Search Results (10,068)

The sign of the maximal almost sure Lyapunov exponent determines the stability of stochastic systems, while its numerical computation for three-dimensional linear Stratonovich stochastic differential equations remains challenging due to the failure of classical two-dimensional strategies. The spherical angular motion of 3D systems produces a Fokker–Planck equation with intractable mixed partial derivatives, preventing conventional analytical solutions. This paper develops a unified computational framework for three-dimensional linear Stratonovich stochastic systems using analytical derivation for degenerate cases and physics-informed neural network (PINN) approximation for general non-degenerate scenarios. For degenerate systems, we reduce the coefficient matrix to a lower triangular form via orthogonal transformation and establish tight upper bounds based on the logarithmic growth property of the Wiener process, yielding closed-form expressions for the maximal almost sure Lyapunov exponent under all parameter sign configurations. For non-degenerate systems, we reformulate the Fokker–Planck equation in spherical coordinates and construct a customized PINN with trigonometric encoding to enforce periodic boundary conditions. The network is trained by joint loss functions of equation residuals, boundary constraints and normalization consistency, and the converged stationary density is substituted into the Furstenberg–Khasminskii formula to calculate the exponent via Gauss–Legendre quadrature. Monte Carlo simulations confirm the accuracy and robustness of the proposed method, which reliably identifies the sign of the maximal almost sure Lyapunov exponent even in near-critical regimes. Numerical experiments on a 3D stochastic Hopf bifurcation model show that noise negatively shifts the bifurcation point, with the offset linearly proportional to the squared noise intensity. This work extends Lyapunov stability analysis from two-dimensional to three-dimensional linear Stratonovich stochastic systems, offering an effective tool for stability evaluation of general three-dimensional stochastic dynamical models. Full article

Renovations aimed at improving energy conservation in older urban residential areas are essential for sustainable urban development; however, they encounter obstacles such as energy inefficiency and issues in sustaining long-term sustainability following renovation. Based on resource-based theory and collaborative governance theory, this study investigates how organisational resilience affects the efficacy of energy-saving renovations and confirms the mediating role of resource allocation efficiency. A mixed-methods approach was used in this investigation. Grounded theory was first used to establish the components of organisational resilience. A questionnaire survey was then used to gather information from those participating in energy-efficient renovation of old urban residential complexes. System dynamics (SD) was applied for empirical validation and simulation analysis across many intervention scenarios after structural equation modelling (SEM) was used to develop and evaluate study hypotheses. The results show that rather than the support of any particular strategy, the crucial elements in improving the efficacy of energy-saving renovations are efficient interdepartmental coordination and rational budget allocation. Notably, all energy-saving renovation outcome measures in this study are based primarily on stakeholder perceptions and survey responses rather than objectively measured energy consumption data. Full article

The transition toward carbon-neutral energy systems has accelerated interest in hydrogen-fueled combustion technologies, where efficient fuel–air mixing is essential for stable and clean combustion. In the present study, the mixing characteristics of under-expanded supersonic jets injected into a pressurized environment are numerically investigated using validated computational fluid dynamics simulations. Two nozzle configurations are examined: a straight nozzle and sudden-expansion nozzles with different expansion ratios and expansion locations. The governing compressible flow equations are solved using the rhoCentralFoam solver with the SST k–ω turbulence model. The numerical framework is validated against Sod’s shock tube solution and experimental data for under-expanded supersonic free jets. The results show that sudden-expansion nozzles significantly modify the shock-wave structure, jet penetration, and lateral spreading compared with the straight nozzle. Among the investigated configurations, nozzles with intermediate expansion-section lengths exhibited pronounced Mach-disk oscillations with a dominant frequency of approximately 10 kHz. The normalized supersonic core length decreased from 17.79 for the straight nozzle to 5.50 for the best-performing sudden-expansion configuration, while the normalized jet half-width increased from 0.82 to 1.70, indicating substantially enhanced mixing performance. The findings demonstrate that nozzle geometry strongly governs the trade-off between flow stability and mixing enhancement in high-pressure supersonic jets. Full article

