Search Results (780)

Wear of the feedback ball head–ball seat interface changes the contact state and reduces the feedback force in electro-hydraulic servo valves, resulting in output nonlinearity and performance degradation. Existing wear models usually assume fixed surface morphology parameters, which their ability to describe time-varying wear evolution during repeated sliding. To address this issue, this study proposes a hybrid wear-prediction framework integrating fractal contact theory, Archard wear law, Gaussian process regression, and a servo-valve mechanical model. The real contact area and wear coefficient are expressed as functions of fractal parameters, while Gaussian process regression is used to predict their evolution under different loading cycles and displacement loads. Repeated loading tests and white-light interferometry measurements were performed to validate the proposed method. The results show that the fractal dimension of the ball seat increased by approximately 4.01%, whereas that of the ball head decreased by approximately 1.71%. After about 12,000 cycles, the fractal parameters tended to stabilize. The prediction error of the Gaussian process regression model was below 3%, and the wear-depth prediction error remained within approximately 1%. These results indicate that the proposed method can effectively capture the time-varying sliding wear behavior of the feedback ball head–ball seat interface. Full article

Ultra-high molecular weight polyethylene (UHMWPE) fibers have recently emerged as a promising reinforcement material in fiber-reinforced concrete (FRC). To investigate the synergistic effects and reinforcing mechanisms of fibers with different elastic moduli within the concrete matrix, a series of hybrid fiber-reinforced concrete (HFRC) specimens were prepared by incorporating 0.25 vol%, 0.5 vol%, and 0.75 vol% carbon fibers (CFs) or polypropylene (PP) fibers into concrete containing 1 vol% UHMWPE fibers. The mechanical performance of the prepared composites was systematically evaluated through compressive, splitting tensile, flexural, and drop-weight impact tests. The experimental results indicate that concrete reinforced solely with UHMWPE fibers exhibits higher compressive strength but lower tensile strength, flexural strength, ductility, and impact toughness than the hybrid fiber systems. For both UHMWPE-CF and UHMWPE-PP hybrid concretes, the initial cracking impact resistance and failure impact resistance increased progressively with increasing CF or PP content. At equivalent fiber volume fractions, UHMWPE-PP hybrid concrete demonstrated superior resistance to initial cracking, whereas UHMWPE-CF hybrid concrete exhibited better post-failure impact resistance. Furthermore, fractal theory was employed to quantitatively characterize the impact damage behavior of HFRC specimens. The impact damage evolution equation is established by using the two-parameter Weibull distribution model. The findings provide theoretical and experimental support for the design and optimization of hybrid fiber-reinforced concrete subjected to impact loading. Full article

Accurate description of phase change heat transfer in porous media relies on precise characterization of pore structures. In this study, fractal theory is employed to characterize the complex microstructure and pore distribution of metallic foams, and the Weierstrass–Mandelbrot (W–M) function is introduced to describe the stochastic spatial distribution of pores. Based on this fractal description, a transient melting heat transfer model is developed for metallic foam/paraffin composite phase change materials (CPCM). The effects of pore fractal dimension, porosity, and pore density on melting dynamics are systematically investigated. The results indicate that reducing porosity significantly accelerates the melting process and improves thermal energy storage efficiency. Crucially, the random pore distribution induces irregular melting fronts but has only a limited effect on the overall thermal response. Furthermore, even at identical porosities, variations in fractal dimension and pore density distinctly influence heat transfer rates, exhibiting similar evolutionary trends in melting behavior and thermal performance. These findings clarify the respective roles of pore structural parameters and stochastic pore heterogeneity in phase change heat transfer and provide guidance for optimizing composite phase change materials in high-performance thermal energy storage systems. Full article

