Search Results (3,025)

A systematic numerical simulation and analysis of the temperature field were conducted for the laser cladding process of CuCrZr alloy onto a 316L stainless steel substrate. First, the thermal properties of the material (density, thermal conductivity, and specific heat capacity) as a function of temperature were calculated using JMatPro software. The equilibrium phase diagram of the CuCrZr alloy was obtained using Thermo-Calc, clarifying the stability of each phase and the solid–liquid phase transition ranges. Based on these findings, three-dimensional transient heat transfer models for single-layer single-pass and single-layer multi-pass cladding were established using ANSYS finite element software and a double-ellipsoidal moving heat source model. The effects of laser power on the evolution of the temperature field, peak temperature, and thermal cycling characteristics were systematically investigated. The simulation results indicate that the temperature field exhibits typical rapid heating and rapid cooling characteristics; the peak temperature increases significantly with rising laser power, and the extent of the high-temperature region expands. A combined analysis of the phase diagram and temperature field results indicates that the peak cladding temperature exceeds the complete melting temperature of the alloy, ensuring sufficient melting. This study provides a reliable theoretical foundation and data support for optimizing laser cladding process parameters, predicting the microstructure of the cladding layer, and controlling thermal stress. Full article

Asthma is one of the most prevalent chronic respiratory diseases worldwide, and environmental pollutants such as desert dust play a significant role in triggering respiratory sensitization and aggravating asthma symptoms. In this study, a mathematical model is proposed to investigate the dynamics of dust-induced asthma progression. The population is divided into unaware susceptible individuals, aware susceptible individuals, dust-sensitized individuals, and asthmatic individuals, while two additional variables describe dust concentration in the human population and the environment. Fundamental qualitative properties of the model, including positivity, boundedness, existence of equilibria, and stability conditions, are established. It is shown that the asthma-free equilibrium is locally and globally asymptotically stable whenever the dust-induced asthma threshold is below unity, whereas a unique asthma-persistent equilibrium exists when the dust-induced asthma threshold exceeds unity. To reduce the burden of asthma, an optimal control problem is formulated by incorporating three time-dependent interventions: awareness campaigns, medical intervention for dust-sensitized individuals, and environmental dust reduction. Pontryagin’s Maximum Principle is employed to characterize the optimal controls and derive the corresponding adjoint system. Numerical simulations, performed using the forward–backward sweep method, demonstrate that the proposed interventions significantly reduce the number of asthmatic individuals compared with the uncontrolled case. Furthermore, a cost-effectiveness analysis based on the Average Cost-Effectiveness Ratio (ACER) and Incremental Cost-Effectiveness Ratio (ICER) is conducted to compare seven intervention strategies. The results indicate that the medical intervention strategy is the most economically attractive option, while the combined strategy involving all controls achieves the largest reduction in asthma burden. Full article

We study a class of evolutionary variational inequalities in a Hilbert space that models the long-run balanced-growth equilibrium of a competitive economy with transaction costs, time-dependent production and infrastructure constraints, and exogenous price dynamics. The paper makes four contributions. First, we introduce a parametrized monotonicity functional ${\mu }_{\alpha }(t;F;u,v;p)$ and prove an exact equivalence theorem: the inequality ${\mu }_{\alpha }\ge \beta {∥u-v∥}^2$ holds if and only if the operator F is strongly monotone with the explicitly computed constant $m=\beta -\alpha (1+{∥p∥}_{\infty })$. This turns the growth parameter $\alpha$ and the price level into explicit terms of a single admissibility threshold and, for $\beta <\alpha (1+{∥p∥}_{\infty })$, produces a scale of conditions that covers operators which are not monotone, i.e., economies with a bounded degree of increasing returns. Second, we prove well-posedness: for every admissible initial state there is exactly one Lipschitz equilibrium trajectory $u^{*}(·)$, obtained through Moreau’s catching-up algorithm for the associated perturbed sweeping process, together with the explicit velocity bound $∥{\dot{u}}^{*}∥\le L_K+2C_F$. Third, we derive one comparison estimate from which global exponential stability, the convergence rate $∥u\left(t\right)-u^{*}\left(t\right)∥\le r e^{-mt}+L_p{m}^{-1}\sup ∥\Delta p∥+\epsilon m^{-1}$, and robustness with respect to perturbations of prices and of the operator all follow; we also show that, when the constraint sets stabilize, the trajectory converges to the stationary equilibrium of the limit problem. Fourth, we prove that strong monotonicity implies the c-covering property with $c=m$, so that the shock-absorbing capacity of the economy is governed by the same constant as the speed of convergence. Two examples—a two-resource system and an n-market network with nonlinear transaction costs—are worked out with a complete verification of every hypothesis and with explicit numerical constants. Full article

