Search Results (157)

Multi-agent systems (MAS) typically model interaction topologies using directed or undirected graphs when analyzing consensus convergence rates. However, as system complexity increases, purely directed or undirected networks may be insufficient to capture interaction heterogeneity. This paper adopts hybrid networks as interaction topology to investigate strategies for improving consensus convergence rates. We propose the Hermitian Kirchhoff index, a novel metric based on resistance distance, to quantify the consensus convergence rates and establish its theoretical justification. We then examine how adding or removing edges/arcs affects the Hermitian Kirchhoff index, employing first-order eigenvalue perturbation analysis to relate these changes to algebraic connectivity and its associated eigenvectors. Numerical simulations corroborate the theoretical findings and demonstrate the effectiveness of the proposed approach. Full article

Effective management of Micropterus salmoides resources requires accurate assessment of their abundance and distribution. Fisheries acoustics is a key method for such evaluations, yet its application is limited by insufficient target strength (TS) data. This study combines the Sobel edge detection technique with the Kirchhoff ray-mode model to estimate the TS of Micropterus salmoides cultured in Guangdong, China, and validates the results through in situ measurements. The relationships between TS and fish body length were established at 38 kHz, 70 kHz, 120 kHz, and 200 kHz. At 200 kHz, the average in situ TS was –42.41 dB, with a fitted formula of TS = 32.00 lgL − 88.24. Further validation was performed using time- and frequency-domain analyses of echo signals. The results show that TS increases with swim bladder volume, indicating its dominant influence. The relationship between TS and frequency is nonlinear and affected by the swim bladder angle, swimming posture, and behavioral patterns. This study also improves the computational efficiency of the Kirchhoff ray-mode model. Overall, it provides essential parameters for acoustic stock assessment of Micropterus salmoides, providing a scientific basis for their sustainable management and conservation. Full article

High-Voltage Alternating Current (HVAC) transmission systems form the backbone of modern power grids, enabling efficient long-distance and high-capacity power delivery. In Saudi Arabia, ongoing initiatives to modernize and strengthen grid infrastructure demand advanced solutions to ensure system reliability, operational stability, and the minimization of economic losses caused by faults. Traditional fault detection and classification methods often depend on the manual interpretation of voltage and current signals, which is both labor-intensive and prone to human error. Although data-driven approaches such as Artificial Neural Networks (ANNs) and Deep Learning have been applied to automate fault analysis, their performance is often constrained by the quality and size of available training datasets, leading to poor generalization and physically inconsistent outcomes. This study proposes a novel hybrid fault detection and classification framework for the 380 kV Marjan–Safaniyah HVAC transmission line by integrating Deep Learning with Physics-Informed Neural Networks (PINNs). The PINN model embeds fundamental electrical laws, such as Kirchhoff’s Current Law (KCL), directly into the learning process, thereby constraining predictions to physically plausible behaviors and enhancing robustness and accuracy. Developed in MATLAB/Simulink using the Deep Learning Toolbox, the proposed framework performs fault detection and fault type classification within a unified architecture. A comparative analysis demonstrates that the hybrid PINN approach significantly outperforms conventional Deep Learning models, particularly by reducing false negatives and improving class discrimination. Furthermore, this study highlights the crucial role of balanced and representative datasets in achieving a reliable performance. Validation through confusion matrices and KCL residual histograms confirms the enhanced physical consistency and predictive reliability of the model. Overall, the proposed framework provides a powerful and scalable solution for real-time monitoring, fault diagnosis, and intelligent decision-making in high-voltage power transmission systems. Full article

The main objective of this study was to investigate boiling heat transfer during refrigerant flow in a mini-channel heat sink. The test section consisted of multiple parallel mini-channels, each with a depth of 1 mm. The working fluid was heated by a thin layer of Haynes-230 alloy with a thickness of 0.1 mm. The outer surface temperature of the heater was measured using infrared thermography, while other thermal and flow-based parameters were recorded via a dedicated data acquisition system. The mini-channel heat sink was tested in seven different spatial orientations, with inclination angles relative to the horizontal plane of 45°, 60°, 75°, 90°, 105°, 120°, and 135°. The analysis focused on the early stage of the experiment, corresponding to the forced convection, boiling incipience, and subcooled boiling region. A time-dependent, two-dimensional model of heat transfer during flow boiling of a refrigerant in asymmetrically heated mini-channels was developed. The temperatures of both the heating foil and the working fluid (Fluorinert FC-770) were described using appropriate forms of the Fourier–Kirchhoff equation, subject to relevant boundary conditions. Two sets of time-dependent Trefftz functions were employed to solve the governing equations: one set corresponding to the two-dimensional Fourier equation and another, newly derived, for the energy equation in the fluid. The results include thermographic images of the heated surface, temperature distributions, fluid temperatures, local heat-transfer coefficients, and boiling curves. A comparison of the heat-transfer coefficients obtained using the Trefftz-based approach and those calculated using Fourier’s law demonstrated satisfactory agreement. Full article