Soil erosion poses a severe threat to agricultural productivity and ecological security on the Loess Plateau. However, previous studies have rarely integrated physical modeling, elasticity coefficients, and spillover effects into a unified framework at the county level. To address this gap, this study coupled the Revised Universal Soil Loss Equation (RUSLE) with the Spatial Durbin Model (SDM) to systematically investigate the spatiotemporal dynamics, factor elasticity characteristics, and spatial dependence mechanisms of soil erosion on the Loess Plateau from 1990 to 2024. Results show that the annual average erosion rate decreased by 15.5%, with a highly volatile phase before 2001 and a stabilized, low-erosion phase thereafter. The driving factors exhibited marked heterogeneity in direction and strength. The land cover and management factor (C) was the strongest erosion-reducing factor, whereas annual precipitation (PRE) was the primary natural erosion-enhancing factor. County-level erosion also displayed significant positive spatial dependence. PRE had a stable positive indirect effect, whereas C and the support practice factor (P) mainly contained erosion within local jurisdictions. These findings of a unified RUSLE–SDM framework reveal a joint driving mechanism of localized human interventions and climate-driven cross-regional spillovers, providing quantitative support for differentiated soil and water conservation strategies on the Loess Plateau. Full article

Aiming at the non-isothermal seepage phenomena in fractured rock mass, this paper conducts nonlinear dynamic research on the coupled seepage problem. Based on solid–fluid heat conduction energy equations and the mutual coupling of temperature and seepage fields, the non-isothermal seepage constitutive relation of fractured rock is derived, and a one-dimensional nonlinear dynamic governing model is established. Theoretical analysis indicates the equilibrium solution of non-isothermal seepage is more complex than that under the isothermal condition. Numerical calculations reveal that temperature variation shifts equilibrium positions and alters the occurrence conditions of hysteresis bifurcation, verifying temperature as a core regulatory factor for seepage dynamic responses. Successive sub-relaxation iteration stability analysis demonstrates obvious differentiated convergence speeds: the seepage field converges markedly faster than the temperature field when the coupled system reaches steady state. Compared with the isothermal seepage, the temperature effect changes the location of abrupt transition points and critical threshold of control parameters, rendering fractured rock seepage systems easier to trigger abrupt structural mutation even at low rock fragmentation degrees. This study clarifies the internal nonlinear dynamic mechanism of thermal–fluid coupled seepage, identifies potential mutation risks in petroleum exploitation and geothermal development, and supplies essential theoretical support for related engineering applications. Full article

Urban Park vegetation plays a crucial role in mitigating air pollution by serving as a natural sink for gaseous and particulate pollutants, thereby enhancing the ecological sustainability of cities. Identifying tree species with high tolerance to air pollution is therefore essential for effective urban park planning and management in highly polluted urban environments. This study evaluated the air pollution tolerance of selected tree species commonly found in urban parks of Kandy City, Sri Lanka, using the Air Pollution Tolerance Index (APTI). Five tree species—Terminalia catappa (Indian almond), Cassia fistula (golden shower tree), Pongamia pinnata (Indian beech), Madhuca longifolia (butter tree), and Tabebuia rosea (pink poui)—were assessed at two urban park locations representing contrasting pollution levels, identified based on ambient SO₂, NO₂, and PM_2.5 concentrations. APTI was calculated using four leaf biochemical parameters: pH, ascorbic acid content, relative water content, and total chlorophyll content. Leaf samples were collected from ten replicates of each species at both sites. Madhuca longifolia exhibited the highest APTI values (17.06 at the HP site and 25.17 at the LP site), followed by Cassia fistula, Terminalia catappa, Tabebuia rosea, and Pongamia pinnata. These findings suggest that the identified species, particularly Madhuca longifolia and Cassia fistula, are well-suited for urban greening and can contribute to mitigating air pollution impacts. However, these findings are constrained by a single cross-sectional sampling term, limited species screening, sequential data collection variances, and fixed mathematical equations. Consequently, future research should implement continuous multi-station monitoring arrays, expand species diversity, establish localized biochemical weightings, and initiate long-term multi-seasonal tracking to resolve temporal dynamics in tropical urban ecosystems. Full article

