Search Results (595)

This paper focuses on the numerical modeling of drug diffusion in biological tissues using fractional time-dependent parabolic equations with non-local boundary conditions. The model includes a Caputo fractional derivative to capture the non-local effects and memory inherent in biological processes, such as drug absorption and transport. The theoretical framework of the problem is based on the work of Alhazzani, et al.,which demonstrates the solution’s goodness, existence, and uniqueness. Building on this foundation, we present a robust numerical method designed to deal with the complexity of fractional derivatives and non-local interactions at the boundaries of biological tissues. Numerical simulations reveal how fractal order and non-local boundary conditions affect the drug concentration distribution over time, providing valuable insights into drug delivery dynamics in biological systems. The results underscore the potential of fractal models to accurately represent diffusion processes in heterogeneous and complex biological environments. Full article

Difficult, extreme operating conditions of parabolic antennas under precipitation and sub-zero temperatures require the creation of effective heating systems. The purpose of the research is to develop a multilayer coating containing two metal-ceramic layers, epoxy composite layers, carbon fabric, and an outer layer of basalt fabric, which allows for effective heating of the antenna, and to study the properties of this coating. The multilayer coating was formed on an aluminum base that was subjected to abrasive jet processing. The first and second metal-ceramic layers, Al₂O₃ + 5% Al, which were applied by high-speed multi-chamber cumulative detonation spraying (CDS), respectively, provide maximum adhesion strength to the aluminum base and high adhesion strength to the third layer of the epoxy composite containing Al₂O₃. On this not-yet-polymerized layer of epoxy composite containing Al₂O₃, a layer of carbon fabric (impregnated with epoxy resin) was formed, which serves as a resistive heating element. On top of this carbon fabric, a layer of epoxy composite containing Cr₂O₃ and SiO₂ was applied. Next, basalt fabric was applied to this still-not-yet-polymerized layer. Then, the resulting layered coating was compacted and dried. To study this multilayer coating, X-ray analysis, light and raster scanning microscopy, and transmission electron microscopy were used. The thickness of the coating layers and microhardness were measured on transverse microsections. The adhesion strength of the metal-ceramic coating layers to the aluminum base was determined by both bending testing and peeling using the adhesive method. It was established that CDS provides the formation of metal-ceramic layers with a maximum fraction of lamellae and a microhardness of 7900–10,520 MPa. In these metal-ceramic layers, a dispersed subgrain structure, a uniform distribution of nanoparticles, and a gradient-free level of dislocation density are observed. Such a structure prevents the formation of local concentrators of internal stresses, thereby increasing the level of dispersion and substructural strengthening of the metal-ceramic layers’ material. The formation of materials with a nanostructure increases their strength and crack resistance. The effectiveness of using aluminum, chromium, and silicon oxides as nanofillers in epoxy composite layers was demonstrated. The presence of structures near the surface of these nanofillers, which differ from the properties of the epoxy matrix in the coating, was established. Such zones, specifically the outer surface layers (OSL), significantly affect the properties of the epoxy composite. The results of industrial tests showed the high performance of the multilayer coating during antenna heating. Full article

Access to clean cooking remains a major challenge in rural and off-grid areas where traditional fuels are costly, harmful, or scarce. Solar cooking offers a sustainable solution, but many existing systems suffer from fixed positioning and low efficiency. This study presents a low-cost, dual-axis solar tracking parabolic dish cooker designed for such regions, featuring adjustable pot holder height and portability for ease of use. The system uses an Arduino UNO, LDR sensors, and a DC gear motor to automate sun tracking, ensuring optimal alignment throughout the day. A 0.61 m parabolic dish with ≥97% reflective silver-coated mirrors concentrates sunlight to temperatures exceeding 300 °C. Performance tests in April, June, and November showed boiling times as low as 3.37 min in high-irradiance conditions (7.66 kWh/m²/day) and 6.63 min under lower-irradiance conditions (3.86 kWh/m²/day). Compared to fixed or single-axis systems, this design achieved higher thermal efficiency and reliability, even under partially cloudy skies. Built with locally available materials, the system offers an affordable, clean, and effective cooking solution that supports energy access, health, and sustainability in underserved communities. Full article

