Search Results (1,226)

This study utilized capric acid (CA), lauric acid (LA), myristic acid (MA), palmitic acid (PA), and stearic acid (SA) as alternative feedstocks to conduct theoretical analyses on ten fatty acid-based ternary eutectic systems. By leveraging the Schrader equation, phase diagrams for each system were constructed, and their theoretical eutectic points were calculated. The CA-LA-MA (capric acid–lauric acid–myristic acid) ternary system was selected as a representative for experimental fabrication: differential scanning calorimetry (DSC) was employed to characterize its thermal properties, while Fourier transform infrared spectroscopy (FT-IR) and thermogravimetric analysis (TGA) were used to assess its functional group composition and thermal stability, respectively. Theoretical calculations indicate that the ten ternary eutectic systems exhibit melting temperatures ranging from 17.11 °C to 37.61 °C, with phase change latent heats spanning 167.8 J·g⁻¹ to 189.6 J·g⁻¹. For the CA-LA-MA system, experimental DSC results confirm that its eutectic melting temperature is 16.0 °C (accompanied by a phase change latent heat of 177.0 J·g⁻¹, with minor deviations from theoretical predictions attributed to reagent impurities and operational errors). TGA characterization further reveals that the CA-LA-MA mixture has an initial weight loss temperature (corresponding to ~1% mass loss) of 115.6 °C and an extrapolated onset weight loss temperature of 164.8 °C, confirming reliable thermal stability below 100 °C—consistent with its low-temperature application design. These results validate the consistency between theoretical predictions and experimental data, and demonstrate that fatty acid-based ternary eutectic mixtures are promising candidates for low-temperature thermal energy storage applications. Full article

Mathematical models for infectious diseases, particularly autonomous ODE models, are generally known to possess simple dynamics, often converging to stable disease-free or endemic equilibria. This paper investigates the dynamic consequences of a crucial, yet often overlooked, component of pandemic response: the saturation of public health testing. We extend the standard SIR model to include compartments for ‘Confirmed’ (C) and ‘Monitored’ (M) individuals, resulting in a new SICMR model. By fitting the model to U.S. COVID-19 pandemic data (specifically the Omicron wave of late 2021), we demonstrate that capacity constraints in testing destabilize the testing-free endemic equilibrium ($E_1$). This equilibrium becomes an unstable saddle-focus. The instability is driven by a sociological feedback loop, where the rise in confirmed cases drive testing effort, modeled by a nonlinear Holling Type II functional response. We explicitly verify that the eigenvalues for the best-fit model satisfy the Shilnikov condition (${\lambda }_u>{\lambda }_s$), demonstrating the system possesses the necessary ingredients for complex, chaotic-like dynamics. Furthermore, we employ Stochastic Differential Equations (SDEs) to show that intrinsic noise interacts with this instability to generate ’noise-induced bursting,’ replicating the complex wave-like patterns observed in empirical data. Our results suggest that public health interventions, such as testing, are not merely passive controls but active dynamical variables that can fundamentally alter the qualitative stability of an epidemic. Full article

This work presents the design of passivity based non-fragile retarded sampled data control (NFRSDC) for the wind energy system using permanent magnet synchronous generator. At first, the proposed system is characterized in terms of non-linear dynamical equations, which is later expressed in terms of linear sub-systems via fuzzy membership functions using the Takagi–Sugeno fuzzy approach. After that, a more applicative NFRSDC is proposed along with the delay involved during signal transmission as well as randomly occurring controller gain perturbations (ROCGPs). Here, the ROCGPs are modeled accordingly using stochastic variable which obeys the certain Bernoulli distribution sequences. Folowing that, an appropriate Lyapunov–Krasovskii functionals are constructed to obtain the sufficient conditions in the form of linear matrix inequalities. These obtained conditions are then used to ensure the global asymptotic stability of the given system with the exogenous disturbances. Finally, numerical simulations are performed using MATLAB/Simulink and the obtained results have clearly demonstrated the efficacy of the proposed controller. Full article

The nonlinear Bagley–Torvik equation is of fundamental importance, as it captures a realistic and intricate interplay among memory effects, nonlinearity, and functional dependence—making it a powerful model for a wide range of natural and engineered systems. Its analysis contributes significantly to both the theoretical development of fractional differential equations and their practical applications across science and technology. In this paper, we employ the inverse operator method, the multivariate Mittag-Leffler function, and several classical fixed-point theorems to establish sufficient conditions for the existence, uniqueness, and Hyers–Ulam stability of solutions to the nonlinear Bagley–Torvik equation with functional initial conditions. Finally, we present several examples by explicitly computing values of the multivariate Mittag-Leffler functions to illustrate the main results. Full article

