Search Results (108)

Thisarticle develops and analyzes a fractional-order Leslie–Gower prey–predator–parasite system incorporating two discrete delays and nonlocal spatial diffusion. The model’s central novelty lies in the simultaneous integration of three biologically realistic features that have not previously been combined: (i) fractional-order memory effects via a Caputo derivative of order $\alpha \in (0,1]$, (ii) two distinct biological delays—an infection transmission delay ${\tau }_1$ and a predator handling delay ${\tau }_2$—and (iii) nonlocal spatial dispersal modeled through fractional Laplacian operators ${(-\Delta )}^{\gamma /2}$. This triple integration enables the model to capture long-range temporal memory, delayed biological responses, and nonlocal spatial interactions simultaneously, offering insights into dynamics that are challenging to capture with classical integer-order or single-delay formulations. The fractional Laplacian generalizes classical diffusion by allowing long-range dispersal events (Lévy flights), where individuals can occasionally move over large distances with heavy-tailed step-size distributions—a phenomenon observed in many animal movement patterns but absent from standard diffusion models. We provide rigorous proofs of solution existence, uniqueness, non-negativity, and boundedness in both temporal and spatiotemporal settings. Local asymptotic stability conditions are derived for all feasible equilibrium states via characteristic equation analysis. The coexistence equilibrium undergoes a Hopf bifurcation when either delay crosses a critical threshold, with fractional order $\alpha$ modulating the bifurcation point and post-bifurcation oscillation frequency. A Lyapunov functional demonstrates global asymptotic stability of the infection-free equilibrium under biologically interpretable conditions. Turing instability analysis reveals conditions for spontaneous pattern formation, with the fractional exponent $\gamma$ controlling pattern wavelength and correlation length. Numerical simulations validate theoretical predictions, including spatial patterns, traveling waves, and chaos. To bridge theory with potential applications, we outline a statistical framework for parameter estimation and uncertainty quantification, suggesting that $\beta$, $\alpha$, and ${\tau }_1$ may be priority targets for parameter estimation. Full article

This study aims to advance the understanding of laminar magnetohydrodynamic (MHD) fluid flow between two parallel plates subjected to a uniform transverse magnetic field, motivated by its significant applications in engineering and industrial systems such as nuclear reactor cooling, MHD generators, and electromagnetic pumping devices. The governing equations are simplified using a one-parameter Lie group symmetry transformation, which exploits the inherent symmetry properties of the system to reduce the original unsteady partial differential equations to a system of ordinary differential equations. The reduced equations are solved exactly under appropriate boundary and initial conditions, ensuring mathematically consistent and physically realistic solutions. A comprehensive analysis is conducted to examine the influence of key physical parameters, along with the applied magnetic field, on the velocity, temperature, and concentration profiles. The selected parameter ranges encompass a broad spectrum of physically relevant cases, enabling a detailed assessment of their effects. The results indicate that the transverse magnetic field exerts a damping effect on the flow, reducing the velocity profile due to the Lorentz force. Moreover, an increase in the Schmidt number accelerates the achievement of a steady-state concentration, while higher Prandtl numbers reduce the temperature profile. In contrast, the radiation parameter enhances the temperature distribution. In addition, the skin-friction coefficient is presented graphically, and the Nusselt number is evaluated to characterize the heat transfer performance. Overall, the findings provide valuable insight into the effects of magnetic, thermal, and solutal parameters on laminar MHD flow between parallel plates. Full article

Relativistic heavy-ion collisions generate ultra-strong magnetic fields that interact with the quark–gluon plasma (QGP), a key focus of high-energy physics research. This study investigates QGP energy density evolution under time-dependent magnetic fields within a (1 + 1)D relativistic magnetohydrodynamic (RMHD) framework integrated with Bjorken flow. Three magnetic field temporal evolution models (Type-1, Type-2, Type-3) are analyzed for two different equations of state: (1) $p={c_s}^{2}e$ (simplified ultra-relativistic), and (2) $p={c_s}^{2}e-2MB$ (magnetized conformal), incorporating a temperature-dependent magnetic susceptibility derived from lattice QCD. Results show that stronger magnetic fields consistently suppress QGP energy density decay, with suppression magnitude dependent on the magnetic field’s temporal profile. Ultra-relativistic fluids exhibit slowed energy decay due to magnetic pressure counteracting hydrodynamic expansion. In contrast, magnetized conformal fluids display faster energy dissipation under identical conditions, arising from the synergistic effect of enhanced magnetic fluid coupling, increased energy dissipation during interaction, and QGP’s perfect fluid expansion at elevated temperatures. Temperature-dependent magnetic susceptibility reveals a transition from diamagnetic (confined phase) to paramagnetic (deconfined QGP phase) behavior, introducing a feedback mechanism that strengthens energy retention at higher temperatures. This work clarifies the interplay between magnetic field dynamics, QCD phase structure, and hydrodynamic expansion, providing key observational signatures for distinguishing fluid types in heavy-ion collisions and advancing realistic modeling of magnetized QGP. Full article

