Search Results (501)

Complex fractal dimensions, defined as poles of appropriate fractal zeta functions, describe the geometric oscillations in fractal sets. In this work, we show that the same possible complex dimensions in the geometric setting also govern the asymptotics of the heat content on self-similar fractals. We consider the Dirichlet problem for the heat equation on bounded open regions whose boundaries are self-similar fractals. The class of self-similar domains we consider allows for non-disjoint overlap of the self-similar copies, provided some control over the separation. The possible complex dimensions, determined strictly by the similitudes that define the self-similar domain, control the scaling exponents of the asymptotic expansion for the heat content. We illustrate our method in the case of generalized von Koch snowflakes and, in particular, extend known results for these fractals with arithmetic scaling ratios to the generic (in the topological sense), non-arithmetic setting. Full article

The large-scale deployment of wind energy underscores the critical need for accurate resource characterization to reduce uncertainty in power estimates and to enable the installation of wind farms in increasingly complex terrains. Accurate wind resource assessment in peri-urban and moderately complex terrains remains a significant challenge due to spatial heterogeneity in surface terrain features and atmospheric thermal stability. This study investigates the influence of surface complexity and atmospheric stratification on vertical wind profiles at a utility-scale wind turbine site in Cedar Rapids, Iowa. One year of multi-level wind data from a 106-meter-tall meteorological tower were analyzed to quantify variations in the wind shear exponent $\alpha$, wind direction veer, and horizontal turbulence intensity (TI) across open-field and complex-surface wind sectors and four thermal stability classes, defined by the bulk Richardson number $R{i}_b$. The results show that the wind shear exponent $\alpha$ increases systematically with atmospheric stability. Over the open-field terrain, $\alpha$ ranges from 0.11 in unstable conditions to 0.45 in strongly stable conditions, compared to 0.17 and 0.40 over the complex surface. A pronounced diurnal variation in $\alpha$ was observed, particularly during the summer months. Wind veer was greatest and exceeded 30° under strongly stable conditions over open terrain. Elevated TI values peaked at 32 m in height due to flow separation and wake turbulence from nearby vegetation and sloping terrain. These findings highlight the importance of incorporating terrain-induced and thermally driven variability into wind resource assessments to improve power prediction and turbine siting in complex heterogeneous terrain environments. Full article

Litter nutrient stoichiometry and its drivers are important for understanding nutrient cycling in desert ecosystems, plant adaptation strategies, and the sustainability of ecosystem functions. However, little is known about the spatial variation in litter nutrient stoichiometry and its environmental drivers in desert shrubs. This study focused on two Nitraria species (N. tangutorum Bobrov and N. sphaerocarpa Maxim) in Northwestern China, analyzing leaf litter N, P, and K stoichiometry, their spatial variation, and environmental drivers. Nutrient concentrations and stoichiometric ratios did not differ significantly between the two species. The average N contents in the litters of N. tangutorum and N. sphaerocarpa were 11.363 mg g⁻¹ and 11.295 mg g⁻¹, respectively. The P contents were 0.591 mg g⁻¹ and 0.611 mg g⁻¹, whereas the K contents were 17.482 mg g⁻¹ and 16.255 mg g⁻¹, respectively. With the changes in geographic and climatic factors, the same nutrient elements of the two Nitraria species showed inconsistent variation patterns. Both species showed low P concentration, indicating high P resorption and possible P limitation, reflecting nutrient vulnerability in desert ecosystems according to the scaling exponents among elements. In litter, the residual nutrient contents ranked as K > P > N, suggesting strong N resorption but low K resorption, especially for N. sphaerocarpa. N was mainly influenced by latitude, P by soil properties, and K by mean annual temperature. Moreover, litter stoichiometric ratios of N. tangutorum were relatively stable, whereas those of N. sphaerocarpa were more sensitive to environmental variables. In conclusion, the two Nitraria shrubs exhibited differential nutrient use strategies under nutrient restriction, providing insights into nutrient cycling and supporting sustainable management of desert ecosystems. Full article

