgi14020093 - 19 Feb 2025
Viewed by 471
Abstract
The equity of medical services is crucial for the quality of life of a population and the sustainable development of cities. Current research on optimizing the maximal equity of medical facilities has the following limitations: (1) In the accessibility calculation models for multiple [...] Read more.
The equity of medical services is crucial for the quality of life of a population and the sustainable development of cities. Current research on optimizing the maximal equity of medical facilities has the following limitations: (1) In the accessibility calculation models for multiple transportation modes, the impact of factors such as public transport transfers and travel distance on the choice of transportation mode is often overlooked. (2) Existing spatial equity indicators are mostly derived from the overall study area, failing to fully consider the differences in population distribution and development gaps within different development zones inside the region. This study proposes a novel Incorporating Multiple Transportation Two-Step Floating Catchment Area (IMT-2SFCA) and a Hierarchical Theil-based Maximal Accessibility Equality model (HT-MAE) to optimize the equity of access to tuberculosis medical institutions in Wuhan. The findings reveal that, compared to single-mode transportation accessibility models, the multimodal accessibility model integrates the characteristics of four transportation modes, providing a more realistic reflection of residents’ access to medical services. The optimization results show a significant improvement in the equity of access to medical services across Wuhan and among different economic development zones, although the equity indicators in non-central urban areas have declined. The results of this study provide a theoretical basis and practical insights for alleviating the inequality of access to medical services across different urban layers. Full article
(This article belongs to the Topic Spatial Decision Support Systems for Urban Sustainability)
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25 pages, 1557 KiB  
Article
Evidential Analysis: An Alternative to Hypothesis Testing in Normal Linear Models
by Brian Dennis, Mark L. Taper and José M. Ponciano
Entropy 2024, 26(11), 964; https://doi.org/10.3390/e26110964 - 10 Nov 2024
Viewed by 1327
Abstract
Statistical hypothesis testing, as formalized by 20th century statisticians and taught in college statistics courses, has been a cornerstone of 100 years of scientific progress. Nevertheless, the methodology is increasingly questioned in many scientific disciplines. We demonstrate in this paper how many of [...] Read more.
Statistical hypothesis testing, as formalized by 20th century statisticians and taught in college statistics courses, has been a cornerstone of 100 years of scientific progress. Nevertheless, the methodology is increasingly questioned in many scientific disciplines. We demonstrate in this paper how many of the worrisome aspects of statistical hypothesis testing can be ameliorated with concepts and methods from evidential analysis. The model family we treat is the familiar normal linear model with fixed effects, embracing multiple regression and analysis of variance, a warhorse of everyday science in labs and field stations. Questions about study design, the applicability of the null hypothesis, the effect size, error probabilities, evidence strength, and model misspecification become more naturally housed in an evidential setting. We provide a completely worked example featuring a two-way analysis of variance. Full article
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31 pages, 17737 KiB  
Article
Examining the Impact of the Built Environment on Multidimensional Urban Vitality: Using Milk Tea Shops and Coffee Shops as New Indicators of Urban Vitality
by Ziqi Xu, Jiang Chang, Fangyu Cheng, Xiaoyi Liu, Tianning Yao, Kuntao Hu and Jingyu Sun
Buildings 2024, 14(11), 3517; https://doi.org/10.3390/buildings14113517 - 4 Nov 2024
Cited by 4 | Viewed by 2497
Abstract
Urban vitality is a critical driver of sustainable urban development, significantly contributing to the enhancement of human well-being. A thorough and multidimensional comprehension of urban vitality is essential for shaping future urban planning and policy-making. This study, focused on Chengdu, proposes a framework [...] Read more.