The nuclear symmetry energy is a key component of the equation of state of neutron stars, controlling their macroscopic parameters and internal structure. Currently, it remains an unknown issue in both experimental and theoretical studies within the density range relevant to the interiors of neutron stars. This paper aims to investigate the density dependence of the symmetry energy, analyzing it in terms of the curvature parameter $K_{sym}$. The analysis is based on a neutron star matter equation of state constructed using the proposed modified polytropic form. The polytropic equations of state used approximate the complex, realistic ones. The realistic equations of state selected for the analysis in this paper are those derived using the relativistic mean-field approach. The proposed method exploits the existing strong correlations between the incompressibility of both symmetric and asymmetric nuclear matter and the calculated values of the neutron star crust–core transition density. Starting from the experimental constraint on the incompressibility of symmetric nuclear matter $K_0$ and based on observationally determined parameters, such as the mass and radius of PSR J0740+6620 pulsar, the formulated method allows for a selection of the range of $K_{sym}$ values acceptable by both the constraints on $K_0$ and the results of astrophysical observations. Full article

Vaccination behavior and epidemic spreading are strongly intertwined processes, and their coevolution is often shaped by both individual decision-making and social interactions. However, most existing studies model such interactions at the pairwise level, overlooking the potential impact of higher-order social influence arising from group interactions. In this work, we develop a coupled vaccination–epidemic spreading model on multilayer higher-order networks, where vaccination behavior evolves on a simplicial complex and epidemic propagation occurs on a physical contact network. The model incorporates imperfect vaccine efficacy, allowing vaccinated individuals to become infected, and introduces a hybrid vaccination strategy that combines rational cost–benefit evaluation with social influence from both pairwise and higher-order interactions, as well as negative effects induced by vaccine failure. By constructing the coupled dynamical equations, we analytically derive the epidemic outbreak threshold and elucidate how higher-order interactions, behavioral responses, and vaccine-related parameters jointly affect epidemic dynamics. Numerical simulations on networks with different structural properties validate the theoretical results and reveal pronounced structure-dependent effects. The results show that higher-order social interactions can significantly reshape vaccination behavior and epidemic prevalence, while network heterogeneity and vaccine imperfection play crucial roles in determining the outbreak threshold and steady-state infection level. These results emphasize the necessity of incorporating higher-order interactions together with realistic vaccination behavior into epidemic modeling and offer new insights for the design of effective vaccination strategies. Full article

This study proposes a Kalman filter-based method to optimize the placement of accelerometers in buildings, formulated as a multi-objective problem that simultaneously minimizes the number of sensors and the state estimation error. State-space equations of 3-, 9-, 15-, and 30-story buildings were developed from a simplified continuous beam model, allowing the method to be evaluated across different structural conditions. The trace of the state error covariance matrix (Tr(P)) was employed as the performance metric, showing a strong correlation with the signal-to-noise ratio (SNR) and the normalized absolute estimation error. The results highlight that measurement noise critically affects sensor placement. As the noise covariance increases, estimation uncertainty grows, and more sensors are required, often concentrated in specific structural regions. Conversely, high-sensitivity low-noise sensors reduce uncertainty, though at a higher sensor unit cost. Maintaining an SNR above 10 dB proved essential to ensure reliable operational modal analysis. Optimal layouts tended to concentrate on upper floors, where accelerations and SNR are higher, avoiding redundant sensors at modal nodes or lower levels. Validation under real and synthetic excitations, including the 2010 Concepción ground motion record and band-limited white noise, confirmed that the method can accurately identify the fundamental frequencies of the structures. These findings demonstrate the effectiveness of the proposed Kalman filter-based methodology for optimizing sensor layouts in structural health monitoring applications under realistic operational conditions. Full article