This study investigates the nonlinear dynamics and control of an underactuated hybrid system consisting of a Duffing oscillator, a pendulum, and a piezoelectric energy harvester. A novel Piezoelectric Harvester Proportional–Derivative (PHPD) control scheme is introduced, which integrates the harvester’s electrical output directly into the feedback loop to achieve simultaneous vibration suppression and energy utilization. The nonlinear governing equations are derived and analyzed using the Multiple-Scale Perturbation Technique (MSPT) to obtain reduced-order dynamics. Bifurcation analysis is employed to identify stability boundaries and critical parameter transitions, while numerical simulations based on the fourth-order Runge–Kutta method validate the analytical predictions. Furthermore, frequency response curves (FRCs) and an ideal system are evaluated under multiple controller and system parameter configurations. Bifurcation classification is performed on the analyzed figure to detect various bifurcations within the system, along with the computation of the Largest Lyapunov Exponent (LLE). The results demonstrate that PHPD control significantly reduces vibration amplitude and accelerates convergence, offering a new pathway for energy-efficient, high-performance control in nonlinear electromechanical systems. Full article

This study investigates the dynamic behaviors of the discrete epidemic model influenced by media coverage through integrated analytical and numerical approaches. The primary objective is to quantitatively assess the impact of media coverage on disease outbreak patterns using mathematical modeling. Firstly, the Euler method is used to discretize the model (2), and the periodic solution is strictly analyzed. Secondly, the coefficients and conditions of restricted flip and Neimark–Sacker bifurcation are studied by using the center manifold theorem and bifurcation theory. By calculating the largest Lyapunov exponent near the critical bifurcation point, the occurrence of chaos and limit cycles is proved. On this basis, the chaotic control of the system is carried out by using state feedback and hybrid control. Under certain conditions, the chaos and bifurcation of the system can be stabilized by control strategies. Numerical simulations further reveal bifurcation dynamics, chaotic behaviors, and control technologies. Our results show that media coverage is a key factor in regulating the intensity of disease transmission and chaos. The control technology can effectively prevent the large-scale outbreak of epidemic diseases. Importantly, enhanced media coverage can effectively promote public awareness and defensive behaviors, thereby contributing to the mitigation of disease transmission. Full article

This study concerns the evaluation of adhesive and wettability energetic signatures of a model orthodontic wire exposed to commercial mouthrinses. The surface wetting properties were evaluated from the contact angle hysteresis (CAH) approach applied to dynamic contact angle data derived from the original drop on a vertical filament method. Young, advancing, receding CA apart from adhesive film pressure, surface energy, work of adhesion, etc. were chosen as interfacial interaction indicators, allowing for the optimal concentration and placement of the key component(s) accumulation to be predicted for effective antibacterial activity to eliminate plaque formation on the prosthetic materials. Surfactant compounds when adsorb at interfaces confer rheological properties to the surfaces, leading to surface relaxation, which depends on the timescale of the deformation. The surface dilatational complex modulus E, with compression elasticity E_d and viscosity E_i parts, determined in the stress–relaxation Langmuir trough measurements, exhibited the viscoelastic surface film behavior with the relaxation times (0.41–3.13 s), pointing to the vertically segregated film structure as distinct, stratified layers with the most insoluble compound on the system top (as indicated with the 2D polymer film scaling theory exponent y = 12.9–15.5). Kinetic rheology parameters could affect the wettability, adhesion, and spreading characteristics of mouthrinse liquids. Full article

This paper investigates the global dynamics of timelike geodesics of a spherically symmetric black hole under Lorentz-violating effects governed by parameters $\lambda$ (scaling exponent) and ${\rm Y}$ (Lorentz violation strength). By employing dynamical system techniques, including Poincaré compactification and blow-up methods, we systematically explore finite and infinite equilibrium states of the system derived from a black hole solution with power-law corrections to the Schwarzschild metric. For varying $\lambda$ (ranging from −2 to 2) and fixed ${\rm Y}$ values, we classify the nature of equilibrium states (saddle, center, and node) and analyze their stability. Key findings reveal that the number of equilibrium states increases as $\lambda$ decreases: two states for $\lambda =2$, three for $\lambda =1$, four for $\lambda =2/3$, and additional configurations for $\lambda =-2$. The phase plane diagrams and global dynamics demonstrate distinct topological structures, including attractors at infinity and multi-horizon black hole solutions. Furthermore, degenerate equilibrium states at infinity are resolved through directional blow-ups, elucidating their non-hyperbolic behavior. This study highlights the critical role of Lorentz-violating parameters in shaping the stability and long-term evolution of timelike geodesics, offering new insights into modified black hole physics and spacetime dynamics. Full article