Efficient modeling of acoustic scattering from water-filled thin shells remains challenging due to prohibitive computational costs of rigorous methods and oversimplifications in ray-based approximations. This paper develops an iterative physical acoustics (IPA) method, presenting simple and explicit formulations for scattering by penetrable objects immersed in fluids. The method combines Kirchhoff integral frameworks with thin-plate effective boundary conditions, discretizes mid-surfaces into triangular facets, and iteratively converges pressure fields to characterize the mechanisms of multiple reflections and transmissions. Validated against analytical solutions, numerical simulations, and scaled experiments, IPA provides comprehensive field predictions encompassing internal cavity fields, external near-fields, and far-field scattering patterns within a unified framework. It achieves significant computational efficiency gains while maintaining engineering practicality, successfully reproducing distant-range highlights from these mechanisms in time-domain spectra. Limitations are observed at low frequencies and high-curvature regions where elastic-wave effects become significant. The IPA framework enables engineering-efficient scattering analysis for complex thin-shell structures. Full article

In this paper, the virtual model development and control for a BallBot Robotic System (BRS) are addressed. A virtual three-dimensional (3-D) EV3 BRS (EV3BRS) model is here developed through the Simscape^™ Multibody^™ environment from a BRS designed using the kit LEGO^® MINDSTORMS^® EV3. The mathematical model from the BRS is obtained through the Euler–Lagrange approach and used as the foundation to develop the EV3BRS Simscape^™ model. The electrical model for the motors is derived through Kirchhoff’s laws. To verify the dynamics of the EV3BRS Simscape^™ model, a Takagi–Sugeno Fuzzy Controller (TSFC) is designed using the Parallel Distributed Compensation (PDC) technique. Control gains are computed via Linear Matrix Inequalities (LMIs). To test the EV3BRS Simscape^™ model under disturbances, an input voltage anomaly is considered. So, adding an $H_{\infty }$ attenuation to the TSFC ensures that the EV3BRS Simscape^™ model faces these kind of anomalies. Simulation results confirm that the TSFC with $H_{\infty }$ attenuation improves the performance under anomalies at the input in contrast with the nominal TSFC, although this latter can maintain the body of the system near the upright position also. The dynamics from the EV3BRS Simscape^™ model here developed allow us to realize how the real system will behave. Full article

A common technique used in factories to shape metal panels is shot peen forming, where the panel is sprayed with a high-velocity stream of small steel pellets called “shot.” The impacts between the hard steel shot and the softer metal of the panel cause localized plastic deformation, which is used to improve the fatigue properties of the material’s surface. The residual stress distribution imparted by impacts also results in bending, which suggests that a torque is associated with it. In this paper, we model shot peen forming as the application of spatially varying torques to a Kirchhoff plate, opting to use the language of thermoelasticity in order to introduce these torque distributions. First, we derive the governing equations for the thermoelastic thin plate model and show that only a torque-type resultant of the temperature distribution shows up in the bending equation. Next, to calibrate from the shot peen operation, an empirical “effective torque” parameter used in the thermoelastic model, a simple and non-invasive test is devised. This test relies only on measuring the maximum displacement of a uniformly shot peened plate as opposed to characterizing the residual stress distribution. After discussing how to handle the unconventional fully free boundary conditions germane to shot peened plates, we introduce an approach to solving the inverse problem whereby the peening distribution required to obtain a specified plate contour can be obtained. Given that the relation between shot peen distributions and bending displacements at a finite set of points is non-unique, we explore a regularization of the inverse problem which gives rise to shot peen distributions that match the capabilities of equipment in the factory. In order to validate our proposed model, an experiment with quantified uncertainty is designed and carried out which investigates the agreement between the predictions of the calibrated model and real shot peen-forming operations. Full article