Urban vitality is a critical driver of sustainable urban development, significantly contributing to the enhancement of human well-being. A thorough and multidimensional comprehension of urban vitality is essential for shaping future urban planning and policy-making. This study, focused on Chengdu, proposes a framework for assessing various dimensions of UV through the distribution of milk tea and coffee shops. Using random forest and multi-scale geographically weighted regression models, this study investigates the factors influencing urban vitality from both mathematical thresholds and spatial heterogeneity, and develops spatial maps of future vitality to inform targeted urban strategies. The results show that (1) the milk tea index is effective in capturing population vitality, while the coffee index is more closely associated with economic vitality and urban renewal; (2) office buildings (13.46%) and commercial complexes (13.70%) have the most significant impact on both economic and population vitality, while the importance of transportation factors has notably decreased; (3) the influence of these factors demonstrates spatial heterogeneity and nonlinear relationships, with subway station density of 0.5–0.8 stations per kilometer being optimal for stimulating both types of vitality. The minimum threshold for economic vitality in a given unit is a housing price exceeding 6000 RMB/m2; (4) the future vitality map suggests that urban planners should pay greater attention to non-central districts with high development potential. Moreover, spontaneous social interactions and consumer behaviors stimulated by various shops are critical components of urban vitality. In designing the physical environment and urban spatial forms, special attention should be given to enhancing the attractiveness of physical spaces and their capacity to accommodate social interaction. Full article
(This article belongs to the Special Issue Research towards the Green and Sustainable Buildings and Cities)
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7 pages, 258 KiB  
Article
Remarks on Limit Theorems for the Free Quadratic Forms
by Wiktor Ejsmont, Marek Biernacki and Patrycja Hęćka
Entropy 2024, 26(10), 870; https://doi.org/10.3390/e26100870 - 17 Oct 2024
Viewed by 712
Abstract
In 2021, Ejsmont and Biernacki showed that the free tangent distribution can be used to measure household satisfaction with durable consumer goods. This distribution arises as the limit of free random variables. This, new article serves as the theoretical introduction to the continuation [...] Read more.
In 2021, Ejsmont and Biernacki showed that the free tangent distribution can be used to measure household satisfaction with durable consumer goods. This distribution arises as the limit of free random variables. This, new article serves as the theoretical introduction to the continuation of the research presented in the paper from 2021. We continue the study of the limit of specific quadratic forms in free probability, which is the first step towards constructing a new distribution for the evaluation of satisfaction with material affluence among household. We formulate a non-central limit theorem for weighted sums of commutators and square of the sums for free random variable. In addition we give the random matrix models for these limits. Full article
(This article belongs to the Special Issue Random Matrix Theory and Its Innovative Applications)
29 pages, 6358 KiB  
Article
A Distributed Deadlock-Free Task Offloading Algorithm for Integrated Communication–Sensing–Computing Satellites with Data-Dependent Constraints
by Ruipeng Zhang, Yikang Yang and Hengnian Li
Remote Sens. 2024, 16(18), 3459; https://doi.org/10.3390/rs16183459 - 18 Sep 2024
Viewed by 1062
Abstract
Integrated communication–sensing–computing (ICSC) satellites, which integrate edge computing servers on Earth observation satellites to process collected data directly in orbit, are attracting growing attention. Nevertheless, some monitoring tasks involve sequential sub-tasks like target observation and movement prediction, leading to data dependencies. Moreover, the [...] Read more.
Integrated communication–sensing–computing (ICSC) satellites, which integrate edge computing servers on Earth observation satellites to process collected data directly in orbit, are attracting growing attention. Nevertheless, some monitoring tasks involve sequential sub-tasks like target observation and movement prediction, leading to data dependencies. Moreover, the limited energy supply on satellites requires the sequential execution of sub-tasks. Therefore, inappropriate assignments can cause circular waiting among satellites, resulting in deadlocks. This paper formulates task offloading in ICSC satellites with data-dependent constraints as a mixed-integer linear programming (MILP) problem, aiming to minimize service latency and energy consumption simultaneously. Given the non-centrality of ICSC satellites, we propose a distributed deadlock-free task offloading (DDFTO) algorithm. DDFTO operates in parallel on each satellite, alternating between sub-task inclusion and consensus and sub-task removal until a common offloading assignment is reached. To avoid deadlocks arising from sub-task inclusion, we introduce the deadlock-free insertion mechanism (DFIM), which strategically restricts the insertion positions of sub-tasks based on interval relationships, ensuring deadlock-free assignments. Extensive experiments demonstrate the effectiveness of DFIM in avoiding deadlocks and show that the DDFTO algorithm outperforms benchmark algorithms in achieving deadlock-free offloading assignments. Full article
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32 pages, 1052 KiB  
Article
A Model of Information Visualization Interpretation
by Michael G. Hilgers
Appl. Sci. 2024, 14(15), 6731; https://doi.org/10.3390/app14156731 - 1 Aug 2024
Viewed by 961
Abstract
Since the groundbreaking work by Cleveland and McGill in 1984, studies have revealed the difficulties humans have extracting quantitative data from visualizations as simple as bar graphs. As a first step toward understanding this situation, this paper proposes a mathematical model of the [...] Read more.