A novel total internal reflection solar end-pumped laser system has been introduced for the first time, aimed at enhancing the solar-to-laser conversion efficiency. Utilizing a conical solid or cavity reflector, this system refocuses sunlight from a 0.2818 $m^2$ parabolic mirror into a single Ce (0.05 at.%): Nd (1 at.%): YAG crystal rod, measuring 4 mm in diameter and 10 mm in length, thereby promoting total internal reflection and extending the pumping path. Simulation results indicate that under the same solar input power conditions (249.05 W), the conversion efficiencies of the conical solid reflector and cavity reflector systems are 1.2 times and 1.33 times higher than the current highest recorded efficiency of single-rod systems, respectively. At 950 ${W/m}^2$, the conical reflector reaches 5.48% efficiency, while the cavity reflector attains 6.09%. Their collection efficiencies are 52.03 ${W/m}^2$ and 57.90 ${W/m}^2$, with slope efficiencies of 6.65% and 7.72%. Full article

This study addresses the standardization of Singular Distributed Parameter Systems (SDPSs). It focuses on classifying and simplifying first- and second-order linear SDPSs using characteristic matrix theory. First, the study classifies first-order linear SDPSs into three canonical forms based on characteristic curve theory, with an example illustrating the standardization process for parabolic SDPSs. Second, under regular conditions, first-order SDPSs can be decomposed into fast and slow subsystems, where the fast subsystem reduces to an Ordinary Differential Equation (ODE) system, while the slow subsystem retains the spatiotemporal characteristics of the original system. Third, the standardization and classification of second-order SDPSs is proposed using three reversible transformations that achieve structural equivalence. Finally, an illustrative example of a building temperature control is built with SDPSs. The simulation results show the importance of system standardization in real-world applications. This research provides a theoretical foundation for SDPS standardization and offers insights into the practical implementation of distributed temperature systems. Full article

In this article, we propose a novel nonlinear cross-diffusion framework to model the distribution of susceptible and infected individuals within their habitat using a reduced SIR model that incorporates saturated incidence and treatment rates. The study investigates solution boundedness through the theory of parabolic partial differential equations, thereby validating the proposed spatio-temporal model. Through the implementation of the suggested cross-diffusion mechanism, the model reveals at least one non-constant positive equilibrium state within the susceptible–infected (SI) system. This work demonstrates the potential coexistence of susceptible and infected populations through cross-diffusion and unveils Turing instability within the system. By analyzing codimension-2 Turing–Hopf bifurcation, the study identifies the Turing space within the spatial context. In addition, we explore the results for Turing–Bogdanov–Takens bifurcation. To account for seasonal disease variations, novel perturbations are introduced. Comprehensive numerical simulations illustrate diverse emerging patterns in the Turing space, including holes, strips, and their mixtures. Additionally, the study identifies non-Turing and Turing–Bogdanov–Takens patterns for specific parameter selections. Spatial series and surfaces are graphed to enhance the clarity of the pattern results. This research provides theoretical insights into the implications of cross-diffusion in epidemic modeling, particularly in contexts characterized by localized mobility, clinically evident infections, and community-driven isolation behaviors. Full article

The growing imperative to mitigate climate change and accelerate the shift toward energy sustainability has called for a critical evaluation of heat and electricity generation methods. This article presents a comparative life cycle assessment (LCA) of solar and biogas energy systems on a common basis of 1 kWh of useful energy using SimaPro, the ReCiPe 2016 methodology (both midpoint and endpoint indicators), and cumulative energy demand (CED) analysis. This study is the first to evaluate co-located solar PV, solar thermal compound parabolic concentrator (CPC) and biogas combined heat and power (CHP) systems with in situ data collected under identical climatic and operational conditions. The project costs yield levelized costs of electricity (LCOE) of INR 2.4/kWh for PV, 3.3/kWh for the solar thermal dish and 4.1/kWh for biogas. However, the collaborated findings indicate that neither solar-based systems nor biogas technology uniformly outperform the others; rather, their effectiveness hinges on contextual factors, including resource availability and local policy incentives. These insights will prove critical for policymakers, industry stakeholders, and local communities seeking to develop effective, context-sensitive strategies for sustainable energy deployment, emissions reduction, and robust resource management. Full article

