Search Results (1,554)

This work illustrates the application of the “First-Order Features Adjoint Sensitivity Analysis Methodology for Neural Integro-Differential Equations of Fredholm-Type” (1st-FASAM-NIDE-F) and the “Second-Order Features Adjoint Sensitivity Analysis Methodology for Neural Integro-Differential Equations of Fredholm-Type” (2nd-FASAM-NIDE-F) to a paradigm heat transfer model. This physically based heat transfer model has been deliberately constructed so that it can be represented either by a neural integro-differential equation of a Fredholm type (NIDE-F) or by a conventional second-order “neural ordinary differential equation (NODE)” while admitting exact closed-form solutions/expressions for all quantities of interest, including state functions and first-order and second-order sensitivities. This heat transfer model enables a detailed comparison of the 1st- and 2nd-FASAM-NIDE-F versus the recently developed 1st- and 2nd-FASAM-NODE methodologies, highlighting the considerations underlying the optimal choice for cases where the neural net of interest is amenable to using either of these methodologies for its sensitivity analysis. It is shown that the 1st-FASAM-NIDE-F methodology enables the most efficient computation of exactly determined first-order sensitivities of the decoder response with respect to the optimized NIDE-F parameters, requiring a single “large-scale” computation for solving the 1st-Level Adjoint Sensitivity System (1st-LASS), regardless of the number of weights/parameters underlying the NIDE-F decoder, hidden layers, and encoder. The 2nd-FASAM-NIDE-F methodology enables the computation, with unparalleled efficiency, of the second-order sensitivities of decoder responses with respect to the optimized/trained weights. Full article

Understanding the rheological properties of fresh cement slurries is essential to maintain optimal pumpability, achieve dependable zonal isolation, and preserve long-term well integrity in oil and gas cementing operations and the 3D printing cement and concrete industry. However, accurately and efficiently modeling the rheological behavior of cement slurries remains challenging due to the complex fluid properties of fresh cement slurries, which exhibit non-Newtonian and thixotropic behavior. Traditional numerical solvers typically require mesh generation and intensive computation, making them less practical for data-scarce, high-dimensional problems. In this study, a physics-informed neural network (PINN)-based framework is developed to solve the governing equations of steady-state cement slurry flow in a tilted channel. The slurry is modeled as a non-Newtonian fluid with viscosity dependent on both the shear rate and particle volume fraction. The PINN-based approach incorporates physical laws into the loss function, offering mesh-free solutions with strong generalization ability. The results show that PINNs accurately capture the trend of velocity and volume fraction profiles under varying material and flow parameters. Compared to conventional solvers, the PINN solution offers a more efficient and flexible alternative for modeling complex rheological behavior in data-limited scenarios. These findings demonstrate the potential of PINNs as a robust tool for cement slurry rheological modeling, particularly in scenarios where traditional solvers are impractical. Future work will focus on enhancing model precision through hybrid learning strategies that incorporate labeled data, potentially enabling real-time predictive modeling for field applications. Full article

A meshless, quasi-convex reproducing kernel particle framework for three-dimensional steady-state thermomechanical coupling problems is presented in this paper. A meshfree, second-order, quasi-convex reproducing kernel scheme is employed to approximate field variables for solving the linear Poisson equation and the elastic thermal stress equation in sequence. The quasi-convex reproducing kernel approximation proposed by Wang et al. to construct almost positive reproducing kernel shape functions with relaxed monomial reproducing conditions is applied to improve the positivity of the thermal matrixes in the final discreated equations. Two numerical examples are given to verify the effectiveness of the developed method. The numerical results show that the solutions obtained by the quasi-convex reproducing kernel particle method agree well with the analytical ones, with a slightly better-improved numerical accuracy than the element-free Galerkin method and the reproducing kernel particle method. The effects of different parameters, i.e., the scaling parameter, the penalty factor, and node distribution on computational accuracy and efficiency, are also investigated. Full article

The non-monotonic behavior of amperometric enzyme-based biosensors under uncompetitive and noncompetitive (mixed) substrate inhibition is investigated computationally using a two-compartment model consisting of an enzyme layer and an outer diffusion layer. The model is based on a system of reaction–diffusion equations that includes a nonlinear term associated with non-Michaelis–Menten kinetics of the enzymatic reaction and accounts for the partitioning between layers. In addition to the known effect of substrate inhibition, where the maximum biosensor current differs from the steady-state output, it has been determined that external diffusion limitations can also cause the appearance of a local minimum in the current. At substrate concentrations greater than both the Michaelis–Menten constant and the uncompetitive substrate inhibition constant, and in the presence of external diffusion limitation, the transient response of the biosensor, after immersion in the substrate solution, may follow a five-phase pattern depending on the model parameter values: it starts from zero, reaches a global or local maximum, decreases to a local minimum, increases again, and finally decreases to a steady intermediate value. The biosensor performance is analyzed numerically using the finite difference method. Full article