In real life, almost all systems are nonlinear in nature. The electromagnetic levitation system (EMLS) is one such system that has a wide range of applications due to its frictionless, fast, and affordable technique. Optimal control and sliding mode control (SMC) techniques are often used controllers for EMLS. However, these techniques can achieve the required levitation but lag in having perfect set-point tracking and robustness against uncertainties. To get over these drawbacks, this article proposes the design of unconstrained mismatched uncertainties, constrained mismatched uncertainties, and integral sliding mode control with mismatched uncertainties for the current-controlled-type electromagnetic levitation system (CC-EMLS). The modeled equations of CC-EMLS are transfomed in terms of the mismatched uncertainties, and the required control action is obtained with and without constraints on the control input. The quadratic performance function is suggested for the unconstrained control scheme and is solved using the Hamilton–Jacobi–Bellman (HJB) equation. The non-quadratic cost function is designed for the constrained control method, and the HJB equation is utilized to obtain the solution. Both control schemes provide robustness to the system, but deviations in the set point are observed in tracking the position of the ball when the changes in the payload occur in the system. Therefore, integral sliding mode control with robust–optimal (IOSMC) gain is proposed for the CC-EMLS to overcome the steady-state error in the other two schemes. The stability is proven using the direct method of Lyapunov stability. The essential studies based on the simulation are carried out to showcase the performance of the proposed control schemes. The integral performance indicators are compared for all three proposed control schemes to highlight the efficacy, robustness, and efficiency of the designed controllers. Full article

In Minkowski 3-space, we establish a geometric framework to osculate Type-II ruled surfaces by utilizing the Type-II Bishop frame in $\left({\mathbb{E}}_1^3\right)$. Our analysis extends to higher-order singularities such as butterflies and pyramids, including explicit singularity loci. We also compare Type-II Bishop frames with rotation-minimizing frames using timelike base curves and spacelike normals. With RK4 integration, we develop a robust computational model for Weingarten surfaces and subclasses with constant curvature. The theoretical foundation for Type-II Bishop frames is extended to higher-dimensional Minkowski spaces ${\mathbb{E}}_1^n$ for $n>3$ through generalized Frenet-type equations and curvature functions. We determine exact stability conditions under perturbations of Bishop curvature using advanced singularity theory. The numerical implementations of our methods, including geometric modeling and relativistic geometry, demonstrate their effectiveness in both theoretical and applied contexts. Full article

With the advancement in deep-sea resource development, the creep behavior of deep-sea remolded sediments under coupled temperature, confining pressure (σ₃), and stress effects has become a critical issue threatening engineering stability. The traditional Singh–Mitchell model, limited by its neglect of temperature effects and prediction of infinite strain, struggles to meet deep-sea environmental requirements. Based on low-temperature, high-pressure triaxial tests (with temperatures ranging from 4 to 40 °C and confining pressures ranging from 100 to 300 kPa), this study proposes a modified model incorporating temperature–stress–time coupling. The model introduces a hyperbolic creep strain rate decay function to achieve strain convergence, establishes a saturated strain–stress exponential relationship, and quantifies the effect of temperature on characteristic time via coupling through the Arrhenius equation. The modified model demonstrates R² values > 0.96 for full-condition creep curves. The results show several key findings: a 10 °C increase in temperature leads to a 30–50% growth in the steady-state creep rate; a 100 kPa increase in confining pressure enhances long-term strength by 20–30%. 20 °C serves as a critical temperature point. At this point, strain amplification reaches 2.1 times that of low-temperature ranges. These experimental findings provide crucial theoretical foundations and technical support for incorporating soil creep effects in deep-sea engineering design. Full article

Time delays are intrinsic to mitotic regulation, particularly within the spindle assembly checkpoint (SAC) and the spindle position checkpoint (SPOC). These delays emerge from multi-step protein activation, molecular transport, force-dependent conformational transitions, and spatial redistribution of regulatory complexes. They span seconds to minutes and strongly influence checkpoint activation, maintenance, and silencing. Increasing evidence shows that such delayed processes shape mitotic timing, checkpoint robustness, and cell-fate decisions. While classical ordinary differential equation (ODE) models assume instantaneous biochemical responses, delay differential equations (DDEs) provide a natural framework for representing these finite timescales by explicitly incorporating system history. Recent DDE-based studies have revealed how delayed signaling contributes to bistability, oscillatory responses, prolonged mitotic arrest, and variability in checkpoint outputs. This review summarizes the biological origins of delays in SAC and SPOC, including Mad2 activation, MCC assembly and turnover, APC/C reactivation, tension maturation at kinetochores, and Bfa1–Bub2 regulation of Tem1. The article further discusses how mechanistic models with explicit delays improve our understanding of SAC–SPOC ordering, error-correction dynamics, and mitotic exit control. Finally, open challenges and future directions are outlined for integrative delay-aware modeling that unifies biochemical, mechanical, and spatial processes to better explain checkpoint function and chromosomal stability. Full article