This study focuses on a hydrocarbon reservoir located in southeastern Mexico. The analysis uses well log data derived from petrophysical evaluations of storage capacity. The structural complexity of the reservoir and observed heterogeneity in Cretaceous units motivate a fractal-based characterization of spatial fluctuations. The objective is to assess the fractal scaling of storage capacity fluctuations using the dynamic Family–Vicsek framework. Critical exponents $\alpha$ (roughness), $\beta$ (growth), and z (dynamic) are obtained through structure function metrics. Data collapse techniques and local Hurst exponent distributions are used to explore long-range memory and spatial heterogeneity across wells. This study aims to classify storage capacity fluctuation records based on Euclidean or fractal geometries. This analysis allows a novel characterization of storage trends in the reservoir. The analysis reveals persistent scaling behavior, indicating long-range correlations in the storage capacity fluctuations. Multiscale patterns and variations in local Hurst exponents highlight the presence of multifractality and regional heterogeneity. Specifically, the spatial distribution of local Hurst exponents obtained in this study enables the inference of statistical properties in synthetic wells, providing key input for the structural and functional characterization of the reservoir’s geological model. This approach aims to identify preferential subsurface flow pathways for hydrocarbons and gas. Full article

Archard’s wear law is among the first and foremost wear models derived from contact mechanics that relates key operating conditions and material hardness to sliding wear through a multifaceted wear coefficient. This entry explores the development, generalization, and critique of the Archard model—a foundational model in wear prediction. It outlines the historical origins of the model, its basis in contact plasticity, and its use of a constant wear coefficient. The discussion highlights modern efforts to extend the model through variable exponents and empirical calibration. Key limitations such as the oversimplification of wear behavior, exclusion of factors like sliding velocity, and scale sensitivity are examined through both theoretical arguments and experimental evidence. The critiques reflect the model’s constrained applicability in diverse wear conditions across varied operating conditions and material phenomena. Full article

Mg-Sc body-centered cubic (BCC) phase-structured alloys not only exhibit superior room-temperature ductility and quasi-isotropic deformation behaviors compared to conventional hexagonal close-packed (HCP) Mg alloys in mechanical applications, but they also demonstrate a shape-memory effect that is applicable to intelligent devices. Due to the introduction of a dual-phase microstructure feature, the unveiled strengthening/toughening mechanism, and the potential benefit of Sc alloying in BCC creep deformation, it is necessary to investigate the composition and time-dependent creep behaviors of BCC Mg-Sc alloys, such as creep resistance and strain rate sensitivity at room temperature, through nano-indentation on the Mg-Sc diffusion couple. A critical finding is that as the Sc content increases from 23.01 at.% to 33.56 at.%, the BCC Mg-Sc alloy exhibits a progressive enhancement in creep resistance at room temperature, evidenced by the creep stress exponent (n) rising from 49.02 to 66.22. Furthermore, the strain rate sensitivity (m) increases from 0.02 at 26.94 at.% Sc to 0.11 at 32.63 at.% Sc, along with the Sc composition gradient. These phenomena can be attributed to the formation of ordered structures with the increasing Sc concentration, which introduce short-range local barriers to dislocation motion, as confirmed through atomic-scale microstructural analysis. Full article