Grain for Green, as an important ecological restoration method, profoundly affects soil nitrogen (N) cycling by altering the soil physicochemical properties and microbial community. Soil nitrogen mineralization is a key process in the terrestrial N cycle. However, the dynamics and underlying driving mechanisms of soil N mineralization rate (Rmin) that respond to afforestation remain unclear. In this study, we selected a typical afforestation sequence in Northeast China, including farmland (F), 21-year-old larch plantation (L21), 42-year-old larch plantation (L42), and natural larch forest (NL). The soil Rmin, associated soil physicochemical properties, and microbial community characteristics were determined to explore the effects of afforestation on soil Rmin and its potential mechanisms of action. The results suggested that soil Rmin was ranked in the order of L42 (0.41 mg kg⁻¹ d⁻¹) > F (0.39 mg kg⁻¹ d⁻¹) > L21 (0.23 mg kg⁻¹ d⁻¹) (p < 0.05) along the afforestation sequence, with no significant difference between L42 and F. Compared to the L42, the NL exhibited significantly lower soil Rmin (0.23 mg kg⁻¹ d⁻¹) (p < 0.05). The changes in soil Rmin during the afforestation were significantly positively related to soil total N (TN) and organic carbon (SOC) concentrations, but significantly negatively related to pH (p < 0.05). Furthermore, the abundances of Proteobacteria and Acidobacteria (bacteria) and Ascomycota (fungi) were also closely correlated with soil Rmin. Structural equation modeling (SEM) analysis further indicated that the afforestation mainly regulated soil Rmin by altering soil temperature (ST) and NH₄⁺-N content. Meanwhile, soil NH₄⁺-N content could also exert a significantly positive effect on soil Rmin by influencing the microbial community. In conclusion, afforestation effectively altered soil Rmin, which was even higher in the plantation than in natural forests. This finding further enhances our understanding of forest restoration and land management practices on soil N cycling in temperate regions. Full article

Natural gas metering is shifting from volume-based measurement to energy-based assessment as gas sources diversify, pipeline networks become more interconnected, and gas quality varies more strongly across time and space. This review examines the key technologies required for natural gas energy metering and evaluates how they support full-chain traceability from production to end use. The reviewed topics include flow measurement, gas composition analysis, calorific value determination, temperature-pressure compensation, state correction, uncertainty evaluation, intelligent data acquisition, and metrological traceability. The literature shows that individual technologies have advanced substantially. Ultrasonic flowmeters, rapid gas-quality sensing methods, dynamic calorific value allocation models, high-accuracy equations of state, and digital metering platforms have improved the technical basis of energy metering. However, these advances remain more mature at the level of individual links than at the level of the complete metering chain. Under multi-source supply, gas-quality fluctuation, hydrogen blending, and digitalized operation, the main challenge is to maintain consistency, uncertainty control, online verification, data credibility, and auditability across different metering stages. Future development should therefore focus on dynamic calorific value allocation, robust state correction under variable gas quality, full-chain uncertainty propagation, online verification, and secure data management for traceable natural gas energy metering. Full article

Different approaches to describing the kinematics and dynamics of a mobile robot equipped with four Mecanum wheels are compared. Due to the no-slip rolling condition, the kinematic constraints imposed on the system are nonholonomic; therefore, the equations of nonholonomic mechanics must be used to model such a system. The necessary and sufficient conditions under which the dynamics of this system can be described using Lagrange equations of the second kind are derived. The solvability of the kinematic constraint equations using the pseudoinverse matrix is also analyzed. Full article

The Difference Equation Matrix Model (DEMM) is presented as an input–output Model Predictive Control (MPC) formulation derived from discrete difference equations. The proposed approach is compared with the widely used Dynamic Matrix Control (DMC) strategy from a structural perspective, highlighting differences in model parameterization, identification requirements, and matrix dimensions. The analysis indicates that DEMM provides a more compact model representation than the DMC formulation considered in this work while preserving the predictive-control framework. Furthermore, the DEMM strategy is applied to a binary distillation column, a multivariable nonlinear process, to illustrate its implementation and closed-loop behavior under disturbance, noise, and setpoint-change scenarios. Simulation results demonstrate satisfactory disturbance-rejection and tracking performance for the considered operating conditions. Full article

The term “entropy” denotes several mathematically distinct quantities across modern physics, including thermodynamic, statistical, quantum-informational, and geometric notions that are often conflated in foundational discussions. We propose an operational distinction among three such quantities: a geometric capacity entropy $S_{\mathrm{capacity}}$ proportional to a region’s bounding area, a microscopic content entropy $S_{\mathrm{content}}$ given by the fine-grained von Neumann entropy of the reduced state, and a thermodynamic entropy $S_{\mathrm{thermo}}$ corresponding to the observer-relative ignorance that remains after accessible information is accounted for. We argue that keeping these quantities distinct is not merely terminological: within this framework, the second law of thermodynamics can be formulated as a typical consequence of unitary dynamics combined with bounded observational access, rather than as an independent postulate. The distinction also clarifies which entropy enters established results such as the Bekenstein–Hawking entropy of black holes and the Clausius relation in Jacobson’s thermodynamic derivation of Einstein’s equations. The proposed framework is conceptual and does not modify established physical theories; it is intended as a useful clarification for informational approaches to physics. Full article