Efficient water heating is essential for wool-washing processes, which demand temperatures above 70 °C. To meet this requirement sustainably, a parabolic trough solar concentrator system is proposed in this paper as an alternative to conventional natural gas systems. The design centers on a water pool constructed from bricks reinforced with an internal steel layer, enhancing heat exchange efficiency. Also, various synthetic oils were analyzed as heat transfer fluids (HTFs) within an immersed heat exchanger, such as Thermia B oil, Heat Transfer Oil 32, biphasic oil, and Therminol vp1 oil. Numerical simulations were performed using ANSYS CFX v19.2 software with the k-ε turbulence model to evaluate the thermal performance and temperature distribution. The results demonstrate the superior efficiency of the solar-powered system, with the steel-reinforced pool achieving optimal water temperatures between 78 °C and 85 °C, exceeding the required threshold for industrial wool washing. Among the various synthetic oils analyzed, Thermia B emerged as the most effective heat transfer fluid, maintaining water temperatures in the range of 75 °C to 85 °C. This superior thermal performance is attributed to its high thermal conductivity and reduced heat loss, ensuring consistent and optimal heat distribution for the wool-washing process. Full article

The hydraulic turbine serves as the cornerstone of hydropower generation systems, with the sealing system’s performance critically influencing energy conversion efficiency and operational cost-effectiveness. The sealing ring is a pivotal component, which mitigates leakage and energy loss by regulating flow within the narrow gap between itself and the frame. This study investigates the intricate flow dynamics within the gap between the sealing ring and the upper frame of a super-large-scale Francis turbine, with a specific focus on the rotating wall’s impact on the flow field. Employing theoretical modeling and three-dimensional transient computational fluid dynamics (CFD) simulations grounded in real turbine design parameters, the research reveals that the rotating wall significantly alters shear flow and vortex formation within the gap. Tangential velocity exhibits a nonlinear profile, accompanied by heightened turbulence intensity near the wall. The short flow channel height markedly shapes flow evolution, driving the axial velocity profile away from a conventional parabolic pattern. Further analysis of rotation-induced vortices and flow instabilities, supported by turbulence kinetic energy monitoring and spectral analysis, reveals the periodic nature of vortex shedding and pressure fluctuations. These findings elucidate the internal flow mechanisms of the sealing ring, offering a theoretical framework for analyzing flow in microscale gaps. Moreover, the resulting flow field data establishes a robust foundation for future studies on upper crown gap flow stability and sealing ring dynamics. Full article

This work presents the design of a control algorithm based on an augmented incremental state-space model, emphasizing its compatibility with Takagi–Sugeno (T–S) fuzzy models for nonlinear systems. The methodology integrates key components such as incremental modeling, fuzzy system identification, discrete Linear Quadratic Regulator (LQR) design, and state observer implementation. To optimize controller performance, the Extremum Seeking Control (ESC) technique is employed for the automatic tuning of LQR gains, minimizing a predefined cost function. The control strategy is formulated within a generalized framework that evolves from conventional discrete fuzzy models to a higher-order incremental-N state-space representation. The simulation results on a nonlinear multivariable thermal mixing tank system validate the effectiveness of the proposed approach under reference tracking and various disturbance scenarios, including ramp, parabolic, and higher-order polynomial signals. The main contribution of this work is that the proposed scheme achieves zero steady-state error for reference inputs and disturbances up to order N−1 by employing the incremental-N formulation. Furthermore, the system exhibits robustness against input and load disturbances, as well as measurement noise. Remarkably, the ESC algorithm maintains its effectiveness even when noise is present in the system output. Additionally, the proposed incremental-N model is applicable to fast dynamic systems, provided that the system dynamics are accurately identified and the model is discretized using a suitable sampling rate. This makes the approach particularly relevant for control applications in electrical systems, where handling high-order reference signals and disturbances is critical. The incremental formulation, thus, offers a practical and effective framework for achieving high-performance control in both slow and fast nonlinear multivariable processes. Full article

We utilize the moving planes technique to prove the radial symmetry along with the monotonic characteristics of solutions for a system of parabolic Laplacian equations. In this system, the solutions of the two equations are interdependent, with the solution of one equation depending on the function of the other. By use of the maximal regularity theory that has been established for fractional parabolic equations, we ensure the solvability of these systems. Our initial step is to formulate a narrow region principle within a parabolic cylinder. This principle serves as a theoretical basis for implementing the moving planes method. Following this, we focus our attention on parabolic systems with fractional Laplacian equations and deduce that the solutions are radial symmetric and monotonic when restricted to the unit ball. Full article