Since the groundbreaking work by Cleveland and McGill in 1984, studies have revealed the difficulties humans have extracting quantitative data from visualizations as simple as bar graphs. As a first step toward understanding this situation, this paper proposes a mathematical model of the interpretation effort of a bar graph using concepts drawn from eye tracking. First, three key areas of interest (AOIs) are identified, and fixations are modeled as random point clouds within the AOIs. Stochastic geometry is introduced via random triangles connecting fixations within the adjacent key visual regions. The so-called landmark methodology provides the basis for the probabilistic analysis of the constructed system. It is found that the random length of interest in a stochastic triangle has a noncentral chi distribution with a known mean. Unique to this model, in terms of previous landmark applications, is the inclusion of a correlation between fixations, which is justified by physiological studies of the eyes. This approach introduces several model parameters, such as the noncentrality parameter, variance of the fixation cloud, correlation between fixations, and a visualization scale. A detailed parametric analysis examining the dependence of the mean on these parameters is conducted. The paper ties this work to the visualization via a definition of the expected visual measurement error. An asymptotic analysis of the visual error is performed, and a simple expression is found to relate the expected visual measurement error to the key model parameters. From this expression, the influence these parameters have on a visualization’s interpretation is considered. Full article
(This article belongs to the Special Issue Recent Applications of Information Visualization and Graphics)
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23 pages, 19196 KiB  
Article
Spatiotemporal Variation in Ecological Environmental Quality and Its Response to Different Factors in the Xia-Zhang-Quan Urban Agglomeration over the Past 30 Years
by Zongmei Li, Wang Man, Jiahui Peng, Yang Wang, Qin Nie, Fengqin Sun and Yutong Huang
Land 2024, 13(7), 1078; https://doi.org/10.3390/land13071078 - 17 Jul 2024
Viewed by 1043
Abstract
The interactions between economic development, environmental sustainability, population growth, and urbanization are vital in assessing the ecological dynamics of urban agglomerations. This study explores the relationship between economic development, environmental sustainability, population growth, and urbanization within the Xia-Zhang-Quan urban agglomeration in Fujian Province [...] Read more.
The interactions between economic development, environmental sustainability, population growth, and urbanization are vital in assessing the ecological dynamics of urban agglomerations. This study explores the relationship between economic development, environmental sustainability, population growth, and urbanization within the Xia-Zhang-Quan urban agglomeration in Fujian Province from 1989 to 2022. Utilizing Landsat remote sensing images, we calculated the Remote Sensing Ecological Index (RSEI) to evaluate changes in ecological quality. The results show that the average RSEI values for 1989, 2000, 2010, and 2022 were 0.5829, 0.5607, 0.5827, and 0.6195, respectively, indicating an initial decline followed by a significant increase, culminating in an overall upward trend. The spatial distribution of RSEI classification shows that the study area has the largest proportion of mainly “good” ecological quality. The proportion of areas with “excellent” ecological environmental quality has increased (13.41% in 1989 and 25.12% in 2022), while those with “general” quality has decreased (28.03% in 1989 and 21.21% in 2022). Over the past three decades, Xiamen experienced substantial ecological degradation (RSEI change of −0.0897), Zhangzhou showed marked improvement (RSEI change of 0.0519), and Quanzhou exhibited slight deterioration (RSEI change of −0.0396). Central urban areas typically had poorer ecological conditions but showed signs of improvement, whereas non-central urban regions demonstrated significant environmental enhancement. The factor detector analysis identified land use as the dominant factor influencing ecological environmental quality, with precipitation having a relatively minor impact. Interaction analysis revealed that all other factors demonstrated bi-variable enhancement or nonlinear enhancement, suggesting that the interactive effects of these factors are greater than the effects of individual factors alone. Land use consistently showed solid explanatory power. Temperature also exhibited significant influence in 2022 when interacting with other factors. Due to urban planning that can plan for land use, these findings suggest that effective urban planning can harmonize economic development with ecological protection within the Xia-Zhang-Quan urban agglomeration. Full article
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19 pages, 10999 KiB  
Article
A Seedling Collection Unit of a Mobile Automatic Device for Forest Tree Planting—An Extended Operating Concept
by Sebastian Sobocki, Florian Adamczyk, Paweł Tylek, Michał Szaroleta, Kamil Żurowski, Mariusz Kormanek, Grzegorz Szewczyk, Sylwester Tabor, Mikołaj Zwierzyński, Michał Kaźmierczak and Jarosław Mac
Forests 2023, 14(12), 2420; https://doi.org/10.3390/f14122420 - 12 Dec 2023
Cited by 3 | Viewed by 1962
Abstract
Agrotechnological procedures related to forest management, including planting, are burdensome and the energy expenditure of the people working is very high. Nowadays, planting is usually carried out manually, and sometimes with the use of planters coupled to universal tractors. Occasionally, planters mounted on [...] Read more.
