Search Results (919)

In this paper, an intelligent simulation method for chloride ion diffusion behavior in marine concrete is established based on a physical information neural network. The dimensionless constraint equation is constructed to solve the influence of different physical parameter dimensions on the generalization ability of the model. The performance of the simulation method is verified by field measured data. The influence of different exposure ages and chloride ion diffusion coefficients on chloride ion diffusion behavior is quantified. The temporal and spatial distribution characteristics of chlorine ion (C) in concrete under a multi-dimensional diffusion state are analyzed, and the reliability model is further constructed to evaluate the degradation law of the service performance of marine concrete. The results show that the dimensionless physical information neural network model can effectively simulate the diffusion behavior and spatial–temporal distribution of C in marine concrete. The maximum error between the predicted value and the experimental value obtained by the method proposed in this paper is less than 15%. The dimension problem of high-order nonlinear equations can be solved by Non-PINN, with the maximum error value less than 5%. The spatial–temporal distributions of C on different exposed surfaces under a multi-dimensional diffusion state are independent of each other. The service performance of marine concrete will increase with an increase in slag content and protective layer thickness, and decrease with an increase in surface chloride ion concentration. Full article

The efficiency of various numerical methods for solving Huxley’s equation—which includes a diffusion term and a nonlinear reaction term—is investigated. Conventional explicit finite difference algorithms often suffer from severe stability limitations and can yield unphysical concentration values. In this study, we collect a range of stable, explicit time integration methods of first to fourth order, originally developed for the diffusion equation, and design treatments of the nonlinear term which ensure that the solution remains within the physically meaningful unit interval. This property, called dynamical consistency, is analytically proven and implies unconditional stability. In addition to this, the most effective ones are identified from the large number of constructed method combinations. We conduct systematic tests in one and two spatial dimensions, also evaluating computational efficiency in terms of CPU time. Our results show that higher-order schemes are not always the most efficient: in certain parameter regimes, second-order methods can outperform their higher-order counterparts. Full article

This study presents the complete analysis of a (2 + 1)-dimensional nonlinear wave-type partial differential equation with anisotropic power-law nonlinearities and a general power-law source term, which arises in physical domains such as fluid dynamics, nonlinear acoustics, and wave propagation in elastic media, yet their symmetry properties and exact solution structures remain largely unexplored for arbitrary nonlinearity exponents. To fill this gap, a complete Lie symmetry classification of the equation is performed for arbitrary values of m and n, providing all admissible symmetry generators. These generators are then employed to systematically reduce the PDE to ordinary differential equations, enabling the construction of exact analytical solutions. Traveling wave and soliton solutions are derived using Jacobi elliptic function and sine-cosine methods, revealing rich nonlinear dynamics and wave patterns under anisotropic conditions. Additionally, conservation laws associated with variational symmetries are obtained via Noether’s theorem, yielding invariant physical quantities such as energy-like integrals. The results extend the existing literature by providing, for the first time, a full symmetry classification for arbitrary m and n, new families of soliton and traveling wave solutions in multidimensional settings, and associated conserved quantities. The findings contribute both computationally and theoretically to the study of nonlinear wave phenomena in multidimensional cases, extending the catalog of exact solutions and conserved dynamics of a broad class of nonlinear partial differential equations. Full article

In this paper, we present Lie symmetry analysis of a generalized (1+1)-dimensional porous medium equation characterized by parameters m and d. Through group classification, we examine how these parameters influence the Lie symmetry structure of the equation. Our analysis establishes conditions under which the equation admits either a three-dimensional or a five-dimensional Lie algebra. Using the obtained symmetry algebras, we construct optimal systems of one-dimensional subalgebras. Subsequently, we derive invariant solutions corresponding to each subalgebra, providing explicit formulas in relevant parameter regimes. These solutions deepen our understanding of the nonlinear diffusion processes modeled by porous medium equations and offer valuable benchmarks for analytical and numerical studies. Full article