The water source protection areas of the Yangtze-to-Huaihe Water Diversion Project (YHWDP) in Anhui Province serve as crucial ecological barriers to water quality protection. Quantifying their eco-environmental quality (EEQ) dynamics and driving mechanisms is critical for sustainable management. This paper calculated the Remote Sensing Ecological Index (RSEI) for the study area using Landsat satellite data (2015–2024). Temporal and spatial variation characteristics were analyzed using the Theil–Sen estimator, Mann–Kendall test, and coefficient of variation. Future trends were predicted using the Hurst exponent. Finally, the Geodetector model was applied to assess the impact of driving factors. EEQ exhibited a declining trend (p < 0.05), with significant intra-regional heterogeneity. Mean RSEI values ranked as follows: (1) Yangtze River–Huaihe River Connection < Yangtze River Water Northward Conveyance < Yangtze River–Chaohu Lake Water Diversion. (2) From 2015 to 2024, eco-environmental quality improved significantly, showing a spatial pattern of “south > north, east > west.” (3) Overall EEQ changes were characterized by slight to moderate fluctuations. Stability rankings: Yangtze River–Huaihe River Connection > Yangtze River–Chaohu Lake Water Diversion > Yangtze River Water Northward Conveyance. (4) Geodetector analysis identified precipitation, impervious area, and vegetation coverage as the primary factors influencing EEQ in the YHWDP’s water source protection areas. This study reveals ecological changes in the YHWDP region and validates the effectiveness of the comprehensive evaluation method. The findings provide actionable insights for ecological protection in large-scale water diversion projects. Full article

Precipitation concentration reflects the uneven temporal distribution of rainfall. It plays a critical role in water resource management and flood–drought risk under climate change. However, its long-term trends, associations with atmospheric teleconnections as potential drivers, and links to extreme heavy precipitation events remain poorly understood in complex basins like the Yangtze River Basin. This study analyzes these aspects using ground station data from 1960 to 2019 and conducts a comparison using the Global Precipitation Measurement Integrated Multi-satellitE Retrievals for GPM (GPM IMERG) satellite product. We calculated three indices—Daily Precipitation Concentration Index (PCID), Monthly Precipitation Concentration Index (PCIM), and Seasonal Precipitation Concentration Index (SPCI)—to quantify rainfall unevenness, selected for their ability to capture multi-scale variability and associations with extremes. Key methods include Mann–Kendall trend tests for detecting changes, Hurst exponents for persistence, Pettitt detection for abrupt shifts, random forest modeling to assess atmospheric teleconnections, and hot spot analysis for spatial clustering. Results show a significant basin-wide decrease in PCID, driven by increased frequency of small-to-moderate rainfall events, with strong spatial synchrony to extreme heavy precipitation indices. PCIM is most strongly associated with El Niño-Southern Oscillation (ENSO) and Pacific Decadal Oscillation (PDO). GPM IMERG captures PCIM patterns well but underestimates PCID trends and magnitudes, highlighting limitations in daily-scale resolution. These findings provide a benchmark for satellite product improvement and support adaptive strategies for extreme precipitation risks in changing climates. Full article

Although the allocation of biomass among floral organs reflects critical trade-offs in plant reproductive strategies, the scaling relationships governing biomass allocations remain poorly resolved, particularly in flowers. Here, we report the fresh mass scaling allocation patterns among four floral organs (i.e., sepals, petals, stamens, and carpels), and the two subtending structural components (i.e., the pedicel and receptacle) of 497 flowers of the hypogynous Rosa chinensis var. minima (miniature rose) using reduced major axis protocols. The two-parameter Weibull probability density function was also applied to characterize the distributions of floral organ mass, and revealed skewed tendencies in all six measured traits. The results show that the numerical values of the scaling exponents (α) for all pairwise power-law relationships significantly exceeded unity (α > 1), indicating disproportionate investments in larger floral structures with increasing overall flower size. Specifically, the scaling exponent of corolla fresh mass vs. calyx fresh mass was α = 1.131 (95% confidence interval [CI]: 1.086, 1.175), indicating that petal investment outpaces sepal investment as flower size increases. Reproductive organs also exhibited significant disproportionate investments (i.e., allometry): the collective carpel (gynoecium) fresh mass scaled allometrically with respect to the collective stamen (androecium) mass (α = 1.062, CI: 1.028, 1.098). Subtending axial structures (pedicel and receptacle) also had hyperallometric patterns, with pedicel mass scaling at α = 1.167 (CI: 1.106, 1.235) with respect to receptacle mass. Likewise, the combined fresh mass of all four foliar homologues (sepals, petals, androecium, and gynoecium) scaled disproportionately with respect to the biomass of the two subtending axial structures (α = 1.169, CI: 1.126, 1.214), indicating a prioritized resource allocation to reproductive and display organs. These findings are in accord with hypotheses positing that floral display traits, such as corolla size, primarily enhance pollen export by attracting pollinators, while maintaining fruit setting success through coordinated investment in gynoecium development. The consistent hyperallometry across all organ pairwise comparisons underscores the role of developmental integration in shaping floral architecture in Rosaceae, as predicted by scaling theory. By integrating morphometric and scaling analyses, this study proposes a tractable methodology for investigating floral resource allocation in monomorphic-flowering species and provides empirical evidence consistent with the adaptive patterns of floral traits within this ecologically and horticulturally significant lineage. Full article