This contribution proposes a conceptual framework for quantum relations understood as operator-based, scale-dependent semantic structures. It explores the “fractaquantum” hypothesis, emphasizing that nature exhibits quantum properties at all scales, from subatomic particles to social structures. Using Pauli operators, we propose a semantic theory of quantum relations based on the “semiotic square” and on eigenlogic. The "two one-half spin" quantum composition defines the exchange operator at the basis of fundamental quantum relations. The approach is applied to macroscopic phenomena such as “social lasers” and the rhythmic “breathing” of entanglement, suggesting that individuality and social coherence are governed by scale-invariant quantum principles. This project aims to unify several quantum-like approaches under a common relational paradigm and highlights the role of fractal scaling, contextuality, non-commutativity, exchange, indistinguishability and entanglement in the emergence of semantic relations across physical, cognitive, social and artistic domains. Full article

This paper extends the metacybernetic framework by grounding its conceptual descriptions in first principles of information physics. We demonstrate that for living systems to organise efficiently under uncertainty, they must adhere to a strict recursive pattern, a “fractal seed” originating in the third-order interaction between potential and action. By utilising Fisher Information Field Theory (FIFT) within an Informational Realism paradigm, we formalise this process through variational analysis on an implicate–explicate manifold. Under a rigorous informational parsimony constraint (a functional analogue of the holographic principle), we treat the J-field as the dispositional reservoir of latent potential and the I-field as the operative field of structured configurations, and show how their autopoietic coupling generates the system’s Potential–Actuation trait poles as a scale-invariant viability structure This coupling reveals that the boundary substructure, which encodes the holographic content, directly conditions the emergent superstructure through a deterministic parity rule inherited from the dyadic logic of the minimal generic living system represented by ${\widehat{\theta }}_2$. Drawing on the application of Fisher Information, we show that maintaining informational parsimony requires the system’s architecture to oscillate: odd-numbered orders express two traits (dyads), whereas even-numbered orders express three (triads). This produces a canonical 2–3–2–3–2 sequence, preventing a combinatorial explosion of traits as systemic depth increases. We present the Cogitor5 model as a complete fifth-order exemplar of this rule, demonstrating how this rhythmic structural pattern enables self-evolution, systemic coherence, and collective intelligence in both biological and artificial agencies. Full article

The Gulong shale oil reservoir is characterized by high clay content and strong heterogeneity, with substantial variations in mineral composition among different intervals. However, existing fracability evaluation methods for such continental shales remain inconsistent and often rely on oversimplified two-dimensional fracture descriptors, lacking a multi-parameter quantitative framework derived from three-dimensional fracture characterization. In this study, the Q1 and Q9 members of the Gulong shale oil were selected, and laboratory-scale hydraulic fracturing simulation experiments were conducted using supercritical carbon dioxide (SC-CO₂), liquid CO₂, and water as the fracturing media. Within a fractal-theory framework based on CT-derived three-dimensional reconstructions, a multi-scale evaluation index system was established by integrating fractal dimension, fracture density, and spatial connectivity. The experimental results demonstrate that fluid properties exert a decisive influence on rock failure behavior. Owing to its ultra-low viscosity and strong diffusivity, SC-CO₂ can significantly reduce formation breakdown pressure while effectively activating natural weak planes to generate a more complex fracture network. For the Q9 shale, the breakdown pressure under SC-CO₂ is reduced by 11.91% and 8.33% relative to water and liquid CO₂, respectively. Moreover, the fracture fractal dimension reaches 2.41 under SC-CO₂, which is markedly higher than the values obtained under liquid CO₂ (2.18) and water (2.12). Mineral composition and densely developed bedding are the key factors inducing fracture branching and deflection, whereas injection rate and an asymmetric stress field regulate the internal energy-release rate and stress path, thereby influencing fracture crossing capability and aperture evolution. Based on the experimental dataset, a fracture complexity index (FCI) evaluation model was developed: under SC-CO₂ fracturing, the FCI values are 8.92 for the Q9 member and 4.43 for the Q1 member, and the model predictions are in good agreement with physical observations. This work elucidates the failure mechanism of the Gulong shale under multi-field coupling and provides a theoretical basis for optimizing hydraulic fracturing and evaluating fracability in unconventional reservoirs through the proposed FCI-based assessment framework. Full article

