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Keywords = physical dimensions of space and time

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20 pages, 266 KiB  
Article
Divine Iconoclasm and the Making of Sacred Space in John Capgrave’s Life of Saint Katherine of Alexandria
by Yun Ni
Religions 2025, 16(6), 684; https://doi.org/10.3390/rel16060684 (registering DOI) - 27 May 2025
Abstract
The polemics of idol worship in John Capgrave’s Life of Saint Katherine of Alexandria have been interpreted by previous scholars as either the author’s engagement with the Lollard image controversy or a political critique of Henry VI. This essay, however, shifts the focus [...] Read more.
The polemics of idol worship in John Capgrave’s Life of Saint Katherine of Alexandria have been interpreted by previous scholars as either the author’s engagement with the Lollard image controversy or a political critique of Henry VI. This essay, however, shifts the focus from Katherine and her iconoclasm to the concept of divine iconoclasm, defined here not only as the divinely sanctioned or divinely motivated destruction of religious images but also as God’s direct intervention to dismantle false representations and correct human perceptions of the divine. It further argues that Capgrave’s Life redefines sacred space as primarily constructed through light, emphasizing its immateriality and exposing the saint’s physical limitations. In these scenarios, divine iconoclasm emerges as a constructive force that resolves the tension between the secular and the sacred. Moreover, Christ’s celestial manipulation of the vision of sacred space and the relationship between body and space—encouraging confidence while discouraging self-inflation—serves as a model for how a monarch should inspire both love and fear. In this way, Capgrave’s Mirrors for Princes is embedded within his hagiography, where the image debate features prominently, addressing the heated political and theological controversies of his time. By combining these elements, the essay bridges two strands of criticism that have previously treated the political and theological dimensions of the text separately. Full article
19 pages, 5373 KiB  
Article
Novel Spatio-Temporal Joint Learning-Based Intelligent Hollowing Detection in Dams for Low-Data Infrared Images
by Lili Zhang, Zihan Jin, Yibo Wang, Ziyi Wang, Zeyu Duan, Taoran Qi and Rui Shi
Sensors 2025, 25(10), 3199; https://doi.org/10.3390/s25103199 - 19 May 2025
Viewed by 172
Abstract
Concrete dams are prone to various hidden dangers after long-term operation and may lead to significant risk if failed to be detected in time. However, the existing hollowing detection techniques are few as well as inefficient when facing the demands of comprehensive coverage [...] Read more.
Concrete dams are prone to various hidden dangers after long-term operation and may lead to significant risk if failed to be detected in time. However, the existing hollowing detection techniques are few as well as inefficient when facing the demands of comprehensive coverage and intelligent management for regular inspections. Hence, we proposed an innovative, non-destructive infrared inspection method via constructed dataset and proposed deep learning algorithms. We first modeled the surface temperature field variation of concrete dams as a one-dimensional, non-stationary partial differential equation with Robin boundary. We also designed physics-informed neural networks (PINNs) with multi-subnets to compute the temperature value automatically. Secondly, we obtained the time-domain features in one-dimensional space and used the diffusion techniques to obtain the synthetic infrared images with dam hollowing by converting the one-dimensional temperatures into two-dimensional ones. Finally, we employed adaptive joint learning to obtain the spatio-temporal features. We designed the experiments on the dataset we constructed, and we demonstrated that the method proposed in this paper can handle the low-data (few shots real images) issue. Our method achieved 94.7% of recognition accuracy based on few shots real images, which is 17.9% and 5.8% higher than maximum entropy and classical OTSU methods, respectively. Furthermore, it attained a sub-10% cross-sectional calculation error for hollowing dimensions, outperforming maximum entropy (70.5% error reduction) and OTSU (7.4% error reduction) methods, which shows our method being one novel method for automated intelligent hollowing detection. Full article
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22 pages, 6843 KiB  
Article
Constructing High-Quality Livable Cities: A Comprehensive Evaluation of Urban Street Livability Using an Approach Based on Human Needs Theory, Street View Images, and Deep Learning
by Minzhi Li and Zhongxiu Fan
Land 2025, 14(5), 1095; https://doi.org/10.3390/land14051095 - 18 May 2025
Viewed by 269
Abstract
Driven by the United Nations’ Sustainable Development Goal (SDG 11), the construction of high-quality livable cities has emerged as a central issue on the global agenda. However, existing research primarily focuses on optimizing physical functions, neglecting the dynamic hierarchical nature and emotional experiences [...] Read more.