We derive multisoliton solutions for a nonisospectral mKdV-sG equation with self-consistent sources by means of the bilinear approach. This nonisospectral equation is a generic one which is related to a time-dependent spectral parameter with time evolution ${\lambda }_t={\mu }_2\lambda +4{\mu }_3{\lambda }^3+{\nu }_2/\left(4\lambda \right)$. Reductions to some soliton equations with self-consistent sources are investigated. One- and two-soliton solutions for the reduced equations are presented and dynamical behaviors are illustrated. Full article

Current deep learning methods for tool wear monitoring suffer from poor interpretability and struggle to reveal the intrinsic relationship between signals and wear states. To address this issue, this paper presents an interpretable tool wear monitoring method based on Sparse Identification of Nonlinear Dynamics (SINDy). Multi-domain features are extracted from cutting force and acoustic emission signals to construct a time series. The SINDy algorithm is used to identify ordinary differential equations that describe the evolution of tool wear. An iterative “predict-validate-correct” mechanism is applied to optimize model parameters. Experimental results show that the mean absolute percentage error (MAPE) between the predicted and actual values is below 6%. Moreover, the optimal model demonstrates an average MAPE as low as 0.067% in cross-condition tests. This study provides an effective solution for online tool wear monitoring that achieves high precision, strong generalization, and physical interpretability. Full article

With the large-scale development of renewable energy such as wind, solar and ocean energy, the demand for energy storage is more urgent. Pumped hydro energy storage (PHES) is one of the fundamental solutions to the problem of intermittent supply of renewable energy. The large-capacity/low-head pumped hydro energy storage (LL-PHES) system with the use of tubular pump turbine is a beneficial extension of traditional PHES systems owing to large flow rate and cheaper civil structures. However, the continuous competition between the “static water pressure difference caused by gravity” and the “pressure increase caused by accelerated impeller rotation” leads to prominent instability in the start-up process of the LL-PHES system under pump conditions. An explicit coupling algorithm is proposed for analyzing the transient characteristics in the start-up process of the LL-PHES system under pump conditions. This algorithm is based on the idea of dimensional transformation, and performs 3D flow calculations and 2D rigid body dynamics equation solution in the pump domain and the flap gate domain, respectively. This algorithm avoids the problems of high computational cost and poor convergence that exist in existing fully three-dimensional coupling algorithms and ensures the efficiency of transient hydraulic characteristic calculation. A comprehensive analysis of the transient characteristics of the LL-PHES system during pump start-up process is conducted using the proposed new algorithm. The entire process of the increase in rotational speed, valve opening, flow rate, and the continuous evolution of blade surface pressure during the start-up process is quantitatively described. The amplitude and spectral characteristics of the alternating pressure on multiple blades are clarified. The evolution law of blade load during the stage of severe pressure fluctuations during the start-up process is explained. The load distribution characteristics of “high in the leading and trailing edge areas and low in the middle” in the blade stream direction is presented. The research results have a direct guiding role in improving the hydraulic design and enhancing the operational stability of LL-PHES systems. Full article

This paper introduces and investigates a novel two-parameter sequence, termed the biparametric Appell extension (B-App-Ex) and denoted by ${\mathcal{B}}_n(x;\lambda ,\alpha )$. Standard classical Appell sequences often lack sufficient structural parameters, which can limit their operational flexibility in certain advanced spectral schemes. To address this limitation, we construct an enhanced operational framework by integrating a binomial structural kernel ${(1+w)}^{\lambda }$ with a linear exponential scaling $e^{\alpha xw}$ entirely within the Appell class. We provide a rigorous logical deduction of the fundamental properties of this sequence, including its explicit power series representation, a characteristic three-term recurrence relation, and a governing second-order differential equation (DEq.). A significant contribution of this work is the establishment of analytically exact connection and inverse connection formulas between the B-App-Ex basis and various classical orthogonal polynomial (COP) families. Numerical verification via a collocation-based projection framework demonstrates that these algebraic kernels achieve near-machine epsilon precision (≈${10}^{-15}$), remaining stable even for high-order approximations. Furthermore, by isolating the dilation factor $\alpha$, we establish an $O\left(N\right)$ computational complexity that offers a reduction in latency by approximately two orders of magnitude compared to classical matrix-based transformations. The results demonstrate that the proposed biparametric (Bip.) extension offers a versatile and highly optimized analytical template for modeling complex dynamic systems where structural shifting and spatial scaling must be tuned simultaneously. Full article