Through-going structures are widely distributed in rock masses of underground engineering, and their dip angles act as the core factor affecting the stress field and mechanical response of surrounding rock. To reveal the mechanical mechanism of rock masses containing through-going structures with different dip angles, this study adopts a combined method of theoretical derivation, indoor model testing and numerical simulation. Firstly, a plane strain mechanical model is established to classify Tectonically-induced Stress, Residual Gravitational Stress and engineering-induced stress, and the theoretical formulas for stress components, stress residual coefficient and stress deflection angle are derived. Secondly, rock-like specimens with through-going structures of various dip angles are prepared and biaxial compression tests are carried out to monitor mechanical parameters such as surrounding rock strain and peak strength. Finally, a large-scale numerical model is built by FLAC2D (version 7.0) software to simulate the whole process of stress equilibrium and excavation unloading of rock mass under a normal stress of 20 MPa. Then the data of principal stress, stress components, stress residual coefficient and deflection angle under different dip angles are extracted. The results show that the dip angle of through-going structure exerts a prominent regulatory effect on the rock mass stress field. With the increase of the dip angle, the Tectonically-induced Stress decreases continuously while the Residual Gravitational Stress rises gradually. The variation trend of stress deflection angle is highly consistent with structural dip angle, and the influence of Residual Gravitational Stress on deflection angle is limited. Due to the differences in loading modes and model sizes between indoor tests and numerical simulations, the evolution laws of stress residual coefficient show opposite trends, but both results verify the dominant effect of structural dip angle. Combined with theoretical, experimental and numerical results, the proposed theoretical system can effectively describe the stress evolution law of rock masses with through-going structures, which provides theoretical reference and technical support for the stability analysis of surrounding rock in similar underground engineering. Full article

Income inequality remains a persistent structural challenge in advanced economies, with important consequences for economic stability, social cohesion, and the effectiveness of public policy. This study investigates the determinants of income inequality in the United Kingdom over the period 1980–2021 by combining ARDL, FMOLS, and NARDL approaches to assess long-run equilibrium relationships and potential nonlinear distributional effects. The ARDL bounds test confirms the presence of a stable long-run cointegrating relationship between the Gini index and its socioeconomic determinants, indicating that fiscal conditions, labour market dynamics, economic development, and income structure move together over time. The FMOLS estimates show that GDP per capita and unemployment are positively associated with inequality, whereas public social spending, government expenditure on education, tax revenue, and the income share of the fourth quintile are negatively related to the Gini index in the long run. These results underline the importance of redistribution, human capital investment, and labour market stability in moderating income disparities. The NARDL estimates suggest directionally different responses to positive and negative changes in the upper-middle-income share. Positive changes are associated with lower inequality (−0.931), while negative changes are associated with higher inequality (0.232); however, neither effect is statistically significant. The Wald test likewise fails to reject long-run symmetry (χ²(1) = 0.212, p = 0.646). Overall, the findings support a stable long-run inequality framework while indicating only limited evidence of asymmetric distributional adjustment in the United Kingdom. Full article

Spray cosmetics couple formulation composition with actuator design and biological targets, so their performance is governed by rapid, nonequilibrium interfacial processes that cannot be predicted from in-bottle stability or equilibrium surface tension alone. This targeted narrative review integrates evidence across storage stability, atomization, droplet flight and evaporation, deposition, film formation, active delivery, inhalation safety and environmental fate. It examines how surfactant molecular structure, micellar replenishment, dynamic surface tension, interfacial viscoelasticity and extensional rheology influence droplet-size distributions, wetting, spreading and deposition. Particular attention is given to competing effects: enhanced breakup may increase airborne fine fractions; stronger interfacial films may impair sprayability; enhanced penetration may reduce barrier tolerance; and bio-based origin does not necessarily imply a lower life-cycle burden. Across moisturizing, sunscreen, hair- and scalp-care, makeup-setting, cleansing-foam and emerging functional sprays, this review develops an interface-to-outcome framework and a multiobjective operating-window concept linking formulation and device variables to efficacy, manufacturability, safety and sustainability. The available evidence supports product-specific, whole-process validation rather than optimization against any single equilibrium property, while highlighting the need for spray-relevant dynamic measurements, realistic exposure assessment and validated formulation–device co-design. Full article