Fissure swarms and dike swarms in Iceland constitute the main parts of volcanic systems that are 40–150 km long, 5–20 km wide, extend to depths of 10–20 km, and contain 2 × 10¹⁴ outcrop-scale (≥0.1 m) and 10^22–23 down to grain-scale (≥1 mm) fractures, suggesting that statistical physics is an appropriate method of analysis. Length-size distributions of 565 outcrop-scale Holocene fissures (tension fractures and normal faults) and 1041 Neogene dikes show good to excellent fits with negative power laws and exponential laws. Here, the Helmholtz free energy is used to represent the energy supplied to the swarms and to derive the Gibbs–Shannon entropy formula. The calculated entropies of 12 sets and subsets of fissures and 3 sets and subsets of dikes all show strong positive correlations with sets/subsets length ranges and scaling exponents. Statistical physics considerations suggest that, at a given time, the probability of the overall state of stress in a crustal segment being heterogeneous is much greater than the state of stress being homogeneous and favourable to the propagation of a fissure or a dike. In a heterogeneous stress field, most fissures/dikes become arrested after a short propagation—which is a formal explanation of the observed statistical size-length distributions. As the size of the stress-homogenised rock volume increases larger fissures/dikes can form, increasing the length range of the distribution (and its entropy) which may, potentially, transform from an exponential distribution into a power-law distribution. Full article

Background: Autism spectrum disorder (ASD) is characterised by atypical behavioural and cognitive diversity, yet the neural underpinnings linking brain activity and individual presentations remain poorly understood. In this study, we investigated the relationship between resting-state functional magnetic resonance imaging (fMRI) signal complexity and intelligence (full-scale intelligence quotient (FIQ); verbal intelligence quotient (VIQ); and performance intelligence quotient (PIQ)) in male adults with ASD (n = 14) and matched neurotypical controls (n = 15). Methods: We used three complexity-based metrics: Hurst exponent (H), fuzzy approximate entropy (fApEn), and fuzzy sample entropy (fSampEn) to characterise resting-state fMRI signal dynamics, and correlated these measures with standardised intelligence scores. Results: Using a whole-brain measure, ASD participants showed significant negative correlations between PIQ and both fApEn and fSampEn, suggesting that increased neural irregularity may relate to reduced cognitive–perceptual performance in autistic individuals. No significant associations between entropy (fApEn and fSampEn) and PIQ were found in the control group. Group differences in brain–behaviour associations were confirmed through formal interaction testing using Fisher’s r-to-z transformation, which showed significantly stronger correlations in the ASD group. Complementary regression analyses with interaction terms further demonstrated that the entropy (fApEn and fSampEn) and PIQ relationship was significantly moderated by group, reinforcing evidence for autism-specific neural mechanisms underlying cognitive function. Conclusions: These findings provide insight into how cognitive functions in autism may not only reflect deficits but also an alternative neural strategy, suggesting that distinct temporal patterns may be associated with intelligence in ASD. These preliminary findings could inform clinical practice and influence health and social care policies, particularly in autism diagnosis and personalised support planning. Full article