Elasticity is a well-established field within mathematical physics, yet new formulations can provide deeper insight and computational advantages. This study explores the geometry of two- and three-dimensional elastic curves using the formalism of geometric algebra, offering a unified and coordinate-free approach. This work systematically derives the Frenet, Darboux, and Bishop frames within the three-dimensional geometric algebra and employs them to integrate the elastica equation. A concise Lagrangian formulation of the problem is introduced, enabling the identification of Noetherian, conserved, multi-vector moments associated with the elastic system. A particularly compact form of the elastica equation emerges when expressed in the Bishop frame, revealing structural simplifications and making the equations more amenable to analysis. Ultimately, the geometric algebra perspective uncovers a natural correspondence between the theory of free elastic curves and classical beam models, showing how constrained theories, such as Euler–Bernoulli and Kirchhoff beam formulations, arise as special cases. These results not only clarify foundational aspects of elasticity theory but also provide a framework for future applications in continuum mechanics and geometric modeling. Full article

The intelligent upgrade of heating systems faces the challenge of accurately identifying high-dimensional pipe-network resistance coefficients; difficulties in accomplishing this can lead to hydraulic imbalance and redundant energy consumption. To address the limitations of traditional Differential Evolution (DE) algorithms under high-dimensional operating conditions, this paper proposes an Improved Differential Evolution Algorithm (SDEIA) incorporating chaotic mapping, adaptive mutation and crossover strategies, and an immune mechanism. Furthermore, a multi-constrained identification model is constructed based on Kirchhoff’s laws. Validation with actual engineering data demonstrates that the proposed method achieves a lower average relative error in resistance coefficients and exhibits a more concentrated error distribution. SDEIA provides a high-precision tool for multi-heat-source networking and dynamic regulation in heating systems, facilitating low-carbon and intelligent upgrades. Full article

In this article, we study a double-phase variable-exponent Kirchhoff problem and show the existence of at least three solutions. The proposed model, as a generalization of the Kirchhoff equation, is interesting since it is driven by a double-phase operator that governs anisotropic and heterogeneous diffusion associated with the energy functional, as well as encapsulating two different types of elliptic behavior within the same framework. To tackle the problem, we obtain regularity results for the corresponding energy functional, which makes the problem suitable for the application of a well-known critical point result by Bonanno and Marano. We introduce an n-dimensional vector inequality, not covered in the literature, which provides a key auxiliary tool for establishing essential regularity properties of the energy functional such as $C^1$-smoothness, the $\left(S_{+}\right)$-condition, and sequential weak lower semicontinuity. Full article

The electrodynamics of current provide much of our technology, from telegraphs to the wired infrastructure powering the circuits of our electronic technology. Current flow is analyzed by its own rules that involve the Maxwell Ampere law and magnetism. Electrostatics does not involve magnetism, and so current flow and electrodynamics cannot be derived from electrostatics. Practical considerations also prevent current flow from being analyzed one charge at a time. There are too many charges, and far too many interactions to allow computation. Current flow is essential in biology. Currents are carried by electrons in mitochondria in an electron transport chain. Currents are carried by ions in nerve and muscle cells. Currents everywhere follow the rules of current flow: Kirchhoff’s current law and its generalizations. The importance of electron and proton flows in generating ATP was discovered long ago but they were not analyzed as electrical currents. The flow of protons and transport of electrons form circuits that must be analyzed by Kirchhoff’s law. A chemiosmotic theory that ignores the laws of current flow is incorrect physics. Circuit analysis is easily applied to short systems like mitochondria that have just one internal electrical potential in the form of the Hodgkin Huxley Katz (HHK) equation. The HHK equation combined with classical descriptions of chemical reactions forms a computable model of cytochrome c oxidase, part of the electron transport chain. The proton motive force is included as just one of the components of the total electrochemical potential. Circuit analysis includes its role just as it includes the role of any other ionic current. Current laws are now needed to analyze the flow of electrons and protons, as they generate ATP in mitochondria and chloroplasts. Chemiosmotic theory must be replaced by an electro-osmotic theory of ATP production that conforms to the Maxwell Ampere equation of electrodynamics while including proton movement and the proton motive force. Full article