This paper establishes some links between Sturm–Liouville problems and the well-known controllability property in linear dynamic systems, together with a control law design that allows any prefixed arbitrary final state finite value to be reached via feedback from any given finite initial conditions. The scheduled second-order dynamic systems are equivalent to the stated second-order differential equations, and they are used for analysis purposes. In the first study, a control law is synthesized for a forced time-invariant nominal version of the current time-varying one so that their respective two-point boundary values are coincident. Afterward, the parameter that fixes the set of eigenvalues of the Sturm–Liouville system is replaced by a time-varying parameter that is a control function to be synthesized without performing, in this case, any comparison with a nominal time-invariant version of the system. Such a control law is designed in such a way that, for given arbitrary and finite initial conditions of the differential system, prescribed final conditions along a time interval of finite length are matched by the state trajectory solution. As a result, the solution of the dynamic system, and thus that of its differential equation counterpart, is subject to prefixed two-point boundary values at the initial and at the final time instants of the time interval of finite length under study. Also, some algebraic constraints between the eigenvalues of the Sturm–Liouville system and their evolution operators are formulated later on. Those constraints are based on the fact that the solutions corresponding to each of the eigenvalues match the same two-point boundary values. Full article

Due to their self-adaptability, low friction, low loss, and high-speed stability, bump foil aerodynamic journal bearings are widely used in high-speed rotating equipment such as turbomachinery and flywheel energy storage. In the process of high-speed operation, the heat generated leads to changes in air parameters (such as viscosity, density, etc.), thus affecting the overall performance of air bearings. In this paper, combined with the compressible Reynolds equation, a fluid–solid coupling model was established to analyze the steady-state characteristics and key influencing factors of bearings. Through the energy equation, the air viscosity–temperature effect was considered, and different boundary conditions were set. The internal temperature distribution of the air bearing and the influence of the temperature on the bearing characteristics were systematically analyzed. It was found that the bearing capacity increased when the temperature was considered. In a certain range, with the increase in ambient temperature, the increase in bearing capacity is reduced. This paper provides a theoretical design basis for the design of high-stability bearings and promotes the design of next-generation air bearings with higher speed, lower loss, and stronger adaptability, which has very important theoretical and engineering significance. Full article

The implementation of chaotic behavior and a sensitivity assessment of the newly developed M-fractional Kuralay-II equation are the foremost objectives of the present study. This equation has significant possibilities in control systems, electrical circuits, seismic wave propagation, economic dynamics, groundwater flow, image and signal denoising, complex biological systems, optical fibers, plasma physics, population dynamics, and modern technology. These applications demonstrate the versatility and advantageousness of the stated model for complex systems in various scientific and engineering disciplines. One more essential objective of the present research is to find closed-form wave solutions of the assumed equation based on the $({\displaystyle \frac{G^{\prime }}{G^{\prime }+G+A}})$-expansion approach. The results achieved are in exponential, rational, and trigonometric function forms. Our findings are more novel and also have an exclusive feature in comparison with the existing results. These discoveries substantially expand our understanding of nonlinear wave dynamics in various physical contexts in industry. By simply selecting suitable values of the parameters, three-dimensional (3D), contour, and two-dimensional (2D) illustrations are produced displaying the diagrammatic propagation of the constructed wave solutions that yield the singular periodic, anti-kink, kink, and singular kink-shape solitons. Future improvements to the model may also benefit from what has been obtained as well. The various assortments of solutions are provided by the described procedure. Finally, the framework proposed in this investigation addresses additional fractional nonlinear partial differential equations in mathematical physics and engineering with excellent reliability, quality of effectiveness, and ease of application. Full article