Agrotechnological procedures related to forest management, including planting, are burdensome and the energy expenditure of the people working is very high. Nowadays, planting is usually carried out manually, and sometimes with the use of planters coupled to universal tractors. Occasionally, planters mounted on high-power carriers are used, and usually the seedlings are removed from their cassettes and placed manually into the planter’s storage unit. In connection with the above, the prototype of a mobile automatic device for performing forest regeneration tasks and afforestation of post-agricultural and reclaimed areas (RoboFoR) was designed. The main task of this vehicle is planting forest tree seedlings with a covered root system, which are collected directly from their nursery cassettes. This study presents the structure, principle of operation and results of operational tests of the seedling storage and feeding unit. It was found that the unit achieved the expected work efficiency. However, imperfections in the system related to the non-centralized distribution of seedlings in containers and the high variability of biometric characteristics of the seedlings were also identified. A new solution for this unit was proposed, which will increase the reliability of collecting the seedlings. A new solution requires greater computational power of the control unit as well as equipping the sensor system with a technologically advanced root neck detection system. The new concept also assumes the possibility of independent movement of each gripper. Full article
(This article belongs to the Section Forest Operations and Engineering)
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35 pages, 27739 KiB  
Article
Study on Influencing Factors and Planning Strategies of Population Spatial Distribution in Urban Fringe Areas from the Perspective of Built Environment—The Case of Wuhan, China
by Yan Long, Zhengyuan Lu, Siyu Hu, Shiqi Luo, Xi Liu, Jingmei Shao, Yuqiao Zheng and Xuejun Liu
Land 2023, 12(9), 1739; https://doi.org/10.3390/land12091739 - 7 Sep 2023
Cited by 4 | Viewed by 1916
Abstract
Rationally relieving the population of urban centers in large cities, such as megacities and supercities, is one of the current goals of population development in China. The fringe area of a large city is a potential area to undertake the population of the [...] Read more.
Rationally relieving the population of urban centers in large cities, such as megacities and supercities, is one of the current goals of population development in China. The fringe area of a large city is a potential area to undertake the population of the central area. Studying the relationship between the population and the built environment in this area can help urban planners formulate targeted construction strategies to attract the population of the city center to move to the fringe areas. This paper takes the fringe areas of Wuhan in 2010 and 2020 as its specific research object and puts forward the “5D” index system of built environments that affects the spatial distribution of population based on population data and built environment data. The OLS model is used to screen the influencing factors. This paper analyzes the correlation between population and built environment using a multi-scale geographic weighted regression model as well. According to the results of the regression analysis combined with the development and construction of the fringe areas of remote urban areas in Wuhan over the past 20 years, some suggestions are put forward for the planning and construction of remote urban areas. The results show that the “5D” index system of the built environment covers the influencing factors of the spatial distribution of the population. MGWR reveals the correlation between the influencing factors and the spatial distribution of population in the marginal areas on the global scale and the local scale, respectively, which provides a clear direction for the development of planning and construction to improve the attractiveness of the non-central areas to the population. Full article
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13 pages, 321 KiB  
Article
Moments of the Negative Multinomial Distribution
by Frédéric Ouimet
Math. Comput. Appl. 2023, 28(4), 85; https://doi.org/10.3390/mca28040085 - 24 Jul 2023
Cited by 1 | Viewed by 1562
Abstract
The negative multinomial distribution appears in many areas of applications such as polarimetric image processing and the analysis of longitudinal count data. In previous studies, general formulas for the falling factorial moments and cumulants of the negative multinomial distribution were obtained. However, despite [...] Read more.