Ultrasonic wave attenuation in biological tissues arises from complex interactions between mechanical, structural, and fluidic properties, making it essential to identify dominant mechanisms for accurate simulation and device design. This work introduces a novel integration of experimentally measured tissue parameters into time-explicit nonlinear acoustic wave simulations, in which the equations are directly solved in the time domain using an explicit solver. This approach captures the full transient waveform without relying on frequency-domain simplifications, offering a more realistic representation of ultrasound propagation in heterogeneous media. The study estimates both sound diffusivity and viscous damping parameters (dynamic and bulk viscosity) for a broad range of ex vivo tissues (skin, adipose tissue, skeletal muscle, trabecular/cortical bone, liver, myocardium, kidney, tendon, ligament, cartilage, and gray/white brain matter). Four regression models (power law, linear, exponential, logarithmic) were applied to characterize their frequency dependence between 0.5 and 5 MHz. Results show that attenuation is more strongly driven by bulk viscosity than dynamic viscosity, particularly in fluid-rich tissues such as liver and myocardium, where compressional damping dominates. The power-law model consistently provided the best fit for all attenuation metrics, revealing a scale-invariant frequency relationship. Tissues such as cartilage and brain showed weaker viscous responses, suggesting the need for alternative modeling approaches. These findings not only advance fundamental understanding of attenuation mechanisms but also provide validated parameters and modeling strategies to improve predictive accuracy in therapeutic ultrasound planning and the design of non-invasive, tissue-specific acoustic devices. Full article

A Lotka–Volterra-type system with porous diffusion, which can be used as an alternative model to the classical Lotka–Volterra system, is under study. Multiparameter families of exact solutions of the system in question are constructed and their properties are established. It is shown that the solutions obtained can satisfy the zero Neumann conditions, which are typical conditions for mathematical models describing real-world processes. It is proved that the system possesses two stable steady-state points provided its coefficients are correctly specified. In particular, this occurs when the system models the prey–predator interaction. The exact solutions are used for solving boundary-value problems. The analytical results are compared with numerical solutions of the same boundary-value problems but perturbed initial profiles. It is demonstrated that the numerical solutions coincide with the relevant exact solutions with high exactness in the case of sufficiently small perturbations of the initial profiles. Full article

There has been considerable scientific interest in third-order nonlinear optical materials for photonic applications. In particular, materials exhibiting a strong electronic optical Kerr effect serve as essential components in the ultrafast nonlinear photonic devices and are instrumental in the development of all-optical signal processing technologies. Therefore, the accurate prediction of material-relevant properties, such as second hyperpolarizabilities, remains a key topic in the search for efficient photonic materials. However, the field standards in quantum chemical computation are still inconsistent, as studies often lack a firm statistical foundation. This work presents a comprehensive in silico investigation based on multiple full-factorial experiments, aiming to clarify the strengths and limitations of various computational approaches. Our results indicate that the coupled-cluster approach at the CCSD level in its current response-equation implementations is not yet able to outperform the range-separated hybrid density functionals, such as LC-BLYP(0.33). The exceptional performance of the specifically tailored basis set Sadlej-pVTZ is also described. Not only was the presence of diffuse functions found to be mandatory, but also adding ample polarization functions is shown to be inefficient resource-wise. HF/Sadlej-pVTZ is proven to be reliable enough to use in molecular screening. Meta functionals are confirmed to produce poorly consistent results, and specific guidelines for constructing range-separated functionals for polarizability calculations are drawn out. Additionally, it was shown that many of the contemporary solvation models exhibit significant limitations in accurately capturing nonlinear optical properties. Therefore, further refinement in the current methods is pending. This extends to the statistical description as well: the mean absolute deviation descriptor is found to be deficient in rating various computational methods and should rather be replaced with the parameters of the linear correlation (the slope, the intercept, and the R²). Full article

Distributed acoustic sensing (DAS), which can provide dense spatial and temporal measurements using optical fibers, is quickly becoming critical for large-scale infrastructure monitoring. However, anomaly detection in DAS data is still challenging owing to the spatial correlations between sensing channels and nonlinear temporal dynamics. Recent approaches often disregard the explicit sensor layout and instead handle DAS data as two-dimensional images or flattened sequences, eliminating the spatial topology. This work proposes GraphDiffusion, a novel generative anomaly-detection model that combines a conditional denoising diffusion probabilistic model (DDPM) and a graph neural network (GNN) to overcome these limitations. By treating each channel as a graph node and building edges based on Euclidean proximity, the GNN explicitly models the spatial arrangement of DAS sensors, allowing the network to capture local interchannel dependencies. The conditional DDPM uses iterative denoising to model the temporal dynamics of standard signals, enabling the system to detect deviations without the need for anomalies. The performance evaluations based on real-world DAS datasets reveal that GraphDiffusion achieves 98.2% and 98.0% based on the area under the curve (AUC) of the F1-score at K different levels (F1_K-AUC), an AUC of receiver operating characteristic (ROC) at K different levels (ROC_K-AUC), outperforming other comparative models. Full article