In this paper, the effects of localized surface plasmons on the nonlinear optical properties of a composite system are studied. The system operates by placing a metal nanoparticle next to a semi-parabolic quantum well under a terahertz laser field. Firstly, the energy expression of the semi-parabolic well in the terahertz laser field is derived via a Kramers–Henneberger transformation, and then the new energy levels and wave functions are solved by the finite difference method. Next, optical absorption coefficients and refraction index changes are derived according to quantum theory. Finally, the study shows that localized surface plasmons can cause a redshift in the peak position, while simultaneously weakening the peak value of optical absorption coefficients. The results confirm that the desired performance can be obtained by adjusting the radius of the particle, the distance between the particle and the quantum well, or the natural frequency of the quantum well. Full article

This paper studies an averaged Linear Quadratic Regulator (LQR) problem for a parabolic partial differential equation (PDE), where the system dynamics are affected by uncertain parameters. Instead of assuming a deterministic operator, we model the uncertainty using a probability distribution over a set of possible system dynamics. This approach extends classical optimal control theory by incorporating an averaging framework to account for parameter uncertainty. We establish the existence and uniqueness of the optimal control solution and analyze its convergence as the probability distribution governing the system parameters changes. These results provide a rigorous foundation for solving optimal control problems in the presence of parameter uncertainty. Our findings lay the groundwork for further studies on optimal control in dynamic systems with uncertainty. Full article

Parabolic trough collector (PTC) systems, often deployed in arid regions, are vulnerable to dust accumulation (soiling), which reduces mirror reflectivity and energy output. This study presents a physically based soiling forecast algorithm (SFA) designed to estimate soiling levels. The model was calibrated and validated using three meteorological data sources—numerical forecasts (YR), METAR observations, and on-site measurements—from a PTC facility in Limassol, Cyprus. Field campaigns covered dry, rainy, and red-rain conditions. The model demonstrated robust performance, particularly under dry summer conditions, with normalized root mean square errors (NRMSE) below 1%. Sedimentation emerged as the dominant soiling mechanism, while the contributions of impaction and Brownian motion varied according to site-specific environmental conditions. Under dry deposition conditions, the reflectivity change rate during spring and autumn was approximately twice that of summer, indicating a need for more frequent cleaning during transitional seasons. A red-rain event resulted in a pronounced drop in reflectivity, showcasing the model’s ability to capture abrupt soiling dynamics associated with extreme weather episodes. The proposed SFA offers a practical, adaptable tool for reducing soiling-related losses and supporting seasonally adjusted maintenance strategies for solar thermal systems. Full article

This paper presents the design and validation of a novel specialized fixture device for machining inclined planes with barrel cutters on 3-axis CNC machine tools. Barrel milling, also known as Parabolic Performance Cutting (PPC), is extensively used on 5-axis machines to enhance the efficiency of machining complex surfaces. While significant research has focused on optimizing barrel milling for aspects such as surface roughness and cutting forces, implementing this technique on 3-axis machines poses a challenge due to limitations in tool orientation. To overcome this, an innovative adaptable device was designed, enabling precise workpiece orientation relative to the barrel cutter. To overcome this limitation, an adaptable device was designed that enables precise workpiece orientation relative to the barrel cutter. The device utilizes interchangeable locating elements for different cutter programming angles (such as 18°, 20°, and 42.5°), thereby ensuring correct workpiece positioning. Rigid workpiece clamping is provided by the device’s mechanism to maintain precise workpiece positioning during machining, and probing surfaces are integrated into the device to facilitate the definition of the coordinate system necessary for CNC machine programming. Device control was performed using a Hexagon RA-7312 3D measuring arm. Inspection results indicated minimal dimensional deviations (e.g., surface flatness between 0.002 mm and 0.012 mm) and high angular accuracy (e.g., angular non-closure of 0.006°). The designed device enables the effective and precise use of barrel cutters on 3-axis CNC machines, offering a previously unavailable practical and economical solution for cutting tool tests and cutting regime studies. Full article