Seismic imaging in areas with complex geological structures, such as steeply dipping strata and lateral velocity variations, remains a significant challenge in geophysical exploration. In this paper, a Kirchhoff pre-stack depth and pre-stack time migration imaging method under the constraint of an initial model is proposed. By establishing the initial velocity model, the method is iteratively optimized under the horizon constraint, and the travel time difference is used to update the model. Finally, Kirchhoff pre-stack imaging is realized. Numerical simulations using a synthetic five-layer velocity model demonstrate that removing direct wave interference and incorporating horizon constraints significantly improve the signal-to-noise ratio and structural accuracy of the migration results. A field case study in a coalfield with monoclinic structures and high-angle faults further validates the method’s effectiveness. Comparative analysis with pre-stack time migration reveals that Kirchhoff pre-stack depth migration achieves superior fault delineation, diffraction wave homing, and event continuity, particularly in steeply dipping formations. The results highlight the method’s potential for improving seismic interpretation accuracy in complex structural settings, offering practical value for coal mine safety and resource exploration. Full article

The closed mesoporous polymer gels have garnered significant attention as advanced thermal insulation materials due to their superior lightweight characteristics and excellent thermal management capabilities. To accurately predict their thermal performance, this study develops a novel mathematical model that integrates fractal geometry theory, Kirchhoff’s thermal conduction principles, comprehensive Rosseland diffusion approximation, and Mie scattering theory. The conductive thermal conductivity component was formulated based on a diagonal cross fractal structure, while the radiative component was derived considering microscale radiative effects. Model predictions exhibit strong agreement with experimental results from various mesoporous polymer gels, achieving a prediction error of less than 11.2%. Furthermore, a detailed parametric analysis was conducted, elucidating the influences of porosity, cell size, temperature, refractive index, and extinction coefficient. The findings identify a critical cell size range (1–100 µm) and porosity range (0.74–0.97) where minimum thermal conductivity occurs. This proposed modeling approach offers a robust and efficient theoretical tool for designing and optimizing the thermal insulation characteristics of closed mesoporous polymer gels, thereby advancing their application in diverse energy conversion and management systems. Full article

A model of the vocal tract that mimicked velopharyngeal insufficiency was created, and acoustic analysis was performed using the boundary element method to clarify the acoustic characteristics of velopharyngeal insufficiency. The participants were six healthy adults. Computed tomography (CT) images were taken from the frontal sinus to the glottis during phonation of the Japanese vowels /i/ and /u/, and models of the vocal tracts were created from the CT data. To recreate velopharyngeal insufficiency, coupling of the nasopharynx was carried out in vocal tract models with no nasopharyngeal coupling, and the coupling site was enlarged in models with nasopharyngeal coupling. The vocal tract models were extended virtually for 12 cm in a cylindrical shape to represent the region from the lower part of the glottis to the tracheal bifurcation. The Kirchhoff–Helmholtz integral equation was used for the wave equation, and the boundary element method was used for discretization. Frequency response curves from 1 to 3000 Hz were calculated by applying the boundary element method. The curves showed the appearance of a pole–zero pair around 500 Hz, increased intensity around 250 Hz, decreased intensity around 500 Hz, decreased intensities of the first and second formants (F1 and F2), and a lower frequency of F2. Of these findings, increased intensity around 250 Hz, decreased intensity around 500 Hz, decreased intensities of F1 and F2, and lower frequency of F2 agree with the previously reported acoustic characteristics of hypernasality. Full article

Hydrogen has attracted widespread attention due to its zero emissions and high energy density, and hydrogen-fueled power systems are gradually emerging. This paper combines the advantages of the high conversion efficiency of fuel cells and strong engine power to propose a hydrogen hybrid energy system architecture based on a mixture of fuel cells and engines in order to improve the conversion efficiency of the energy system and reduce its fuel consumption rate. Firstly, according to the topology of the hydrogen hybrid energy system and the circuit model of its core components, a state-space model of the hydrogen hybrid energy system is established using the Kirchhoff node current principle, laying the foundation for the control and management of hydrogen hybrid energy systems. Then, based on the state-space model of the hydrogen hybrid system and Pontryagin’s minimum principle, a hydrogen hybrid system management strategy based on adaptive equivalent fuel consumption minimum strategy (A-ECMS) is proposed. Finally, a hydrogen hybrid power system model is established using the AVL Cruise simulation platform and a control strategy is developed using matlab 2021b/Simulink to analyze the output power and fuel economy of the hybrid energy system. The results show that, compared with the equivalent fuel consumption minimum strategy (ECMS), the overall fuel economy of A-ECMS could improve by 10%. Meanwhile, the fuel consumption of the hydrogen hybrid energy system is less than half of that of traditional engines. Full article