Driven by the United Nations’ Sustainable Development Goal (SDG 11), the construction of high-quality livable cities has emerged as a central issue on the global agenda. However, existing research primarily focuses on optimizing physical functions, neglecting the dynamic hierarchical nature and emotional experiences of residents’ needs. This study, employing Guangzhou’s Tianhe District as an empirical case, proposes an innovative framework that integrates Maslow’s Hierarchy of Needs theory, the Method of Empathy-Based Stories (MEBS), and deep learning technology for the first time. It constructs a dynamic assessment model of “needs-streetscape elements-spatial quality”, systematically analyzing the livability characteristics and driving mechanisms of high-density urban streets. Tianhe District’s street spaces exhibit the common issue of “functional-experiential imbalance” faced by high-density cities. Furthermore, different streetscape elements in the city demonstrate significant variability in satisfying different hierarchical demand dimensions, with strong sequential relationships among these hierarchies. Adjusting and optimizing the relationships between elements can result in the creation of higher-quality street spaces that meet higher-level needs. The research findings provide differentiated renewal pathways for tropical high-density cities, offer methodological support for global urban governance under the SDG 11 objectives, and indicate directions for improving street quality in urban regeneration practices. Full article
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35 pages, 15247 KiB  
Article
A Multi-Objective Approach for Optimizing Aisle Widths in Underground Parking
by Igor Kabashkin, Alua Kulmurzina, Assel Zhandarbekova, Zura Sansyzbayeva and Timur Sultanov
Infrastructures 2025, 10(4), 100; https://doi.org/10.3390/infrastructures10040100 - 21 Apr 2025
Viewed by 414
Abstract
This study presents a multi-objective optimization approach for determining optimal aisle widths in underground parking facilities, balancing vehicle maneuverability against parking capacity. The research methodology integrates geometric modeling, computational simulations, and empirical validation to establish evidence-based recommendations for aisle width design. Through systematic [...] Read more.
This study presents a multi-objective optimization approach for determining optimal aisle widths in underground parking facilities, balancing vehicle maneuverability against parking capacity. The research methodology integrates geometric modeling, computational simulations, and empirical validation to establish evidence-based recommendations for aisle width design. Through systematic testing of aisle widths ranging from 4.5 to 6.0 m across various vehicle types, the study identifies 5.0–5.5 m as the optimal range that maximizes both objectives for modern vehicle fleets. Geometric modeling establishes theoretical minimum widths based on vehicle turning radii, while software simulations quantify maneuverability metrics including parking success rates, time requirements, and collision probabilities. Physical testing in operational underground parking facilities validates these findings through controlled experiments with drivers of varying experience levels. The research demonstrates that aisle widths below 5.0 m significantly compromise maneuverability, particularly for larger vehicles, while widths exceeding 5.5 m provide negligible additional benefits while reducing capacity. A case study application in Kazakhstan, examining regional vehicle distributions and regulatory frameworks, confirms the model’s practical utility. The findings suggest that current parking standards in some regions may require revision to accommodate changing vehicle dimensions. This optimization framework provides urban planners, architects and engineers with a data-driven methodology for designing underground parking facilities that enhance both user experience and space utilization efficiency. Full article
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21 pages, 5983 KiB  
Article
Approach Design Inheriting Traditional Spatial Ambiguity: An Analysis of Arrangement and Composition in Takehara Yoshiji’s Independent Residential Works
by Luyang Li, Boyang Liu and Houjun Li
Buildings 2025, 15(7), 1191; https://doi.org/10.3390/buildings15071191 - 5 Apr 2025
Viewed by 386
Abstract
This study explores the design characteristics of approach spaces in architect Yoshiji Takehara’s independent residential works, focusing on their spatial arrangement, sinuosity, and experiential qualities. Through the analysis of Takehara’s projects and interviews with the architect, the research identifies key patterns in approach [...] Read more.