Resistivity is a key parameter in shale reservoir characterization. Diverse micro-pore types and complex conduction mechanisms in shale result in poor accuracy when applying existed conductivity models. Establishing a high-precision conductivity response model requires comprehensive consideration of the pore structure and clay-bound water conduction. The primary novelty of this work lies in replacing macroscopic empirical fitting parameters with a mechanistic, multi-dimensional fractal framework. We develop a novel conductivity response characterization model that explicitly couples multi-dimensional fractal pore structure theory with clay-bound water conduction. Experimental data verification demonstrates the new model’s superior characterization accuracy. Results indicate three distinct zones in the shale conductivity-pore water conductivity relationship: a nonlinear zone, a transition zone, and a linear zone. A higher cation exchange rate on clay surfaces leads to an increase in the nonlinear characteristics of the conductivity for both the shale and the pore water in low-salinity regions. An increase in the values of the conduction path fractal dimension, pore morphology fractal dimension, and pore fractal dimension all contribute to reduced shale conductivity. While sharing clay-induced conductivity terms with conventional dual-water and shale volume models, the new model offers advantages in operational simplicity and parameter accessibility. This research provides a physically rigorous and highly accessible approach for conductivity-based reservoir parameter calculation, offering new technical perspectives for complex shale oil/gas evaluation. Full article

This paper presents a novel proportional–integral–derivative (PID) control framework for first $\alpha$-order systems evolving in fractal time. The main contribution is the extension of classical control theory to systems exhibiting anomalous temporal scaling by employing local fractal derivatives. In contrast to fractional-order PID (FOPID) approaches, which primarily model memory effects, the proposed fractal PID framework captures time-scaling behavior arising in non-smooth environments, such as viscoelastic friction and irregular contact surfaces. The closed-loop dynamics are formulated as a second $\alpha$-order fractal differential equation, from which a characteristic equation is derived to establish conditions for asymptotic stability. It is shown that, for a constant reference input and positive controller gains, the tracking error converges to zero as $t\to \infty$. In addition, a quantitative performance analysis demonstrates that the fractal-order $\alpha$ governs temporal stretching: smaller values of $\alpha$ lead to increased rise and settling times and reduced oscillation frequency. The effectiveness of the proposed approach is illustrated through applications to a thermal system with fractal heat input and robotic actuators operating in irregular environments. These results highlight the potential of fractal-time control as a systematic framework for modeling and controlling dynamical systems with non-integer temporal structure. Full article

Railways constitute a core component of China’s national comprehensive transportation network, and their spatial organization and temporal accessibility jointly shape transport integration and system efficiency. Identifying their evolution from the dual perspectives of spatial expansion and time compression is therefore of both theoretical and practical significance. Drawing on fractal theory, this study examines the structural characteristics, evolutionary trends, and driving factors of railway networks in China’s five major urban systems from 2014 to 2024 from a “space–time” dual perspective. The results show that railway networks exhibit a staged pattern of “spatial filling preceding temporal correlation”, with a lag of approximately 1–8 years—about 1 year in the Guangdong–Hong Kong–Macao Greater Bay Area (GBA), 5 years in the Middle Yangtze River (MYR) region and Beijing–Tianjin–Hebei (BTH), and up to 8 years in the Chengdu–Chongqing (CC) region. In addition, clear regional differences are observed: the Yangtze River Delta (YRD) is polycentric, with the greatest potential, projected to continue rapid spatial growth until 2027 and to remain in a fast-growth phase of temporal correlation; GBA is highly coordinated; BTH is developed but characterized by dual-core agglomeration; CC grows rapidly with lagging functionality; and MYR is corridor-dependent with limited potential. These findings indicate that network functionality does not emerge synchronously with infrastructure expansion, but depends on subsequent improvements in operational organization and service capacity. Compared with single-scale-based indicators, the “spatial distribution–temporal correlation” framework more effectively captures network performance and provides quantitative support for transport optimization and coordinated regional development. Full article