As a crucial vehicle for green technological innovation, cooperative networks significantly promote resource integration and knowledge sharing. Yet, their dynamic evolution and micro-mechanism remain underexplored. Drawing on data from the joint applications of green invention patents between 2006 and 2021, this study constructed a multi-agent GTCIN involving multiple stakeholders, such as enterprises, universities, and research institutions, and analyzed the topological structure and evolutionary characteristics of this network; an exponential random graph model (ERGM) was introduced to elucidate its endogenous and exogenous driving mechanisms. The results indicate that while innovation connections increased significantly, the connection density decreased. The network evolved from a “loose homogeneity” to “core aggregation” and then to “outward diffusion”. State-owned enterprises in the power industry and well-known universities are located at the core of the network. Preferential attachment and transitive closure as endogenous mechanisms exert strong and continuous positive effects by reinforcing local clustering and cumulative growth. The effects of exogenous forces exhibit stage-specific characteristics. State ownership and regional location become significant positive drivers only in the mid-to-late stages. The impact of green innovation capability is nonlinear, initially promoting but later exhibiting a significant inhibitory effect. In contrast, green knowledge diversity exerts an opposite pattern, having a negative effect in the early stage due to integration difficulties that turns positive as technical standards mature. Geographical, technological, social, and institutional proximity all have a positive promoting effect on network evolution, with technological proximity being the most influential. However, organizational proximity exerts a significant inhibitory effect in the later stages of GTCIN evolution. This study reveals the shifting influence of endogenous and exogenous mechanisms across different evolutionary phases, providing theoretical and empirical insights into the formation and development of green innovation networks. Full article

The digital creative industries have emerged as a critical driver of regional economic transformation, upgrading, and sustainable development. While previous research has primarily focused on creative industry layout and agglomeration in urban areas, with the integration of digital technology and the creative industry, existing research has an insufficient explanation for the digital creative industry. Specifically, few people have studied the spatial distribution and diffusion of digital creative industries in emerging economies from the macro-regional level. To address this gap, this study analyzes the spatial diffusion mode and regional spatial response law of digital creative industries in the Yangtze River Delta during three critical time windows (2016, 2019, and 2022) in the context of national strategy implementation. A range of spatial analysis technologies is utilized to process the full sample of big data from digital creative industries. This study utilizes OLS and a quantile regression model to determine the dominant factors that affect spatial diffusion and response in the digital creative industries. The results demonstrate that, against the backdrop of regional development strategies, digital creative industries exhibit a variety of diffusion modes, including contagious, hierarchical, corridor, and jump diffusion. The response of industries to regional strategies has different rules in terms of regional space, urban development, and sub-industries. Furthermore, the comprehensive influence of institutional environment, urban economy, development and innovation significantly impacts industrial spatial diffusion and regional response. Among them, government investment in science and technology and the number of universities have consistently been important influencing factors, and policy exhibits nonlinear effects and asymmetric characteristics on industry agglomeration and diffusion. This study enhances the understanding of digital creative industry development in the YRD and offers a theoretical basis for optimizing regional industrial spatial structure and promoting the sustainable development of digital industries. Full article

With the growing demand for secure image communication, effective encryption solutions are critical for safeguarding visual data from unauthorized access. The substitution box (S-box) in AES (Advanced Encryption Standard) is critical for ensuring nonlinearity and security. However, the static S-box used in AES is vulnerable to algebraic attacks, side-channel attacks, and so on. This study offers a novel Lorenz key and Chua key-based Reversible Substitution Box (LCK-SB) for image encryption, which takes advantage of the chaotic behavior of the Lorenz and Chua key systems to improve security due to nonlinear jumps and mixed chaotic behavior while maintaining optimal quantum cost, area, and power. The suggested method uses a hybrid Lorenz and Chua key generator to create a highly nonlinear and reversible S-box, which ensures strong confusion and diffusion features. The performance of the LCK-SB approach is examined on field-programmable gate array (FPGA) and application-specific integrated circuit (ASIC) platforms, and the findings show that quantum cost, delay, and power are decreased by 97%, 74.6%, and 35%, respectively. Furthermore, the formal security analysis shows that the suggested technique efficiently resists threats. The theoretical analysis and experimental assessment show that the suggested system is more secure for picture encryption, making it suitable for real-time and high-security applications. Full article