This study explores the design characteristics of approach spaces in architect Yoshiji Takehara’s independent residential works, focusing on their spatial arrangement, sinuosity, and experiential qualities. Through the analysis of Takehara’s projects and interviews with the architect, the research identifies key patterns in approach configurations, including entrance positioning, path complexity, and site-specific adaptations. The findings reveal that Takehara’s designs emphasize winding paths and deliberate spatial sequences, contrasting the simpler approaches of contemporaneous residential designs. The study categorizes approach configurations into distinct typologies, influenced by the site dimensions and entrance placement, and highlights a shift from physical obstructions to subtler, psychologically guided design elements over time. Takehara’s design method translates the concept of “Ma” from traditional tea gardens into the language of modern pathways, integrating traditional Japanese spatial ambiguity into contemporary residential design. This offers strategies to enhance spatial perception and experiential richness. Particularly in compact urban settings, the research provides valuable insights for contemporary residential design, emphasizing the importance of landscape-oriented approaches and spatial sequencing in creating meaningful entry experiences. Full article
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25 pages, 7110 KiB  
Article
Regenerative and Connective Green Cells to Address Fragmentation and Climate Change in Cities: The TALEA Project Integrated Solution
by Rossella Roversi and Danila Longo
Sustainability 2025, 17(7), 3175; https://doi.org/10.3390/su17073175 - 3 Apr 2025
Viewed by 396
Abstract
Cities are facing the combined effects of multiple challenges, e.g., climate change, biodiversity, pollution, and lacking resources. Synergic innovative solutions are required to simultaneously address them while also considering their social impacts. In this context, the TALEA—Green Cells Leading the Green Transition project, [...] Read more.
Cities are facing the combined effects of multiple challenges, e.g., climate change, biodiversity, pollution, and lacking resources. Synergic innovative solutions are required to simultaneously address them while also considering their social impacts. In this context, the TALEA—Green Cells Leading the Green Transition project, funded by the European Urban Initiative, called Greening Cities (EUI02-064)—aims to tackle urban climate challenges in Bologna (Italy) by mitigating Urban Heat Islands (UHI) and Urban Heat Waves (UHW) through an innovative, nature-based, and data-driven approach. TALEA introduces the TALEA Green Cells (TGCs) concept, modular spatial units that integrate nature-based solutions, creative technological innovation, real-time environmental monitoring, and citizen-science-driven data collection within a broader green infrastructure strategy (Bologna Verde project). TGCs bridge the physical and digital dimensions of urban planning: at the macroscale, they contribute to restoring a continuous urban green corridor; at the microscale, they regenerate underused urban spaces, transforming them into climate shelters and hubs for community engagement. A key feature of TALEA is its digital innovation ecosystem, which integrates data from different sources, including remote sensing, sensors, and citizen-generated inputs, within the Systemic Urban Observation Atlas, the Smart Innovation Package and the Digital Twin that the city of Bologna is developing. These tools enable data-driven decision-making, supporting both urban planners and local communities in designing resilient, adaptive, and inclusive urban environments. The scalability and transferability potential of this integrated approach is tested through its real implementation in three Bologna urban pilots. Full article
(This article belongs to the Special Issue A Systems Approach to Urban Greenspace System and Climate Change)
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21 pages, 20232 KiB  
Article
Promoting Public Health Through Urban Walkability: A GIS-Based Assessment Approach, Experienced in Milan
by Pei Ma, Andrea Rebecchi, Fabio Manfredini, Moritz Ahlert and Maddalena Buffoli
Sustainability 2025, 17(7), 2939; https://doi.org/10.3390/su17072939 - 26 Mar 2025
Viewed by 375
Abstract
Introduction. The global challenge of physical inactivity necessitates innovative approaches and strategies to optimize built environments in order to promote healthy and sustainable lifestyles, such as active transportation. For this reason, walkability is a crucial area of research in urban health, with several [...] Read more.
