Search Results (3,282)

Despite the increased interest in neuromorphic materials—a physical implementation of neural networks that could overcome the so-called von Neumann architecture’s limitations—most studies have been performed on the basis of systems specially constructed for this purpose. It has previously been shown that analogues of neural networks can spontaneously arise in solutions of hydrophilic polymers, but these systems involved molecules of different natures or required direct interaction between macromolecular clusters. The present paper proposes a theory that indicates the possibility of an analogue of neural network formation even in a single-component solution of a relatively weak polyacid. A model is suggested based on the account of heterogeneous distribution of polymer ionogenic groups within the volume leading to the fluctuations of electric fields and, as a result, to the local changes in the degree of ionisation of functional groups. Theoretical description of the system shows how it was reduced to a solution of the analogue based on the Poisson–Boltzmann equation. The results obtained showed that it is just fluctuations in the distribution of charges that provide the collective response of the system to external influences and serve as an argument in favour of analogy of such a solution within a neural network. The results are discussed in the context of a potential simple hydrophilic polymer system as a prototypical neuromorphic and evolving material that is relevant for organic electronics, metamaterials, and studies on prebiological evolution. Full article

We consider the Poisson stable solutions and their exponential attractiveness for the linear difference equation $z(n+1)=Az\left(n\right)+g\left(n\right)$ and semi-linear difference equation $z(n+1)=Az\left(n\right)+G(n,z(n\left)\right).$ Via Shcherbakov’s comparability principle, we show that if the forcing g (respectively, G) has some Poisson stable property, there is precisely one bounded solution that shares the same recurrence character as $g(\mathrm{respectively}, G)$ under appropriate assumptions. Moreover, the unique Poisson stable solution exponentially attracts every other solution. Full article

Frequency domain methods used in electromagnetic analyses, such as the Method of Auxiliary Sources (MAS) and the various Moment Methods (MoM), share many similarities but have notable differences in terms of numerical stability, accuracy, and computational cost. Computational cost differs from algorithmic complexity, which is easier to define. Consequently, it is rarely analyzed systematically in numerical studies. To this end, this work deals with the canonical problem of electromagnetic scattering from an externally excited circular cylinder of infinite conductivity and applies both MAS and MoM in order to assess their solutions and behaviors from the aforementioned perspectives. This problem is solved by meticulously applying MAS and two popular variants of MoM to achieve comparable stability and accuracy. Then, the methods are compared in terms of the associated computational cost, not only in solving the ensuing matrix equations, but also in computing the near and far fields at a large number of points. Full article

This paper presents a method for dimensional synthesis of a pulse-type adjustable speed mechanical drive, realized through a Watt II six-bar linkage combined with an overrunning clutch. The goal is to achieve a transmission ratio that varies smoothly and linearly by adjusting the angle of a control lever, while meeting kinematic, geometric, and force constraints. The kinematic characteristics are derived analytically using vector-loop equations, enabling comparison with a predefined linear reference function. An optimization problem is formulated to minimize the maximum deviation between the actual and reference output angles across the entire operating interval. The solution employs a metaheuristic algorithm for global search followed by a local refinement phase. Three optimization scenarios are analyzed, each with different levels of design freedom regarding the parameters defining the linear reference function. The results demonstrate a clear trade-off between accuracy and functional tunability, highlighting the most effective balance for practical applications. This approach can be used for designing mechanical drives with adjustable speed features and can be applied to other complex linkage systems. Full article