Persistence, coexistence, competitive exclusion, and global asymptotic stability (GAS) are closely related problems in mathematical epidemiology that are often treated by model-specific arguments. We develop a unified approach to GAS based on Perron–Volterra Lyapunov functions $L_p$, for multi-strain epidemic reaction networks. For bilinear m-strain models with irreducible rank-one infection blocks and block-diagonal next-generation structure, these functions yield a generic competitive-exclusion partition of parameter space into at most $m+1$ regions: either the disease free equilibrium is GAS, or exactly one dominant strain persists and its boundary endemic equilibrium is GAS; see non-generic tie surfaces on which the corresponding reproduction numbers coincide. We also prove a second complete GAS partition, for two-strain models with increasing concave incidence and scalar, non-interacting strain blocks, extending the Rahman–Zou result beyond rational saturating incidence. In this class, the disease-free, single-strain, and coexistence equilibria may all occur, and explicit Lyapunov functions provide the full exclusion/coexistence partition among the four possible equilibrium supports. The construction combines five ingredients: siphons, which determine forward-invariant boundary faces; triangular Jacobian structure on siphon faces; the Metzler property of transversal Jacobians and their Perron eigenvectors; regular next-generation splittings, whose spectral radii determine invasibility; and boundary transcritical invasion relays linking eigenvalue crossings to the emergence of equilibria on adjacent faces. The resulting Perron–Volterra functions combine Volterra entropy terms for resident variables with Perron-weighted linear functionals for absent strain blocks. These constructions are implemented in the Mathematica package EpidCRN, which computes siphons, transversal blocks, invasion data, Perron weights, and candidate Lyapunov functions. For the two model classes considered here, these candidates are proved to be genuine Lyapunov functions and yield complete generic GAS partitions. Full article

Organic–inorganic hybrid crystalline materials formed in multicomponent aqueous systems are of interest because their phase behavior and physicochemical properties can be controlled by composition and crystallization conditions. In this study, the phase equilibria and crystallization behavior of the ternary aqueous Ca(ClO₃)₂·2CO(NH₂)₂–CH₂ClCOOH·(C₂H₄OH)₃N–H₂O system were investigated over the temperature range of −24 to 60 °C using the visual-polythermal method. Experimental data obtained for the two boundary binary subsystems and eight internal sections were used to construct the polythermal phase diagram. The diagram revealed distinct crystallization fields corresponding to ice, Ca(ClO₃)₂·2CO(NH₂)₂·2H₂O, CH₂ClCOOH·(C₂H₄OH)₃N, and a separate crystallization region associated with a previously unreported crystalline phase with the proposed composition ClCH₂COOH·Ca(ClO₃)₂·(C₂H₄OH)₃N. The solid phase was isolated from its crystallization region, washed with cold distilled water, dried to constant mass, and characterized by complementary Fourier-transform infrared spectroscopy (FT-IR), scanning electron microscopy coupled with energy-dispersive X-ray spectroscopy (SEM–EDS), thermogravimetric analysis, derivative thermogravimetry, and differential scanning calorimetry (TG–DTG–DSC), and powder X-ray diffraction (PXRD). The experimentally determined Ca²⁺ and ClO₃⁻ contents were reasonably consistent with the proposed composition, while FT-IR spectroscopy revealed characteristic chlorate vibrations and changes in the vibrational environment of the organic component. SEM showed predominantly prismatic and plate-like crystalline morphologies, and EDS confirmed the presence of Ca, Cl, O, C, and N. Thermal analysis demonstrated multistage decomposition, with comparatively good thermal stability below approximately 150 °C. PXRD revealed a diffraction fingerprint distinct from those of the starting components and the corresponding physical mixture. Preliminary indexing of 19 principal reflections was consistent with a tetragonal candidate lattice with a = b = 7.7411(5) Å, c = 24.7182(10) Å, V = 1481.2(5) ų, and M₂₀ ≈ 23.0. The crystallographic analysis is considered preliminary because the diffraction profile was reconstructed from the available pattern and was not subjected to complete structure refinement. Overall, the combined phase-equilibrium, compositional, spectroscopic, morphological, thermal, and diffraction data support the isolation of a distinct organic–inorganic crystalline phase with the proposed composition. Full article