Introduction. The global challenge of physical inactivity necessitates innovative approaches and strategies to optimize built environments in order to promote healthy and sustainable lifestyles, such as active transportation. For this reason, walkability is a crucial area of research in urban health, with several studies focusing on assessment frameworks. However, a gap persists between theoretical development and practical implementation. This study explores the application of the Milan Walkability Measurement Tool (MWM-Tool), a walkability assessment framework previously developed by Politecnico di Milano, to evaluate the urban features in favor of walkability by integrating GIS technology with an extended testing scope. It is based on a scientific approach utilizing 10 sub-indicators divided into three macro-areas (Density, Diversity, Design), identified through a comprehensive literature review. Method. Focusing on the application of the MWM-Tool in Milan, the study employs the 88 Nuclei of Local Identity (NILs), which are the official designations for Milan’s neighborhoods, as the units of urban analysis. Based on previous experience, the digitalization of the assessment framework has been improved: geospatial data corresponding to 10 sub-indicators were filtered to generate vector layers, primarily sourced from two public geographical platforms. The GIS-based method produces thematic maps evaluating all neighborhoods according to the dimensions of Density, Diversity, and Design. Darker and lighter colors represent the range of the scores. Both single indicators and macro-area maps, as well as overall walkability level maps, were generated to illustrate the results. Result. The results of the macro dimension assessment, combining 10 sub-indicators, provide an objective view of the distribution of walkable space quality in Milan. Only 7 out of 88 neighborhoods achieved the highest score, all of which are located in the city center, while suburban areas showed significantly lower scores. By incorporating census GIS data, the study also identified the population distribution across areas with varying walkability levels. Based on the results of the assessment, it may be possible to develop and prioritize the optimization of walkable features, revitalizing underserved areas and fostering a healthier community environment. Conclusion. The georeferenced-data maps represent an effective tool to highlight both neighborhoods with high urban quality, which could be used to promote active mobility and healthy lifestyle adoption, as well as those requiring improvement strategies from policy and decision makers. The research output provides a reference for further urban planning initiatives in Milan and contributes to enhancing pedestrian-oriented built environments. Using GIS open-source data, the method is scalable and can be easily replicated in other cities. It could also be used as a system for monitoring walkability over time. Full article
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23 pages, 6849 KiB  
Article
Rethinking the Sustainability of Industrial Buildings in High-Density Urban Areas: Balancing Adaptability and Public Satisfaction
by Xiao Ding, Yuchen Shao and Botao Feng
Buildings 2025, 15(5), 747; https://doi.org/10.3390/buildings15050747 - 25 Feb 2025
Viewed by 753
Abstract
In the context of land scarcity and high-density urban areas, the adaptive reuse of abandoned historical industrial buildings plays a critical role in achieving sustainable development goals. This study proposes a sustainability assessment framework for the adaptive reuse of industrial buildings as exhibition [...] Read more.
In the context of land scarcity and high-density urban areas, the adaptive reuse of abandoned historical industrial buildings plays a critical role in achieving sustainable development goals. This study proposes a sustainability assessment framework for the adaptive reuse of industrial buildings as exhibition spaces within the context of high-density urban development, addressing multiple dimensions of sustainability, including the building’s physical structure, economic factors, environmental impact, social considerations, and governance. The framework consists of 55 design indexes, categorized into 15 subcategories and 5 main categories. We conducted a survey of experts with experience in high-density urban renewal design and implemented a weighting analysis to identify priority intervention measures for industrial building redevelopment in the era of urban stock. Finally, a fuzzy comprehensive evaluation was carried out on ten cases in Shenzhen where industrial buildings were converted into exhibition spaces over the past 12 years. The findings reveal the following: (1) “Reuse of old architectural spaces” is the most critical category to prioritize, and, at the indicator level, “adaptability and efficiency of building reuse”, “public participation in the renewal process”, “cooperative operation structures”, and “planning vision” are identified as the four key influencing factors. (2) The functional layout, historical value, and richness of public amenities in the transformed industrial buildings have a significant positive impact on the evaluation results, while the building’s construction time and floor area do not significantly affect public post-evaluation. (3) Younger and more highly educated groups tend to view the transformed exhibition spaces as tourist attractions, particularly expressing satisfaction with the repurposing of the Kinwei Brewery and OCAT B10 New Hall, and consider the adaptive reuse of industrial buildings to promote sustainable urban renewal (SUR). This study provides concrete policy recommendations and practical guidance for the adaptive reuse of both new and existing industrial buildings, contributing to the creation of sustainable urban environments. Full article
(This article belongs to the Special Issue Urban Sustainability: Sustainable Housing and Communities)
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24 pages, 10874 KiB  
Article
Evaluation of Pedestrian-Perceived Comfort on Urban Streets Using Multi-Source Data: A Case Study in Nanjing, China
by Jiarui Qin, Yizhe Feng, Yehua Sheng, Yi Huang, Fengyuan Zhang and Kaixuan Zhang
ISPRS Int. J. Geo-Inf. 2025, 14(2), 63; https://doi.org/10.3390/ijgi14020063 - 5 Feb 2025
Cited by 1 | Viewed by 1913
Abstract
Urban street comfort is a crucial measure of street environmental quality. However, traditional evaluations primarily focus on physical elements, often neglecting pedestrian perceptions. In this study, considering five core evaluation dimensions—safety, mobility, aesthetics, perceptibility, and convenience—an innovative quantitative evaluation model is proposed to [...] Read more.