Understanding the impact of ash on nanopore heterogeneity is crucial for evaluating deep coalbed methane (CBM) reservoirs. This study investigates the Benxi Formation coal Seam 8 in the Nalinhe Block, Ordos Basin. Based on proximate analysis, samples were categorized by ash yield (A_ad%). Pore structures were characterized using low-temperature nitrogen adsorption (<2 nm) and carbon dioxide adsorption (2–100 nm). Fractal theory was employed to quantitatively assess pore heterogeneity across different scales. The results indicate that ash content significantly constrains the development of both micropores (<2 nm) and mesopores (2–100 nm), with the most pronounced effect on micropores in the 0.3–0.6 nm range. Ash, primarily derived from kaolinite, occludes pores, reducing pore volume and specific surface area, thereby diminishing methane adsorption capacity. Notably, pore heterogeneity is found to decrease with increasing pore volume. These findings provide valuable insights for the efficient exploration and development of deep CBM resources in the Nalinhe and Suide blocks. Full article

Red mud (RM), a waste residue from alumina extraction, poses serious environmental impacts on water resources, land resources, and ecological systems due to its large production, high alkalinity, and low resource utilization. To enhance the overall utilization rate of RM solid-waste materials, this study focuses on RM, blast furnace slag (BFS), and fly ash (FA) cementitious materials as the research objects. Through mechanical tests and microstructural analysis, the optimal mix ratio of the ternary RM-based cementitious material is determined, and a systematic study of its microstructural evolution is conducted. Concurrently, fractal theory was used to quantify the microstructure of the material, revealing the evolution laws of the mechanical properties of ternary red-mud-based cementitious materials from a mesoscopic perspective. The results indicate that reducing the proportion of RM or slag alone to increase the FA content yields inferior modification effects compared to simultaneously reducing the proportions of both RM and BFS to increase FA content. Compared with the binary RM-based cementitious material made of RM and BFS, the 28-day compressive strength increases by approximately 25%, reaching 50 MPa. The incorporation of FA can reduce the volume of harmful pores in the cementitious matrix, providing ample reactive material for subsequent hydration reactions, promoting later hydration products, and improving the distribution of the internal pore structure. This leads to increases in both fractal dimensions, and a rational mix proportion can effectively improve the microstructure and mechanical properties of the ternary RM-based cementitious material. Full article

Characterizing multiscale fracture networks in shale gas reservoirs remains challenging, while the limited applicability of conventional continuum-based models and insufficient multi-objective coordination often lead to low efficiency in development optimization. To address these issues, this study proposes a production history matching and multi-objective collaborative optimization framework for shale gas horizontal wells based on an equivalent fractal fracture (EFF) model. By integrating fractal theory with intelligent optimization techniques, a multiscale equivalent fractal permeability tensor is constructed, forming a hybrid machine-learning framework that combines physics-based fractal constraints with data-driven learning for efficient representation of complex fracture networks. Microseismic event clouds were converted into continuous fracture-density and fractal-geometry descriptors through denoising, temporal alignment, and spatial interpolation, and these descriptors were mapped to the equivalent fractal fracture model to dynamically update key flow parameters for history matching and parameter inversion. On this basis, a multi-objective collaborative optimization strategy is developed to achieve simultaneous time-varying fracture characterization and dynamic regulation of development parameters. Comparative results indicate that the EFF-based approach yields a production prediction error of 6.8%, slightly higher than the 4.2% obtained using discrete fracture network (DFN) models, while requiring only one-eighteenth of the computational time. Using the net present value (NPV) as the unified objective function, constraints are imposed on bottom-hole flowing pressure, flowback rate and system switching time for optimization. With the optimized pressure drop being more uniform and the gas saturation distribution being more balanced, it is verified that “EFF + NPV” can achieve the coordinated optimization of “production capacity—decline—cost” and enhance the development efficiency. Full article