Active-power ceilings create a control challenge in droop-controlled grid-forming converter networks because the electrical response is faster than the measurements and outer control. Projected and projection-free power limiting use filtered active power in the outer power–frequency channel and therefore cannot act directly on the first electrical power peak. This paper proposes constraint-activated projection-free control, which coordinates a shaped projection-free multiplier with a bounded resistance term in the capacitor-voltage reference driven by instantaneous terminal power. A general full-order dynamic model describes the converters, controllers, and network without tying the formulation to a particular benchmark. Local well-posedness is established, and the proposed controller is shown to preserve the constrained projection-free equilibrium and active-branch Jacobian, allowing the same full-order stability assessment. Across ten tested scenarios with unchanged controller parameters, the proposed controller reduces peak power exceedance by 38.7–55.4% and accumulated excess energy by 34.1–62.2%. The corresponding DC-buffer requirement decreases without activating the independent current limiter, which isolates the source-side power constraint from AC overcurrent. A network-level study demonstrates sequential transitions between one and two constrained sources while the remaining converter supplies the feasible power imbalance. Full-order stability verification, component studies, and parameter sweeps establish the role and useful range of each controller path. Full article

In addition to barges, floating conveyor belt routes are used to ensure the continuous transport of granular materials extracted by floating dredgers from the water environment. This paper deals with the graphical and analytical determination of the coordinates of the centre of gravity of the buoyant force and the stability arm during the deflection of a floating body, consisting of two floats with a circular cross-section, from the equilibrium position. The coordinates of the centre of buoyancy were determined by a graphical–numerical method in the 3D CAD environment on the three-dimensional model created of the floating body. The coordinates of the centre of buoyancy were determined by analysing the geometric and physical properties of the model using the “Physical Properties” tool. The analytical procedure for determining the coordinates of the centre of buoyancy when a floating body is deflected from its equilibrium position is divided into three characteristic phases, which are mathematically described by means of certain integrals with differently defined integration limits corresponding to the given state of immersion of the body. Under laboratory conditions, the magnitude of the buoyant force was detected on the experimental apparatus using two force transducers. The experiment was carried out for three levels of float immersion, where the floating body was gradually tilted from the equilibrium position in a range of angles from 0° to 50°. Full article

We develop a reaction–diffusion–chemotaxis model for spatial tumour–immune–chemokine dynamics that couples logistic tumour growth, immune-mediated killing, chemokine-dependent immune recruitment, chemotactic migration, and signal production. For the non-dimensional system, we establish local classical solvability, nonnegativity, a uniform tumour-density bound, and global mass estimates for the immune and chemokine components. The tumour-free equilibrium is stable precisely when the baseline immune-control index satisfies ${\sigma }_0/\delta >1$, whereas positive homogeneous coexistence is characterized by a scalar nonlinear equation. Linearization in the Neumann Laplacian eigenbasis yields a mode-dependent cubic dispersion relation, showing that chemotaxis does not alter the tumour-invasion threshold but can destabilize homogeneous coexistence through a finite-wavelength oscillatory instability above a critical sensitivity ${\xi }_c$. A conservative finite-volume discretization with upwind chemotactic fluxes and implicit backward differentiation formula time integration is used to test these predictions. Numerical experiments recover the analytical equilibria and growth rates, identify the dominant unstable mode, reproduce the transition to spatial heterogeneity, and quantify the effects of immune recruitment, decay, and diffusion on the stability boundary. Grid-refinement, mass-balance, residual, and nonnegativity diagnostics support the computational reliability of the results. Full article

Ag-Ti₃SiC₂ composites are promising electrical contact materials, yet the atomic-scale interfacial behaviour between Ti₃SiC₂ and Ag remains poorly understood. Here, first-principles calculations were performed to investigate the interfacial stability, electronic structure, and alloying effects at the Ti₃SiC₂(0001)/Ag(111) interface. Surface-energy calculations for six terminations of Ti₃SiC₂(0001) show that the TiC(TiC) termination is preferred at low carbon chemical potential, whereas the TiC(TiSi) termination becomes the most stable once ΔμC exceeds −1.50 eV. Eighteen interface models combining the six terminations with three stacking sequences (OT, MT, and HCP) were constructed, and their work of adhesion (Wad) and equilibrium spacing (d₀) were determined by the Universal Binding Energy Relation and full structural relaxation. The HCP stacking is preferred for all terminations, and the C(TiC)-terminated HCP interface exhibits the highest work of adhesion among all configurations, with Wad = 9.25 J/m² at d₀ = 1.2 Å; relaxation enhances Wad by 10%–75%. Charge density, charge density difference, and partial density of states analyses reveal that the interfacial bonding is dominated by C 2p-Ag 4d hybridization accompanied by electron transfer from Ag and Ti atoms to the interfacial C atoms, which accounts for the adhesion hierarchy. Substitutional alloying with Cu, Ni, Zn, and Cr preferentially segregates into the interfacial Ag layer, where the defect formation energies, although positive, are the lowest, and Wad increases in the order Cu < Zn < Ni < Cr, reaching 11.0 J/m² for interfacial Cr, an enhancement of 19% over the pristine interface. The strengthening correlates directly with the filling of the dopant 3d band. These results provide theoretical guidance for the interfacial design of high-performance Ag-Ti₃SiC₂ electrical contact composites. Full article