In the context of power electronic interfaces in photovoltaic (PV), fuel cell, battery, and microgrid applications, the low output voltage of the DC source necessitates a voltage-boosting inverter. This paper proposes a single-source seven-level switched-capacitor boost inverter, particularly for low-voltage applications. The proposed inverter has the capability to produce seven different output voltage levels, i.e., intermediate boosted levels, with a total gain of three times the input voltage. The inverter has the advantage of a reduced number of power switches, diodes, and a switched-capacitor unit, which allows for single-stage operation without the need for a second DC-DC converter. The operating principle of the proposed inverter is explained in detail with a complete switching state analysis, conduction path analysis, and output voltage generation. The capacitor size is calculated using a charge balance-based equation. The self-balancing capability is validated for mismatched initial voltages with a bounded steady-state ripple. To evaluate the performance of the proposed inverter in a more realistic scenario, the effects of non-ideal device characteristics are considered, and the efficiency of the inverter is estimated using a loss model. A predictive current control technique is applied to control the output current under inductive load conditions. The simulation results obtained in MATLAB/Simulink software validate the proper seven-level operation of the inverter, the self-balancing capability of the capacitors, improved output waveform quality, and current control. The proposed inverter can be extended to grid-connected applications, where conventional output filters can be applied to meet the harmonic standards. Full article

With the rapid advancement of deepfake generation technologies, forged videos have become increasingly realistic in visual quality and temporal consistency, posing serious threats to multimedia security. Existing detection methods often struggle to effectively model temporal dynamics and capture subtle inter-frame anomalies. To address these challenges, we propose a Stochastic Differential Equation and Quantum Uncertainty Network (SDEQ-Net), a novel deepfake video anomaly detection framework that integrates continuous time stochastic modeling with quantum uncertainty mechanisms. First, a Continuous Time Neural Stochastic Differential Filtering Module (CNSDFM) is introduced to characterize the continuous evolution of latent inter-frame states using neural stochastic differential equations, enabling robust temporal filtering and uncertainty estimation. Second, a Quantum Uncertainty Aware Fusion Module (QUAFM) incorporates Hermitian-symmetric density matrix representations and von Neumann entropy to enhance feature fusion under uncertainty, leveraging the mathematical symmetry properties of quantum state representations for principled uncertainty quantification. Third, a Fractional Order Temporal Anomaly Detection Module (FOTADM) is proposed to generate fine grained temporal anomaly scores based on fractional order residuals, which are used as dynamic weights to guide attention toward anomalous frames. Extensive experiments on three benchmark datasets, including FaceForensics++, Celeb-DF, and DFDC, demonstrate the effectiveness of the proposed method. SDEQ-Net achieves AUC scores of 99.81% on FF++ (c23) and 97.91% on FF++ (c40). In cross dataset evaluations, it obtains 89.55% AUC on Celeb-DF and 86.21% AUC on DFDC, consistently outperforming existing state-of-the-art methods in both detection accuracy and generalization capability. Full article

Nonlinear transport of tracer particles immersed in a sheared dilute gas with inelastic collisions is analyzed within the framework of the Boltzmann kinetic equation. Two different yet complementary approaches are employed to obtain exact results. First, we maintain the structure of the inelastic Boltzmann collision operator but consider inelastic Maxwell models (IMMs) instead of the realistic model of inelastic hard spheres (IHS). Using IMMs enables us to compute the collisional moments of the inelastic Boltzmann operator for mixtures without explicitly knowing the velocity distribution functions of the mixture. Second, we consider a kinetic model of the Boltzmann equation for IHS. This kinetic model is based on the equivalence between a gas of elastic hard spheres subjected to a drag force proportional to the particle velocity and a gas of IHS. We solve the Boltzmann–Lorentz kinetic equation for tracer particles using a generalized Chapman–Enskog-like expansion around the shear flow distribution. This reference distribution retains all hydrodynamic orders in the shear rate. The mass flux is obtained to first order in the deviations of the concentration, pressure, and temperature from their values in the reference state. Due to the anisotropy induced in the velocity space by shear flow, the mass flux is expressed in terms of tensorial quantities rather than conventional scalar diffusion coefficients. Unlike the previous results obtained for IHS using different approximations, the results derived in this paper are exact. Generally, the comparison between the IHS results and those found here shows reasonable quantitative agreement, especially for IMM results. This good agreement shows again evidence of the reliability of IMMs for studying rapid granular flows. Finally, we analyze segregation by thermal diffusion as an application of the theory. Phase diagrams illustrating segregation are presented and compared with previous IHS results, demonstrating qualitative agreement. Full article