Urban street comfort is a crucial measure of street environmental quality. However, traditional evaluations primarily focus on physical elements, often neglecting pedestrian perceptions. In this study, considering five core evaluation dimensions—safety, mobility, aesthetics, perceptibility, and convenience—an innovative quantitative evaluation model is proposed to assess pedestrian-perceived comfort on urban streets by integrating physical environmental factors and subjective experiences. This analysis comprises two steps: evaluation indicator extraction and weight application. Indicators are extracted from multi-source data (street-view images, real-time traffic data, points of interest, and pedestrian surveys) using a deep learning method. A comprehensive weighting method combining entropy weight and the analytic hierarchy process is used to determine the relative importance of each factor. This study focuses on Nanjing as a case study, and the results reveal significant variations across the five dimensions and their 11 secondary indicators. Street environment safety (0.143) is critical for street safety, while the degree of street traffic congestion (0.121) dominates street mobility. Street aesthetics is primarily influenced by building enclosure (0.105), and street convenience is strongly affected by the number of surrounding bus stops (0.260). Spatial analysis indicates higher comfort levels in urban centers due to well-developed infrastructure, whereas peripheral areas face challenges from inadequate facilities. Notably, areas around parks demonstrate elevated pedestrian-perceived comfort levels, highlighting the importance of green spaces. Overall, the proposed evaluation system provides new insights from the perspective of pedestrian experience and offers valuable guidance for urban planning and policy. Full article
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34 pages, 423 KiB  
Review
Topology Unveiled: A New Horizon for Economic and Financial Modeling
by Yicheng Wei, Junzo Watada and Zijin Wang
Mathematics 2025, 13(2), 325; https://doi.org/10.3390/math13020325 - 20 Jan 2025
Viewed by 2042
Abstract
Sinceits introduction in the 19th century to address geometric problems, topology as a methodology has undergone a series of evolutions, encompassing branches of geometric topology, point-set topology (analytic topology), algebraic topology, and differential topology, gradually permeating into various interdisciplinary applied fields. Starting from [...] Read more.
Sinceits introduction in the 19th century to address geometric problems, topology as a methodology has undergone a series of evolutions, encompassing branches of geometric topology, point-set topology (analytic topology), algebraic topology, and differential topology, gradually permeating into various interdisciplinary applied fields. Starting from disciplines with typical geometric characteristics such as geography, physics, biology, and computer science, topology has found its way to economic fields in the 20th century. Given that the introduction of topology to economics is relatively new and presents features of being fragmented and non-systematic, this review aimed to provide scholars with a systematic evolution map to refine the characteristics of topology as a methodology applied in economics and finance, thereby aiding future potential interdisciplinary developments in these fields. By collecting abundant literature indexed in SCOPUS/WoS and other famous databases, with a qualitative analysis to classify and summarize it, we found that topological methods were introduced to modern economics when dealing with dynamic optimization, functional analysis, and convex programming problems, including famous applications such as uncovering equilibrium with fixed-point theorems in Walrasian economics. Topology can help uncover and refine the topological properties of these function space transformations, thus finding unchangeable features. Meanwhile, in contemporary economics, topology is being used for high-dimension reduction, complex network construction, and structural data mining, combined with techniques of machine learning, and applied to high-dimensional time series and structure analysis in financial markets. The most famous practical applications include the use of topological data analysis (TDA) and topological machine learning (TML) for different applied problems. Full article
14 pages, 9538 KiB  
Technical Note
Eliminating Inductive Coupling in Small-Loop TEM Through Differential Measurement with Opposing Coils
by Xinghai Chen, Haiyan Yang, Tong Xia, Xiaoping Wu and Shengdong Liu
Remote Sens. 2025, 17(2), 254; https://doi.org/10.3390/rs17020254 - 13 Jan 2025
Viewed by 759
Abstract
The small-loop transient electromagnetic method (TEM) refers to a system in which the coil frame length or diameter is less than 2 m. Due to the inductive effects of the multi-turn coils used for both transmission and reception, the induced electromotive force in [...] Read more.