Accurate characterization of rock anisotropy is crucial for underground engineering stability assessment. In this study, multi-directional drilling tests were performed on sandy mudstone and argillaceous sandstone, with real-time monitoring of feed force (F), torque (M), rotational speed (n), power (P), drilling velocity (v), and depth (h). Drilling-derived apparent friction angles (φ) in different directions were estimated using a force-equilibrium-based model. Based on drill bit geometry, an energy balance model for hollow drilling was developed, and a unit grinding energy (η_e) was derived. A preliminary drilling-derived anisotropy index ($B_{\phi -{\eta }_e}$), based on the coefficient of variation (CV) and integrating φ and η_e, was proposed. Results show a strong linear correlation between thrust force and torque, both exhibiting a two-stage increase with drilling depth. For the tested drilling orientations, the anisotropy determined using the proposed method decreases in the following order: sandy mudstone 1, sandy mudstone 2, argillaceous sandstone 2, and argillaceous sandstone 1. The proposed index provides a preliminary basis for evaluating directional variations in rock anisotropy. Full article

A Lyapunov-based framework for stability analysis and synthesis of adaptive neural-network (NN) controllers for a class of uncertain second-order nonlinear systems (SNS) with bounded external perturbations and unmodelled dynamics is presented. Online learning is employed for the reconstruction of the plant nonlinearity with the use of a radial-basis-function (RBF) network whose weights are adapted using a direct adaptation law deduced from a single composite Lyapunov function. The proposed controller couples the weight update to a persistent robustifying action, while the closed-loop stability is guaranteed throughout the learning transient, in contrast to schemes that guarantee stability after learning has converged. Using a composite Lyapunov function in the filtered tracking error and the weight-estimation error, we prove that all closed-loop signals are uniformly ultimately bounded (UUB) and that the tracking error converges to an explicitly characterized residual set whose radius is governed by the network reconstruction accuracy, the disturbance bound and the design gains. A $\sigma$-modification ensures parameter boundedness without persistency of excitation, and a robustness theorem shows that bounded parametric perturbations of the plant preserve stability and enlarge the ultimate bound only gradually (a graceful degradation, rather than a loss of the guarantee). The open-loop plant (a forced double-well Duffing oscillator) is characterized by means of equilibrium and Jacobian analyses. A bifurcation diagram and the largest Lyapunov exponent are presented, which show a chaotic regime (with ${\lambda }_1\approx 0.17$). Numerical experiments indicate that the proposed controller is able to suppress the chaotic motion with a small value of the ultimate bound, and maintain a smooth reference motion with a small and constant RMS error of order ${10}^{-3}$, which is approximately 26 times less than the RMS error obtained with a tuned fixed-gain baseline, and the theoretical dependence of the ultimate bound on the disturbance and the design gains is confirmed by sensitivity sweeps. Full article

When a robot performs a grinding operation, the steady-state force/position tracking accuracy of its end-effector is critical to achieving high grinding quality. To solve this problem, a fuzzy adaptive impedance method is incorporated into the robot’s compliant control framework. Firstly, the robot dynamics model is established based on the Newton–Euler method. To describe the robot dynamics more comprehensively, a linear friction compensation model is also introduced. Secondly, a dynamic feedforward trajectory-tracking controller is proposed based on the dynamic model, and its stability is verified using a Lyapunov function. The impedance parameters are adjusted in real time according to the feedback contact force and its rate of change, thereby enabling dynamic equilibrium between the end contact force and end position. This allows the robot end-effector to exhibit compliance during external environmental interactions. Finally, a control platform of a force/position compliance controller was constructed, and two grinding conditions of plane and arc were designed to validate the effectiveness of force/position compliance control based on impedance control. Compared with the fixed impedance approach, the proposed method reduces overshoot by 11.6% (plane) and 12.45% (arc), improves surface roughness from Ra 0.042 μm to Ra 0.021 μm, and achieves faster force tracking with fewer oscillations. Full article