This paper presents a modeling framework for hysteretically nonlinear piezoelectric composite beams using functional differential equations (FDEs). While linear piezoelectric models are well established, they fail to capture the complex nonlinear behaviors that emerge at higher electric field strengths, particularly history-dependent hysteresis effects. This paper develops a cascade model that integrates a high-dimensional linear piezoelectric composite beam representation with a nonlinear Krasnosel’skii–Pokrovskii (KP) hysteresis operator. The resulting system is formulated using a state-space model where the input voltage undergoes a history-dependent transformation. Through modal expansion and discretization of the Preisach plane, we derive a tractable numerical implementation that preserves essential nonlinear phenomena. Numerical investigations demonstrate how system parameters, including the input voltage amplitude, and hysteresis parameters significantly influence the dynamic response, particularly the shape and amplitude of limit cycles. The results reveal that while the model accurately captures memory-dependent nonlinearities, it depends on numerous real and distributed parameters, highlighting the need for efficient reduced-order modeling approaches. This work provides a foundation for understanding and predicting the complex behavior of piezoelectric systems with hysteresis, with potential applications in vibration control, energy harvesting, and precision actuation. Full article

Vibration control has long been a key concern in engineering, with low-frequency vibration isolation remaining particularly challenging. Traditional linear isolators are limited in their ability to provide high load-bearing capacity and effective low-frequency isolation simultaneously. In contrast, quasi-zero stiffness (QZS) isolators offer low dynamic stiffness near equilibrium while maintaining high static stiffness, thereby enabling superior isolation performance in the low and ultra-low frequency range. This paper proposes a novel vibration isolation system that combines a grounded dynamic absorber with a QZS isolator, incorporating time-delay feedback control to enhance performance. The dynamic equations of the system are derived using Newton’s second law. The harmonic balance method combined with the arc-length continuation technique is employed to obtain steady-state responses under harmonic force excitation. The influence of feedback gain and time delay on vibration isolation effectiveness and dynamic behavior is analyzed, demonstrating the ability of time-delay feedback to modulate system responses and suppress primary resonance peaks. To further enhance performance, a genetic algorithm is used to optimize the control parameters under harmonic force excitation. The force transmissibility is defined as fitness functions, and the effects of control parameters on these metrics are examined. The results show that the optimized time-delay feedback parameters significantly reduce the transmitted force, improving the overall isolation efficiency. The proposed system provides a promising approach for achieving high-performance vibration isolation in low-frequency environments. Full article

This is a numerical investigation of optical and electronic characteristics of GaAs spherical quantum dots based on single and double quartic potentials and presenting a hydrogenic impurity at their center. The radial Schrödinger equation was solved using the finite difference method (FDM) to obtain the energy levels and the wavefunctions. These physical quantities were then used to compute the dipole matrix elements, the total optical absorption coefficient (TOAC), and the binding energies. The impact of the structural parameters in the confining potentials on the red and blue shifts of the TOAC is discussed in the presence and absence of hydrogenic impurity. Our results indicate that the structural parameter $k$ in both potentials plays a crucial role in tuning the TOAC. In the case of single quartic potential, increasing $k$ produces a blue shift; however, its augmentation in the case of double quartic potential displays a blue shift at first, and then a red shift. Furthermore, the augmentation of the parameter $k$ can control the binding energies of the two lowest states, ($1s$) and ($1p$). In fact, enlarging this parameter reduces the binding energies and converges them to constant values. In general, the modification of the potential’s parameters, which can engender two shapes of confining potentials (single quartic and double quartic), enables the experimenters to control the desired energy levels and consequently to adjust and select the suitable TOAC between the two lowest energy states (ground ($1s$) and first excited ($1p$)). Full article

In this study, we investigate the fractional Tzitzéica equation, a nonlinear evolution equation known for modeling complex phenomena in various scientific domains such as solid-state physics, crystal dislocation, electromagnetic waves, chemical kinetics, quantum field theory, and nonlinear optics. Using the (G′/G, 1/G)-expansion approach, we derive different categories of exact solutions, like hyperbolic, trigonometric, and rational functions. The beta fractional derivative is used here to generalize the classical idea of the derivative, which preserves important principles. The derived solutions with broader nonlinear wave structures are periodic waves, breathers, peakons, W-shaped solitons, and singular solitons, which enhance our understanding of nonlinear wave dynamics. In relation to these results, the findings are described by showing the solitons’ physical behaviors, their stabilities, and dispersions under fractional parameters in the form of contour plots and 2D and 3D graphs. Comparisons with earlier studies underscore the originality and consistency of the (G′/G, 1/G)-expansion approach in addressing fractional-order evolution equations. It contributes new solutions to analytical problems of fractional nonlinear integrable systems and helps understand the systems’ dynamic behavior in a wider scope of applications. Full article