The description of the Earth’s gravitational field, governed by the fundamental potential equation (the Laplace equation), is conventionally expressed using spherical harmonics, yet the Cartesian formulation, using a Taylor series representation, offers significant algebraic advantages. This paper proposes a novel Direct Cartesian Method for generating spherical basis functions and coefficients directly within the Cartesian coordinate system, utilising the partial derivatives of the inverse distance ($1/R$) function. The present study investigates the structural correspondence between the Cartesian form of spherical basis functions and the high-order partial derivatives of $1/R$. The study reveals that spherical basis functions can be categorised into four distinct groups based on the parity of the degree n and order m. It is demonstrated that each spherical basis function is equivalent to a weighted summation of the partial derivatives of the inverse distance ($1/R$) with respect to Cartesian coordinates. Specifically, the basis functions are combined with those derivatives that share the same order of Z-differentiation and possess matching parities in their orders of differentiation with respect to X and Y. In order to facilitate the practical calculation of these high-degree derivatives, a recursive numerical algorithm has been developed. The method generates the polynomial coefficients for the numerator of the $1/R$ derivatives. A pivotal innovation is the implementation of a step-wise normalization scheme within the recursive relations. The integration of the recursive ratios of global normalization factors (including full Schmidt normalization) into each step of the algorithm effectively neutralises factorial growth, rendering the process immune to numerical overflow. The validity and numerical stability of the proposed method are demonstrated through a detailed step-by-step derivation of a sectorial basis function ($n=8,m=2$). Full article

Polymer-assisted hot water flooding (PAHWF) is an important enhanced oil recovery technique involving strongly coupled thermal, chemical, and multiphase flow processes. Accurate prediction of water saturation, polymer concentration, and temperature evolution in PAHWF is challenging due to the highly nonlinear and multiscale governing equations. In this study, a physics-informed neural network (PINN) framework is developed for one-dimensional PAHWF simulation as a controlled benchmark system to systematically investigate PINN behavior in multiphysics-coupled problems. The PAHWF governing equations incorporating temperature- and concentration-dependent viscosity are embedded into the PINN loss function. Three progressively designed numerical examples are conducted to examine the effects of temperature normalization, network architecture (PINN-1 versus PINN-2), and network depth on training stability and solution accuracy. The results demonstrate that temperature normalization effectively mitigates gradient-scale imbalance, significantly improving convergence stability and prediction accuracy. Furthermore, the PINN-2 architecture, which employs a dedicated network for temperature, exhibits enhanced robustness and accuracy compared with the unified PINN-1 structure. Variations in network depth show limited influence on solution quality, indicating the inherent robustness of PINNs under the proposed framework. Although conventional numerical methods remain more efficient for one-dimensional forward problems, this study establishes a methodological foundation for extending PINNs to higher-dimensional, strongly coupled PAHWF simulations and inverse reservoir problems. The proposed framework provides insights into improving PINN trainability and reliability for complex enhanced oil recovery processes. Full article

Alpine grasslands on the Qinghai–Tibet Plateau are highly sensitive to climate change and human disturbances, and their degradation poses serious threats to ecosystem stability and soil conservation. Belowground bud banks form the foundation of vegetative regeneration, yet their variation along degradation gradients and the soil factors regulating these changes remain insufficiently understood. In this study, we investigated the density and composition of belowground buds in grasses, sedges, and forbs across four degradation levels during the peak growing season and examined the soil controls shaping these responses. The results showed that moderate degradation significantly increased total bud density, indicating enhanced clonal renewal capacity, whereas severe degradation markedly reduced bud-bank potential. Bud types from different functional groups responded differently to soil conditions: rhizome buds of grasses were mainly driven by soil fertility, while tiller buds were more sensitive to soil compaction and carbon–nitrogen availability; rhizome buds of sedges could still develop in compact, nutrient-poor soils; and bud types of forbs were more responsive to variations in soil nutrient status or soil structure. Structural equation modeling further revealed that the formation of the belowground bud is primarily influenced by soil physico-chemical properties, particularly soil nutrients, which regulate regenerative capacity under degraded alpine grasslands. This study reveals the variation patterns of belowground bud banks along degradation gradients in alpine grasslands on the Qinghai–Tibet Plateau and their responses to soil factors, and it elucidates the pathways through which degradation mediates belowground bud bank dynamics via soil physico-chemical properties, particularly soil nutrients, thereby providing a scientific basis for understanding the regeneration potential of alpine grasslands and for the sustainable management and ecological restoration of degraded alpine grasslands. Full article