In this contribution, we propose and study long-time behaviors of a new class of N-dimensional delayed Kirchhoff–Carrier-type problems with variable transfer coefficients involving a logarithmic nonlinearity. We take into account the dependence of diffusion and damping coefficients on the position and direction, as well as the presence of different types of delays. This class of nonlocal anisotropic and nonlinear wave-type equations with multiple time-varying mixed delays and dampings, of a fairly general form, containing several arbitrary functions and free parameters, is of the following form: ${\displaystyle \frac{{\partial }^{2}u}{\partial t^2}-{div(\mathcal{K}(\Vert \sigma \nabla u\Vert }_{L^2(\Omega )}^2)A_{\sigma }{(\mathbf{x})\nabla u)+\mathcal{M}(\Vert u\Vert }_{L^2(\Omega )}^2)u-div(\zeta (t)A_{\sigma }(\mathbf{x})\nabla \frac{\partial u}{\partial t})+d_0(t)\frac{\partial u}{\partial t}+{\mathbb{D}}_r(\mathbf{x},t;\frac{\partial u}{\partial t})=\mathbb{G}(u),}$ where $u(\mathbf{x},t)$ is the state function, $\mathcal{M}$ and $\mathcal{K}$ are the nonlocal Kirchhoff operators and the nonlinear operator $\mathbb{G}(u)$ corresponds to a logarithmic source term. The symmetric tensor $A_{\sigma }$ describes the anisotropic behavior and processes of the system, and the operator ${\mathbb{D}}_r$ represents the multiple time-varying mixed delays related to velocity ${\displaystyle \frac{\partial u}{\partial t}}$. Our problem, which encompasses numerous equations already studied in the literature, is relevant to a wide range of practical and concrete applications. It not only considers anisotropy in diffusion, but it also assumes that the strong damping can be totally anisotropic (a phenomenon that has received very little mathematical attention in the literature). We begin with the reformulation of the problem into a nonlinear system coupling a nonlocal wave-type equation with ordinary differential equations, with the help of auxiliary functions. Afterward, we study the local existence and some necessary regularity results of the solutions by using the Faedo–Galerkin approximation, combining some energy estimates and the logarithmic Sobolev inequality. Next, by virtue of the potential well method combined with the Nehari manifold, conditions for global in-time existence are given. Finally, subject to certain conditions, the exponential decay of global solutions is established by applying a perturbed energy method. Many of the obtained results can be extended to the case of other nonlinear source terms. Full article

In today’s increasingly serious environmental problems, a growing number of enterprises are upgrading remanufacturing as an important corporate strategy. This paper compares two third-party remanufacturing models: the entrusting and Authorizing Models, and introduces two different levels of consumer low-carbon preferences: medium and high. By establishing game equations, we find the equilibrium solution of each model. The results reveal that in the basic model, OEM tends to choose the Authorizing Model when consumers have a pronounced quality bias against remanufactured products. Contrary to intuition, TRM always prefers the Entrusting Model. In scenarios where consumers possess medium low-carbon preferences, OEM tends to choose the Authorizing Model when consumers have a high bias against the quality of the remanufactured products or a low bias against the carbon emissions of the new products. Conversely, OEM tends to choose the entrusting remanufacturing model under the opposite conditions. In scenarios where consumers express high low-carbon preferences, the situation becomes the complete opposite. When consumers exhibit a low bias against remanufactured products’ quality or a high bias against carbon emissions from new products, OEM tends to choose the Authorizing Model. Conversely, OEM prefers the Entrusting Model when consumers’ biases differ. In addition, the consumer surplus and social welfare of the Entrusting Model are higher than those of the Authorizing Model, regardless of the research scenario. Full article