During electron beam cold hearth melting (EBCHM) of Ti-6wt%Al-4wt%V titanium alloy, aluminum volatilization causes compositional segregation in the ingot, significantly degrading material performance. Traditional methods (e.g., the Langmuir equation) struggle to accurately predict aluminum diffusion and compensation behaviors, while computational fluid dynamics (CFD), although capable of resolving multiphysics fields in the molten pool, suffer from high computational costs and insufficient research on segregation control. To address these issues, this study proposes a CFD-machine learning (backpropagation neural network, CFD-ML(BP)) approach to achieve precise prediction and optimization of aluminum segregation. First, CFD simulations are performed to obtain the molten pool’s temperature field, flow field, and aluminum concentration distribution, with model reliability validated experimentally. Subsequently, a BP neural network is trained using large-scale CFD datasets to establish an aluminum concentration prediction model, capturing the nonlinear relationships between process parameters (e.g., casting speed, temperature) and compositional segregation. Finally, optimization algorithms are applied to determine optimal process parameters, which are validated via CFD multiphysics coupling simulations. The results demonstrate that this method predicts the average aluminum concentration in the ingot with an error of ≤3%, significantly reducing computational costs. It also elucidates the kinetic mechanisms of aluminum volatilization and diffusion, revealing that non-monotonic segregation trends arise from the dynamic balance of volatilization, diffusion, convection, and solidification. Moreover, the most uniform aluminum distribution (average 6.8 wt.%, R² = 0.002) is achieved in a double-overflow mold at a casting speed of 18 mm/min and a temperature of 2168 K. Full article

To meet the demand for sustainable pavement infrastructure, reclaimed asphalt pavement (RAP) has become a key strategy to enhance material circularity. This study investigates the coupled mobilization and blending behaviors between virgin and aged asphalt mastic in RAP systems. Fourier-Transform Infrared Spectroscopy (FTIR) was utilized to quantify the mobilization rate (MR) of aged mastic on RAP aggregate surfaces using the Composite Aging Index (CAI). Scanning Electron Microscopy (SEM) and Fluorescence Microscopy (FM), combined with digital image analysis, were employed to assess the blending interface and quantify the degree of blending (DoB). A 3D model was developed to describe the nonlinear relationship between MR and DoB. The results show that regeneration is dominated by physical diffusion, while mixing temperature has a stronger effect on MR than time. The binder interface displays a smooth transition, whereas the mastic interface exhibits a gear-like structure. DoB in the binder system is higher than that in the mastic system under the same condition, with early-stage temperature elevation playing a key role. Even near 100%, MR does not lead to full blending due to interfacial saturation. These insights are valuable for guiding the design of RAP and optimizing mixing conditions to enhance recycling efficiency in practical applications. Full article

Based on the spatial compact finite difference (SCFD) method, an improved high-order temporal accuracy scheme for high-dimensional time-fractional diffusion equations (TFDEs) is presented in this work. Combining the temporal piecewise quadratic interpolation and the high-dimensional SCFD method, the proposed numerical method is described. In order to establish the stability and convergence analysis, we introduce a norm $\left|\right|·{\left|\right|}_{{\tilde{H}}^1}$, which is rigorously proved equivalent to the standard $H^1$-norm. Considering that the coefficients of high-order numerical schemes are not entirely positive, we introduce an appropriate parameter to transform the numerical scheme into an equivalent form with positive coefficients. Based on the equivalent form, we prove that the temporal and spatial convergence orders are $(3-\gamma )$ and 4 by applying the convergence of geometric progression. The proposed scheme ensures that the theoretical convergence accuracy at each time step is of order $(3-\gamma )$ without requiring any additional processing techniques. Ultimately, the convergence of the proposed high-order accurate scheme is verified through numerical experiments involving (non-)linear high-dimensional TFDEs. Full article

In this work, we proposed a dynamic inverse solution with spatio-temporal constraints of the nonlinear heat diffusion problem in 1D and 2D based on a regularized Gauss–Newton and Krylov subspace with a preconditioner. The preconditioner is computed by approximating the Jacobian of the nonlinear system at each Gauss–Newton iteration. The proposed approach is used for estimation of the initial value from measurements of the last value by considering spatial and spatio-temporal constraints. The system is compared to a dynamic Tikhonov inverse solution and generalized minimal residual method (GMRES) with and without a preconditioner. The system is evaluated under noise conditions in order to verify the robustness of the proposed approach. It can be seen that the proposed spatio-temporal regularized Gauss–Newton method with GMRES and a preconditioner shows better estimation results than the other methods for both spatial and spatio-temporal constraints. Full article