Background: The management of inventory under realistic supply chain disruptions, which are often non-exponential, challenges classical control theory. This study addresses the critical question of whether the optimality of simple base-stock policies holds under the combined influence of non-exponential disruptions and random yield. Methods: We model the system as a Piecewise Deterministic Markov Process (PDMP) with impulse control, using Phase-Type (PH) distributions to capture non-memoryless event timings. The analysis involves proving the existence of a solution to the Average Cost Optimality Equation (ACOE) via a vanishing discount approach, and the framework is validated with a numerical experiment. Results: Our primary finding is a rigorous proof that a state-dependent base-stock policy is optimal, a significant generalisation of classical theory. We establish this by demonstrating the value function’s convexity. The numerical experiment quantifies the significant cost penalties (over 12%) incurred by using simpler, memoryless models for supply disruptions. Conclusions: The study provides a crucial theoretical justification for the robustness of simple threshold-based control policies in complex, realistic settings. It highlights for managers the importance of modelling the variability of disruptions, not just their average duration, to avoid costly strategic errors. Full article

Economic development and its sustainability are influenced not only by material, human, financial, and intellectual factors, but also by psychological factors. In particular, the levels of business expectations, trust, and confidence significantly affect the resilience of the economy, especially in crucial sectors such as industry and, more specifically, industrial production. Based on political, economic, social, and legal stability, businesses are likely to assess their opportunities more optimistically and realistically. This, in turn, enables them to look confidently toward the future and provides a foundation for investing in further development. Conversely, a decline in business expectations and confidence can slow socio-economic development, potentially leading to recession or depression. The purpose of the article is to identify the association between business confidence (Impact of the Business Confidence Indicator, IBCI) and the level of industrial production (Industrial Production Index, IPI), as a crucial aspect of ensuring sustainable economic development. A correlation–regression analysis conducted using Ukraine as a case study—a country candidate for EU accession—and statistical data from the State Statistics Service of Ukraine (SSSU) for the period from 1 February 2022 to 1 September 2024 demonstrated that there is a stable, positive, and strong relationship between IBCI and IPI levels (r = 0.7; D = 0.49). The constructed linear correlation model indicates that, with other factors held constant, a one-percentage-point increase in positive business expectations may lead to a 2.23-point rise in the industrial production activity of enterprises in Ukraine’s manufacturing sector. Furthermore, approximately 49.0% of the variation in industrial production levels is likely explained by changes in business expectations. Verification of the constructed regression equation and assessment of its parameters indicate that it is statistically reliable and consistent with real economic processes. Specifically, the Fisher coefficient (F = 5.30) exceeds the critical (tabular) value (Ft = 2.04), with Se = 0.45 and C_95% = 1.96; the causality test based on the Granger methodology revealed the presence of a causal relationship, indicating that the IBCI influences the IPI. The obtained statistical results for the applied models and tests are as follows: MDF (p < 0.05), KPSS (p > 0.10), Durbin–Watson ≈ 2.0, Breusch–Godfrey (p = 0.32), White (p = 0.41), ARCH (p = 0.27), and SER (p = 0.36). The constructed correlation–regression equation also allowed forecasting based on trend line modeling—how IPI levels will change depending on business confidence. According to the forecast, the IPI in Ukraine at the beginning of 2030 is expected to increase by 63.48 percentage points compared to the beginning of 2024, reaching 153.6%. Full article

Sandflies spread the neglected vector-borne disease anthroponotic cutaneous leishmaniasis (ACL), which only affects humans. Despite decades of control, asymptomatic carriers, vector pesticide resistance, and low public awareness prevent eradication. This study proposes a fractional-order optimal control model that integrates biological and behavioral aspects of ACL transmission to better understand its complex dynamics and intervention responses. We model asymptomatic human illnesses, insecticide-resistant sandflies, and a dynamic awareness function under public health campaigns and collective behavioral memory. Four time-dependent control variables—symptomatic treatment, pesticide spraying, bed net use, and awareness promotion—are introduced under a shared budget constraint to reflect public health resource constraints. In addition, Caputo fractional derivatives incorporate memory-dependent processes and hereditary effects, allowing for epidemic and behavioral states to depend on prior infections and interventions; on the other hand, standard integer-order frameworks miss temporal smoothness, delayed responses, and persistence effects from this memory feature, which affect optimal control trajectories. Next, we determine the optimality conditions for fractional-order systems using a generalized Pontryagin’s maximum principle, then solve the state–adjoint equations numerically with an efficient forward–backward sweep approach. Simulations show that fractional (memory-based) dynamics capture behavioral inertia and cumulative public response, improving awareness and treatment efforts. Furthermore, sensitivity tests indicate that integer-order models do not predict the optimal allocation of limited resources, highlighting memory effects in epidemiological decision-making. Consequently, the proposed method provides a realistic and flexible mathematical basis for cost-effective and sustainable ACL control plans in endemic settings, revealing how memory-dependent dynamics may affect disease development and intervention efficiency. Full article