High-intensity conditioning (HIC) is a common pretreatment process for enhancing the flotation of fine-grained minerals. This study introduces fractal theory into the structural design of pulp conditioning impellers. A fractal blade with multi-scale fractal edge features was proposed, and its separation performance was evaluated in a fine-grained malachite (−20 μm) and quartz flotation system. Computational fluid dynamics simulation revealed that the fractal blade altered the energy dissipation pattern. Compared with conventional rectangular blades, it induced stronger fluid compression and collision effects in localized regions. These hydrodynamic changes improved the suspension homogeneity and dispersion efficiency of fine-grained malachite. Furthermore, the fractal blade reduced the scale of turbulent vortices while increasing local turbulent kinetic energy and shear rates. This optimized turbulent flow field effectively reduced mass-transfer resistance and promoted interfacial interactions between flotation reagents and mineral particles. Adsorption experiments and optical microscopy indicated that after conditioning at 1500 rpm for 3 min, the fractal blade increased sodium oleate adsorption on malachite compared to the conventional blade. This enhanced adsorption promoted the aggregation of fine-grained malachite, increasing its aggregate size by 15.52%, while no significant aggregation was observed for quartz particles. Consequently, the single mineral flotation recovery of fine-grained malachite increased by 4.13%. For artificial mixed minerals, the copper concentrate grade and recovery were improved by 2.28% and 1.04%, respectively. This study provides a theoretical basis for equipment optimization and structural innovation design in HIC processes. Full article

Urban heritage structures are most commonly understood as memorial artifacts, tourism assets, or redevelopment resources. While this common view acknowledges cultural and economic value, it overlooks a deeper function of heritage within the long evolution of human settlements. This paper advances a counter thesis: in addition to its historic contingencies and power relationships—which are real, but only part of the picture—urban heritage embodies valuable but often hidden intelligence that is highly relevant to contemporary urban challenges. Specifically, heritage environments encode useful structured information about spatial configurations that have gained adaptive value over time in a process known as stigmergy. Drawing on complexity science, network theory, the mathematics of symmetry, and theories of extended cognition, the paper argues that enduring urban forms persist not only for symbolic or historical reasons, but because they embed structural properties conducive to resilience, legibility, social interaction, climatic adaptation, and human well-being. Recurring characteristics include fine-grained network connectivity, fractal scaling hierarchies, organized symmetry, articulated thresholds, and biophilic integration. Evidence from environmental psychology, public health, and urban morphology suggests that such properties correlate with reduced stress, increased walkability, stronger social capital, and improved ecological performance. The paper proposes a methodological framework—what we call the Adaptive Patterns Model—for identifying, evaluating, and translating this embedded intelligence into contemporary regeneration practice. The Model is presented as a four-phase, conceptually synthesized framework—integrating insights from complexity science and stigmergy, urban morphological analysis, and pattern-language methodology—comprising documentation, pattern extraction, encoding, and performance correlation. It concludes by challenging a still-prevalent assumption that contemporary conditions invalidate accumulated spatial knowledge. Instead, urban heritage is understood as adaptive capital within an ongoing evolutionary process, offering a structurally grounded foundation for resilient urban transformation. Full article

Zagreb-type indices are topological indices derived from the degrees of nodes. The first Zagreb index, the F-index, and the Y-index represent the sum of the squares, cubes, and fourth powers of all node degrees, respectively. These indices are valuable for understanding the chemical reactions, physical characteristics, and biological activities of various substances. In this study, we explore the connection between Y-index and the graph Laplacian spectrum. Additionally, we introduce the fractal graphs based on star graphs, a class of extended Vicsek graphs, and derive the rules for eigenvalue evolution between two generations of the graph. Ultimately, we provide exact closed-form expressions for the first Zagreb index, F-index, and Y-index of the fractal graphs based on star graphs by using spectral graph theory. Full article