Addressing the challenges of online measurement of oil-gas-water three-phase flow under high gas–liquid ratio (GVF > 90%) conditions (fire-driven mining, gas injection mining, natural gas mining), which rely heavily on radioactive sources, this study proposes an integrated, radiation-source-free three-phase measurement scheme utilizing a “Venturi tube-microwave resonator”. Additionally, a physics-informed neural network (PINN) is introduced to predict the volumetric flow rate of oil-gas-water three-phase flow. Methodologically, the main features are the Venturi differential pressure signal ($\mathrm{\Delta }P$) and microwave resonance amplitude ($V$). A PINN model is constructed by embedding an improved L-M model, a cross-sectional water content model, and physical constraint equations into the loss function, thereby maintaining physical consistency and generalization ability under small sample sizes and across different operating conditions. Through experiments on oil-gas-water three-phase flow, the PINN model is compared with an artificial neural network (ANN) and a support vector machine (SVM). The results showed that under high gas–liquid ratio conditions (GVF > 90%), the relative errors (REL) of PINN in predicting the volumetric flow rates of oil, gas, and water were 0.1865, 0.0397, and 0.0619, respectively, which were better than ANN and SVM, and the output met physical constraints. The results indicate that under current laboratory conditions and working conditions, the PINN model has good performance in predicting the flow rate of oil-gas-water three-phase flow. However, in order to apply it to the field in the future, experiments with a wider range of working conditions and long-term stability testing should be conducted. This study provides a new technological solution for developing three-phase measurement and machine learning models that are radiation-free, real-time, and engineering-feasible. Full article

Freshwater scarcity in arid regions is driving increased use of saline irrigation, yet salinity severely degrades soil structure and suppresses enzymatic function. To address this critical challenge for sustainable soil management, this study systematically evaluated magnetized saline water (MSW) across three salinity levels (1, 3, and 6 g L⁻¹) and four magnetic field strengths (0, 0.2, 0.4, and 0.6 T), confirming the magnetic field intensity (C) × salinity (S) interaction. The comprehensive analysis integrated data on aggregate stability, key ion concentrations (Ca²⁺, Mg²⁺, Cl⁻), and major enzyme activities. Structural Equation Modeling (SEM) was utilized to quantify the underlying mechanisms, demonstrating that structural improvement is primarily driven by strong indirect pathways, mediated by optimized ion dynamics and increased enzyme-mediated organic matter turnover. The moderate-salinity (3 g L⁻¹), moderate-magnetic-field (0.4 T) regime emerged as the optimal balanced strategy for overall soil health. These findings offer a scalable approach, guiding future field-scale research toward long-term agricultural sustainability. Full article

For the study, we used four kerosene-based ferrofluid samples containing magnetite nanoparticles stabilized with oleic acid. Starting from the initial sample (A0), the other three samples were obtained by dilution with kerosene. The complex magnetic permeability measurements were performed in the microwave region (0.5–6) GHz, for different H values of the polarizing magnetic field, between (0–115) kA/m. These measurements revealed the ferromagnetic resonance phenomenon for each sample, allowing the determination of the anisotropy field (H_A) and the effective anisotropy constant (K_eff) of nanoparticles, depending on the volume fraction of particles (φ). At the same time, the measurements allowed the determination of the specific magnetic loss power (p_m), effective heating rate (HR_eff), intrinsic loss power (ILP), and specific absorption rate (SAR) as functions of the frequency (f) and magnetic field (H), of all investigated samples, using newly proposed equations for their calculation. For the first time, this study evaluates the maximum limit of the applied polarizing magnetic field (H_max ≈ 80 kA/m) and the minimum limit volume fraction of nanoparticles (φ_min ≈ 3.5%) at which microwave heating of the ferrofluid remains efficient. At the same time, the results obtained show that the temperature increase of the ferrofluid samples, upon interaction with a microwave field, can be controlled by varying both H and φ, pointing to possible applications in magnetic hyperthermia. Full article

This work introduces a new category of proportional fractional integro-differential equations (PFIDEs) governed by functional boundary conditions. We derive verifiable sufficient criteria that guarantee the Ulam–Hyers Stability, existence and uniqueness of solutions to this problem. Our analytical approach leverages Babenko’s method to construct an inverse operator, which allows us to reformulate the differential problem into an equivalent integral equation. The analysis is then conducted using key mathematical tools, including contraction mapping principle of Banach, the Leray–Schauder alternative, and properties of multivariate Mittag–Leffler functions. The Ulam–Hyers Stability is rigorously examined to assess the system’s resilience to small perturbations. The applicability and effectiveness of the established theoretical results are demonstrated through two illustrative examples. This research provides a unified and adaptable framework that advances the analysis of complex fractional-order dynamical systems subject to nonlocal constraints. Full article