The impacts of land use on stormwater runoff quality and Best Management Practices to mitigate these impacts have been investigated since the 1970s, yet challenges remain in providing a modeling approach that concomitantly considers contributions from different land use types. In densely developed urban areas, a buildup/washoff approach is often applied, while in rural areas, some type of erosion modeling is employed, as the processes of detachment, entrainment, and transport are fundamentally different. This study presents a coupled modeling approach within PCSWMM, integrating exponential buildup/washoff for impervious surfaces with the Modified Universal Soil Loss Equation (MUSLE) for pervious areas, including construction sites, to characterize water quality in the large mixed urban–rural Sparrovale catchment in Geelong, Australia. The watershed includes an innovative cascading system of 12 online NbS wetlands along one of the main tributaries, Armstrong Creek, to manage runoff quantity and quality, as well as 16 offline NbS wetlands that are tributary to the online system. A total of 78 samples for Total Suspended Solids (TSS), Total Phosphorus (TP), and Total Nitrogen (TN) were collected from six monitoring sites along Armstrong Creek during wet- and dry-weather events between May and July 2024 for model validation. The data were supplemented with six other catchment stormwater quality datasets collected during earlier studies, which provided an understanding of water quality status for the broader Geelong region. Results showed that average nutrient concentrations across all the sites ranged from 0.44 to 2.66 mg/L for TP and 0.69 to 5.7 mg/L for TN, spanning from within to above the ecological threshold ranges for eutrophication risk (TP: 0.042 to 1 mg/L, TN: 0.3 to 1.5 mg/L). In the study catchment, upstream wetlands reduced pollutant levels; however, downstream wetlands that received runoff from agriculture, residential areas, and, importantly, construction sites, showed a substantial increase in sediment and nutrient concentration. Water quality modeling revealed washoff parameters primarily influenced concentrations from established urban neighborhoods, whereas erosion parameters substantially impacted total pollutant loads for the larger system, demonstrating the importance of integrated modeling for capturing pollutant dynamics in heterogeneous, urbanizing catchments. The study results emphasize the need for spatially targeted management strategies to improve stormwater runoff quality and also show the potential for cascading wetlands to be an important element of the Nature-based Solution (NbS) runoff management system. Full article

During the last decade, F-contraction has been a widely investigated problem in the fixed point theory. There are various outcomes regarding the extensions and generalizations of F-contraction in different perspectives, along with the findings concerning the application of those ideas, mostly in the area of differential and difference equations, fractional calculus, etc. The present article concludes some existence and uniqueness outcomes on fixed points for $(\phi ,\mathrm{F})$–contractions in the context of a metric space endowed with a local class of transitive binary relations. Some illustrative examples are furnished to justify that our contraction conditions are more general than many others in this area. The findings presented herein are used to obtain a unique solution to certain fractional boundary value problems. Full article

This study takes a further step forward in the analytical treatment of Langmuir–Hinshelwood (LH) kinetics for heterogeneous catalysis by deriving its closed-form solution. Unlike previous studies, we present a general solution that does not impose severe restrictions on the experimental conditions. This solution not only recovers the typical first- and zeroth-order regimes but also enables the simultaneous determination of the reaction rate constant and absorption–desorption equilibrium constant, unlike the traditional approaches to this equation, which needed additional isotherm experiments. The final solution requires a fine mathematical treatment for its numerical implementation, but enhanced approximations of the closed-form solution overcome this problem without losing the main advantage of calculating both constants at the same time. A parameter called “critical time” has been introduced, whose calculation allows us to distinguish quantitatively between kinetic regimes. Finally, the validation of these approximations has been carried out with experiments on zinc oxide and anatase (TiO₂) under different conditions. Anatase experiments undoubtedly show a first-order tendency, regardless the quantity of powder. On the other hand, the degradation regime of the ZnO case cannot be easily ascribed to the zeroth or first order by simple inspection, but the model can mathematically rule out the zeroth order and confirm that it undergoes first-order degradation. Full article

The study concerns the Duffing oscillator (Duffing equation) with softening stiffness. Using numerical simulations, the upper and lower limits of the unstable region for damping equal to 0 were identified, and analytic formulas describing them were developed. The analysis shows that the developed formulas are effective for all combinations of stiffness coefficient values that were tested. The curve of the upper limit of the unstable region is a jump-down curve, and in the theory of nonlinear systems, this curve for damping equal to zero is identified as a backbone curve (the curve of natural frequency of a system). However, the classical backbone curve calculated via a formula that is commonly known and used differs visibly from that actually obtained via numerical simulations of the upper boundary of the unstable region at large amplitudes. It could therefore be concluded that the backbone curve is not equal to the upper boundary of the unstable solution region. Moreover, the paper shows that the use of the scale relative to a critical oscillation amplitude leads to the conclusion that for damping equal to 0, systems with different parameters have the same instability regions in dimensionless space. Full article