The negative multinomial distribution appears in many areas of applications such as polarimetric image processing and the analysis of longitudinal count data. In previous studies, general formulas for the falling factorial moments and cumulants of the negative multinomial distribution were obtained. However, despite the availability of the moment generating function, no comprehensive formulas for the moments have been calculated thus far. This paper addresses this gap by presenting general formulas for both central and non-central moments of the negative multinomial distribution. These formulas are expressed in terms of binomial coefficients and Stirling numbers of the second kind. Utilizing these formulas, we provide explicit expressions for all central moments up to the fourth order and all non-central moments up to the eighth order. Full article
(This article belongs to the Topic Mathematical Modeling)
14 pages, 4270 KiB  
Article
Numerical Analysis on Fatigue Crack Growth at Negative and Positive Stress Ratios
by Abdulnaser M. Alshoaibi and Yahya Ali Fageehi
Materials 2023, 16(10), 3669; https://doi.org/10.3390/ma16103669 - 11 May 2023
Cited by 7 | Viewed by 2044
Abstract
The finite element method was used to investigate the effect of the stress ratio on fatigue crack propagation behavior within the framework of the linear elastic fracture mechanics theory. The numerical analysis was carried out using ANSYS Mechanical R19.2 with the unstructured mesh [...] Read more.
The finite element method was used to investigate the effect of the stress ratio on fatigue crack propagation behavior within the framework of the linear elastic fracture mechanics theory. The numerical analysis was carried out using ANSYS Mechanical R19.2 with the unstructured mesh method-based separating, morphing, and adaptive remeshing technologies (SMART). Mixed mode fatigue simulations were performed on a modified four-point bending specimen with a non-central hole. A diverse set of stress ratios (R = 0.1, 0.2, 0.3, 0.4, 0.5, −0.1, −0.2, −0.3, −0.4, −0.5), including positive and negative values, is employed to examine the influence of the load ratio on the behavior of the fatigue crack propagation, with particular emphasis on negative R loadings that involve compressive excursions. A consistent decrease in the value of the equivalent stress intensity factor (ΔKeq) is observed as the stress ratio increases. The observation was made that the stress ratio significantly affects both the fatigue life and the distribution of von Mises stress. The results demonstrated a significant correlation between von Mises stress, ΔKeq, and fatigue life cycles. With an increase in the stress ratio, there was a significant decrease in the von Mises stress, accompanied by a rapid increase in the number of fatigue life cycles. The results obtained in this study have been validated by previously published literature on crack growth experiments and numerical simulations. Full article
(This article belongs to the Special Issue Metals Processing, Finite Element Analysis and Fatigue Design)
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29 pages, 4100 KiB  
Article
Analytically Computing the Moments of a Conic Combination of Independent Noncentral Chi-Square Random Variables and Its Application for the Extended Cox–Ingersoll–Ross Process with Time-Varying Dimension
by Sanae Rujivan, Athinan Sutchada, Kittisak Chumpong and Napat Rujeerapaiboon
Mathematics 2023, 11(5), 1276; https://doi.org/10.3390/math11051276 - 6 Mar 2023
Cited by 5 | Viewed by 2371
Abstract
This paper focuses mainly on the problem of computing the γth, γ>0, moment of a random variable Yn:=i=1nαiXi in which the αi’s are positive [...] Read more.
This paper focuses mainly on the problem of computing the γth, γ>0, moment of a random variable Yn:=i=1nαiXi in which the αi’s are positive real numbers and the Xi’s are independent and distributed according to noncentral chi-square distributions. Finding an analytical approach for solving such a problem has remained a challenge due to the lack of understanding of the probability distribution of Yn, especially when not all αi’s are equal. We analytically solve this problem by showing that the γth moment of Yn can be expressed in terms of generalized hypergeometric functions. Additionally, we extend our result to computing the γth moment of Yn when Xi is a combination of statistically independent Zi2 and Gi in which the Zi’s are distributed according to normal or Maxwell–Boltzmann distributions and the Gi’s are distributed according to gamma, Erlang, or exponential distributions. Our paper has an immediate application in interest rate modeling, where we can explicitly provide the exact transition probability density function of the extended Cox–Ingersoll–Ross (ECIR) process with time-varying dimension as well as the corresponding γth conditional moment. Finally, we conduct Monte Carlo simulations to demonstrate the accuracy and efficiency of our explicit formulas through several numerical tests. Full article
(This article belongs to the Special Issue Probability, Statistics and Their Applications 2021)
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