The small-loop transient electromagnetic method (TEM) refers to a system in which the coil frame length or diameter is less than 2 m. Due to the inductive effects of the multi-turn coils used for both transmission and reception, the induced electromotive force in the measuring coil increases, causing a reduction in the decay rate and an extension of the shutoff time. This results in coupling between the primary and secondary fields in early-time signals, making them difficult to separate and creating a detection blind spot in the shallow subsurface. The opposing coil TEM transmission and reception method can significantly reduce early-time signal distortion caused by coil inductance. However, this approach is constrained by the physical symmetry of the coil dimensions, which makes it challenging to achieve balance in a zero-field space. By performing both forward and reverse measurements at the same location using the opposing coil setup and calculating the difference between the signals, the inductive coupling between coils at the measurement site can theoretically be eliminated. This eliminates the induced potential of the TEM signal, enhancing the induced electromotive force from the formation. As a result, more accurate resistivity values are obtained, detection blind spots are eliminated, and the resolution in shallow TEM exploration is improved. Field experiments were conducted to validate the method on both high-resistivity and low-resistivity anomalies. The results demonstrated that this method effectively identified a high-resistivity corrugated pipe at a depth of 1.2 m and two low-resistivity gas pipelines at a depth of 2 m, thereby essentially eliminating detection blind spots in the shallow subsurface. Full article
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28 pages, 14974 KiB  
Article
Multidimensional Particle Separation by Tilted-Angle Standing Surface Acoustic Waves—Physics, Control, and Design
by Sebastian Sachs, Jörg König and Christian Cierpka
Powders 2025, 4(1), 2; https://doi.org/10.3390/powders4010002 - 8 Jan 2025
Viewed by 873
Abstract
Lab-on-a-Chip devices based on tilted-angle standing surface acoustic waves (tasSAWs) emerged as a promising technology for multidimensional particle separation, highly selective in particle size and acoustic contrast factor. For this active separation method, a tailored acoustic field is used to focus and separate [...] Read more.
Lab-on-a-Chip devices based on tilted-angle standing surface acoustic waves (tasSAWs) emerged as a promising technology for multidimensional particle separation, highly selective in particle size and acoustic contrast factor. For this active separation method, a tailored acoustic field is used to focus and separate particles on stationary pressure nodes by means of the acoustic radiation force. However, additional non-linear acoustofluidic phenomena, such as the acoustically induced fluid flow or dielectrophoretic effects, are superimposed on the separation process. To obtain a particle separation of high quality, control parameters that can be adjusted during the separation process as well as design parameters are available. The latter are specified prior to the separation and span a high-dimensional parameter space, ranging from the acoustic wavelength to the dimensions and materials used for the microchannel. In this paper, the physical mechanisms to control and design tasSAW-based separation devices are reviewed. By combining experimental, semi-analytical, and numerical findings, a critical channel height and width are derived to suppress the influence of the acoustically induced fluid flow. Dealing with the three-dimensional nature of the separation process, particles are focused at different height levels of equal force balance by implementing a channel cover of high acoustic impedance while achieving an approx. three-times higher acoustic pressure. Using this improved channel design, the particle shape is identified as an additional separation criterion, rendering the continuous acoustofluidic particle separation as a multidimensional technology capable of selectively separating microparticles below 10 μm with regard to size, acoustic contrast, and shape. Full article
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12 pages, 1032 KiB  
Article
Fractal Continuum Maxwell Creep Model
by Andriy Kryvko, Claudia del C. Gutiérrez-Torres, José Alfredo Jiménez-Bernal, Orlando Susarrey-Huerta, Eduardo Reyes de Luna and Didier Samayoa
Axioms 2025, 14(1), 33; https://doi.org/10.3390/axioms14010033 - 2 Jan 2025
Viewed by 720
Abstract
In this work, the fractal continuum Maxwell law for the creep phenomenon is introduced. By mapping standard integer space-time into fractal continuum space-time using the well-known Balankin’s approach to variable-order fractal calculus, the fractal version of Maxwell model is developed. This methodology employs [...] Read more.