Polycystic Ovary Syndrome (PCOS) is a widespread hormonal disorder affecting women of reproductive age, often leading to infertility and associated complications. This study presents a comprehensive stochastic mathematical framework to analyze the dynamics of PCOS with a particular focus on infertility and treatment outcomes. Here, the transitions between compartments represent progression of women through clinical states of PCOS (risk, diagnosis, treatment, recovery) rather than infection or transmission, since PCOS is a non-communicable disorder. The model incorporates probabilistic elements to break the symmetric and predictable assumptions inherent in deterministic approaches. This allows it to reflect the randomness and asymmetry in hormonal regulation and ovulation cycles, enabling a more realistic representation of disease progression. By utilizing stochastic differential equations, the study evaluates the impact of treatment adherence on fertility restoration. We establish the conditions for disease extinction versus the existence of an ergodic stationary distribution, which represents a form of long-term statistical symmetry. The results emphasize the importance of early diagnosis and consistent treatment. Furthermore, the proposed approach provides a valuable tool for clinicians to predict patient-specific trajectories and optimize individualized treatment plans, accounting for the asymmetric nature of patient responses. Full article

A simplified kinetic model for the quantitative analysis of a potentiometric, pH-based urea biosensor is presented. The device was an electrolyte–insulator–semiconductor capacitor (EISCAP) with a pH-sensitive Ta₂O₅ gate functionalized by a polyallylamine hydrochloride (PAH)/urease bilayer. Within the steady-state approximation, the kinetic equations yielded an implicit algebraic relation linking the bulk urea concentration to the local pH at the sensor surface. Numerical solution of this equation, combined with a fitting routine, provides the apparent Michaelis–Menten constant ($K_M$) and the normalized maximum reaction rate (${\overline{k}}_V$). Validation against the literature data confirmed the reliability of the approach. Experimental results were then analyzed in both phosphate buffer (PBS) and artificial urine (AU), covering urea concentrations of 0.1–50 mM. The fitted parameters showed comparable $K_M$ values of 10.9 mM (PBS) and 32.4 mM (AU), but strongly different ${\overline{k}}_V$ values: $2.2\times {10}^{-4}$ (PBS) versus $8.6\times {10}^{-7}$ (AU). The three-order reduction in AU was attributed to the inhibitory effects inherent to complex biological fluids. These findings highlight the importance of the model-based quantitative analysis of EISCAP biosensors, enabling the accurate characterization of immobilized enzyme layers and guiding optimization for applications in realistic sample matrices. Full article

In the present work, a new analytical model of polytropic flow in constant-diameter pipelines is developed to accurately describe the flow of compressible gases, including natural gas and hydrogen, explicitly accounting for heat exchange between the fluid and the environment. In contrast to conventional models that assume isothermal or adiabatic conditions, the proposed model simultaneously accounts for variations in pressure, temperature, density, and entropy, i.e., it is based on a realistic polytropic gas flow formulation. A system of differential equations is established, incorporating the momentum, continuity, energy, and state equations of the gas. An implicit closed-form solution for the specific volume along the pipeline axis is then derived. The model is universal and allows the derivation of special cases such as adiabatic, isothermal, and isentropic flows. Numerical simulations demonstrate the influence of heat flow on the variation in specific volume, highlighting the critical role of heat exchange under real conditions for the optimization and design of energy systems. It is shown that achieving isentropic flow would require the continuous removal of frictional heat, which is not practically feasible. The proposed model therefore provides a clear, reproducible, and easily visualized framework for analyzing gas flows in pipelines, offering valuable support for engineering design and education. In addition, a unified sensitivity analysis of the analytical solutions has been developed, enabling systematic evaluation of parameter influence across the subsonic, near-critical, and heated flow regimes. Full article