Citrus is one of the most widely consumed fruits in the world, and its cultivation industry continues to develop rapidly. However, the roles of soil protistan communities during citrus growth are not yet fully understood, despite the potential significance of these communities to the health and quality of citrus. In this study, we examined the soil properties and protistan communities in Eureka lemon farmlands located in Chongqing, China, during the flowering and fruiting stages of cultivation, both in greenhouse and open-field settings. In general, the majority of the measured soil properties (including nutrients and enzyme activities) exhibited higher values in open-field farmlands in comparison to those observed in greenhouse counterparts. According to the results of high-throughput sequencing based on the V9 region of eukaryotic 18S rRNA gene, the diversity of soil protistan communities was also higher in open-field farmlands, and both lemon growth stage and cultivation modes showed significant effects on soil protistan compositions. The transition from traditional agricultural practices to greenhouse farming resulted in a significant transformation of the soil protistan community. This transformation manifested as a shift towards a state characterized by diminished nutrient cycling capabilities. This decline was evidenced by an increase in phototrophs (Archaeplastida) and a concomitant decrease in consumers (Stramenopiles and Alveolata). Community assembly analysis revealed deterministic processes that controlled the succession of soil protistan communities in lemon farmlands. It has been established that environmental associations have the capacity to recognize nitrogen in soils, thereby providing a deterministic selection process for protistan community assembly. Furthermore, a production index was calculated based on 12 quality parameters of lemons, and the results indicated that lemons from greenhouse farms exhibited a lower quality compared to those from open fields. The structure equation model revealed a direct correlation between the quality of lemons and the cultivation methods employed, as well as the composition of soil protists. The present study offers insights into the mechanisms underlying the correlations between the soil protistan community and lemon quality in response to changes in the cultivation modes. Full article

In this paper, we analytically investigate a diatomic molecule subject to the Morse potential under the small oscillations regime, immersed in a medium with a point defect representing impurities or vacancies in an elastic system. Initially, we apply the small oscillations method to the Morse potential to obtain an analogue to the harmonic potential, and then we solve the generalized Schrödinger equation considering the geometric effects of the defect. The solutions obtained for the bound states reveal that the energy levels and the radial stability point of the molecule are modified by the presence of the defect, depending on the parameters associated with the geometry of the medium. In a second step, we analyze the thermodynamic properties of the system in contact with a thermal reservoir at finite temperature. We derive analytical expressions for the internal energy, Helmholtz free energy, entropy, and specific heat, showing that all these quantities are influenced by the presence of the point defect. The results demonstrate how structural defects alter the quantum and thermodynamic behavior of confined molecules, contributing to the understanding of systems in non-trivial elastic media. Full article

Studies of subradiance in a chain N two-level atoms in the single excitation regime focused mainly on the complex spectrum of the effective Hamiltonian, identifying subradiant eigenvalues. This can be achieved by finding the eigenvalues N of the Hamiltonian or by evaluating the expectation value of the Hamiltonian on a generalized Dicke state, depending on a continuous variable k. This has the advantage that the sum above N can be calculated exactly, such that N becomes a simple parameter of the system and no longer the size of the Hilbert space. However, the question remains how subradiance emerges from atoms initially excited or driven by a laser. Here we study the dynamics of the system, solving the coupled-dipole equations for N atoms and evaluating the probability to be in a generalized Dicke state at a given time. Once the subradiant regions have been identified, it is simple to see if subradiance is being generated. We discuss different initial excitation conditions that lead to subradiance and the case of atoms excited by switching on and off a weak laser. This may be relevant for future experiments aimed at detecting subradiance in ordered systems. Full article

To address the need for intelligent scheduling and model integration under spatiotemporal variability and uncertainty in water systems, this study proposes a hybrid correction method for pump characteristic curves that integrates data-driven techniques with an affine modeling framework. Steady-state data are extracted through adaptive filtering and statistical testing, and representative operating conditions are identified via unsupervised clustering. An affine transformation is then applied to the factory-provided characteristic equation, followed by parameter optimization using the clustered dataset. Using the Hongze Pump Station along the eastern route of the South-to-North Water Diversion Project as a case study, the method reduced the mean blade angle prediction error from 1.73° to 0.51°, and the efficiency prediction error from 7.32% to 1.30%. The results demonstrate improved model accuracy under real-world conditions and highlight the method’s potential to support more robust and adaptive hydrodynamic scheduling models, contributing to the advancement of sustainable and smart water resource management. Full article