In this work, the fractal continuum Maxwell law for the creep phenomenon is introduced. By mapping standard integer space-time into fractal continuum space-time using the well-known Balankin’s approach to variable-order fractal calculus, the fractal version of Maxwell model is developed. This methodology employs local fractional differential operators on discontinuous properties of fractal sets embedded in the integer space-time so that they behave as analytic envelopes of non-analytic functions in the fractal continuum space-time. Then, creep strain ε(t), creep modulus J(t), and relaxation compliance G(t) in materials with fractal linear viscoelasticity can be described by their generalized forms, εβ(t),Jβ(t) and Gβ(t), where β=dimS/dimH represents the time fractal dimension, and it implies the variable-order of fractality of the self-similar domain under study, which are dimS and dimH for their spectral and Hausdorff dimensions, respectively. The creep behavior depends on beta, which is characterized by its geometry and fractal topology: as beta approaches one, the fractal creep behavior approaches its standard behavior. To illustrate some physical implications of the suggested fractal Maxwell creep model, graphs that showcase the specific details and outcomes of our results are included in this study. Full article
(This article belongs to the Special Issue Fractal Analysis and Mathematical Integration)
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14 pages, 3274 KiB  
Article
Reconstructed Phase Space of Tropical Cyclone Activity in the North Atlantic Basin for Determining the Predictability of the System
by Sarah M. Weaver, Christopher A. Steward, Jason J. Senter, Sarah S. Balkissoon and Anthony R. Lupo
Atmosphere 2024, 15(12), 1488; https://doi.org/10.3390/atmos15121488 - 12 Dec 2024
Viewed by 1006
Abstract
Tropical cyclone prediction is often described as chaotic and unpredictable on time scales that cross into stochastic regimes. Predictions are bounded by the depth of understanding and the limitations of the physical dynamics that govern them. Slight changes in global atmospheric and oceanic [...] Read more.
Tropical cyclone prediction is often described as chaotic and unpredictable on time scales that cross into stochastic regimes. Predictions are bounded by the depth of understanding and the limitations of the physical dynamics that govern them. Slight changes in global atmospheric and oceanic conditions may significantly alter tropical cyclone genesis regions and intensity. The purpose of this paper is to characterize the predictability of seasonal storm characteristics in the North Atlantic basin by utilizing the Largest Lyapunov Exponent and Takens’ Theorem, which is rarely used in weather or climatological analysis. This is conducted for a post-weather satellite era (1960–2022). Based on the accumulated cyclone energy (ACE) time series in the North Atlantic basin, cyclone activity can be described as predictable at certain timescales. Insight and understanding into this coupled non-linear system through an analysis of time delay, embedded dimension, and Lyapunov exponent-reconstructed phase space have provided critical information for the system’s predictability. Full article
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24 pages, 7225 KiB  
Review
CESE Schemes for Solar Wind Plasma MHD Dynamics
by Yun Yang and Huichao Li
Universe 2024, 10(12), 445; https://doi.org/10.3390/universe10120445 - 30 Nov 2024
Viewed by 794
Abstract
Magnetohydrodynamic (MHD) numerical simulation has emerged as a pivotal tool in space physics research, witnessing significant advancements. This methodology offers invaluable insights into diverse space physical phenomena based on solving the fundamental MHD equations. Various numerical methods are utilized to approximate the MHD [...] Read more.
Magnetohydrodynamic (MHD) numerical simulation has emerged as a pivotal tool in space physics research, witnessing significant advancements. This methodology offers invaluable insights into diverse space physical phenomena based on solving the fundamental MHD equations. Various numerical methods are utilized to approximate the MHD equations. Among these, the space–time conservation element and solution element (CESE) method stands out as an effective computational approach. Unlike traditional numerical schemes, the CESE method significantly enhances accuracy, even at the same base point. The concurrent discretization of space and time for conserved variables inherently achieves higher-order accuracy in both dimensions, without the need for intricate higher-order time discretization processes, which are often challenging in other methods. Additionally, this scheme can be readily extended to multidimensional cases, without relying on operator splitting or direction alternation. This paper primarily delves into the remarkable progress of CESE MHD models and their applications in studying solar wind, solar eruption activities, and the Earth’s magnetosphere. We aim to illuminate potential avenues for future solar–interplanetary CESE MHD models and their applications. Furthermore, we hope that the discussions presented in this review will spark new research endeavors in this dynamic field. Full article
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