Particle-in-Cell (PIC) simulations require accurate solutions of the electrostatic Poisson equation, yet accuracy often degrades near irregular Dirichlet boundaries on Cartesian meshes. While prior work has focused on left-hand-side (LHS) discretization errors, the impact of right-hand-side (RHS) inaccuracies arising from charge deposition near boundaries remains largely unexplored. This study analyzes numerical errors induced by underestimated RHS values at near-boundary nodes when using embedded finite difference schemes with linear and quadratic boundary treatments. Analytical results in one dimension and truncation error analyses in two dimensions show that RHS inaccuracies affect the two schemes in fundamentally different ways: They reduce boundary-induced errors in the linear scheme but introduce zeroth-order truncation errors in the quadratic scheme, leading to larger global errors. Numerical experiments in one, two, and three dimensions confirm these predictions. In two-dimensional tests, RHS inaccuracies reduce the $L_{\infty }$ error of the linear scheme by a factor of 2–3, while increasing the quadratic-scheme error by several times, and in some cases by nearly an order of magnitude, with both schemes retaining second-order global convergence. A simple $\overline{\delta }$-based RHS calibration is proposed and shown to effectively restore the accuracy of the quadratic scheme. Full article

With a specific Darboux transformation, we construct solutions to the sine-Gordon equation. We use both the simple Darboux transformation as well as the multiple Darboux transformation, which enables the obtainment of compact solutions of this equation. We give a complete description of the method and the corresponding proofs. We explicitly construct some solutions for the first orders. Using particular generating functions, we give Wronskian representations of the solutions to the sine-Gordon equation. In this case, we give different solutions to this equation. We deduce generalized Wronskian representations of the solutions to the sine-Gordon equation. As an application, we give the general expression of the k-negaton-l-positon-n-soliton solutions of the sine-Gordon equation and we construct some explicit examples of these solutions as well as m complexitons. Full article

The rapid development of China’s high-speed railways (HSRs) and the implementation of revenue management policies have promoted the marketization of railway passenger transport, which is mainly reflected in the gradual transformation from a seller’s market dominated by operating companies to a buyer’s market dominated by passenger demand. Passenger travel needs are becoming increasingly diverse. In order to improve the quality of HSR services and attract more passengers, this paper starts from passenger satisfaction and considers the heterogeneity of travel preferences of passengers with different travel distances. Based on the passenger travel data of the Nanning-Guangzhou (NG) HSR line, the K-means clustering method is used to classify passengers into three categories: short-distance, medium-distance, and long-distance travel. A structural equation modeling–multinomial logit (SEM-MNL) model integrating both explicit and latent variables was constructed to analyze passenger travel origin-destination (OD) choices. Stata software was used to estimate passenger preferences for perceived satisfaction functions across different travel distances. Finally, considering constraints such as load factor, departure capacity, and spatiotemporal passenger flow demand, a line planning optimization model was constructed with the goal of minimizing train operating costs and maximizing passenger travel satisfaction. An improved subtraction optimizer algorithm was designed for the solution. Using the NG Line as a case study, the proposed method achieved a reduction in train operating costs while enhancing overall passenger satisfaction. Full article

Mid-infrared (MIR) supercontinuum (SC) sources are critical for spectroscopy, biomedical imaging, and environmental monitoring. However, conventional generation methods based on free-space experiments using optical parametric amplifiers (OPAs) and difference frequency generation (DFG) lasers suffer from narrow bandwidth and low power distribution in the MIR region. This paper presents a cascaded pumping technique using two soft-glass fibers. A picosecond thulium-doped fiber amplifier (TDFA) pumps a Germania-doped fiber (GDF) to generate an intermediate broadband spectrum, which then pumps a fluorotellurite fiber (TBY) with higher nonlinearity and a wider transmission window. Using this configuration, we achieved an Octave-Spanning SC generation covering 1–4 μm with 7.20 W output power. Notably, 32.8% of total power lies above 3.0 μm, with 11.2% beyond 3.5 μm, demonstrating excellent long-wavelength performance. In addition, we applied numerical simulation methods to investigate SC generation in GDF and TBY by solving the nonlinear Schrödinger equation. The close match between simulated and experimental results facilitates theoretical examination of how SC broadening occurs. This cascaded approach offers a feasible solution in terms of spectral band matching, material compatibility, and system integration potential. Full article

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