Search Results (391)

In this paper, we focus on one-dimensional vertical infiltration, assuming constant diffusivity and a quadratic relationship between hydraulic conductivity and water content. Under these assumptions, Richards’ equation reduces to Burgers’ equation, which we then linearize via the Hopf–Cole transformation. This turns the initial boundary value problem into a diffusion equation on a finite interval with mixed boundary conditions. To solve it, we use the Unified Transform Method (also known as the Fokas method). This approach gives an explicit integral representation of the solution, and when evaluated numerically, the results match classical Fourier series solutions exactly, but with better convergence and stability. Two examples from hydrological applications are examined. Full article

This paper establishes the global-in-time existence and uniqueness of mild solutions to the relativistic Vlasov–Maxwell–Fokker–Planck (VMFP) system near a global Maxwellian equilibrium. We adopt a low-regularity functional framework, namely the mixed-norm space $L_k^1{L}_T^{\infty }{L}_p^2$ introduced for kinetic equations, which requires only integrability in the Fourier frequency variable and avoids high-order spatial differentiability. By employing a macro–micro decomposition, we derive macroscopic estimates for the hydrodynamic density and electric field, complemented by coercive estimates for the microscopic dissipation. Under a smallness assumption on the initial perturbation measured in this low-regularity norm, we derive a uniform a priori bound for the associated energy functional. This work provides the global existence result for the relativistic VMFP system in such low-regularity spaces, significantly relaxing the regularity requirements of previous classical Sobolev approaches. Full article

In this paper, based on the Schauder fixed point theorem, the (generalized) Darbo fixed point theorem, and the (generalized) Banach contraction mapping principle, we study the mixed-type fractional impulse evolution equation with non-local and delay terms, and obtain the existence and uniqueness theorems under whether the operator is compact or not. The order of the derivative in this paper is $0<\alpha <1$, this fractional order introduces a series of problems concerning compactness, continuity, and convergence. We overcome these problems using methods such as H$\ddot{o}$lder inequality and Minkowski inequality. Moreover, under the condition of the non-compact measure, the non-negative constant is extended to an unbounded Lebesgue-integrable function. In addition, when obtaining the uniqueness of the solution through the (generalized) Banach contraction mapping principle, the non-negative constant L in the Lipschitz condition is extended to an unbounded Lebesgue integrable function. Finally, a case study is conducted to demonstrate the validity of the theoretical results. Full article

Mie lidar has been profoundly applied in the profiling of aerosol optical coefficients in atmosphere. However, few studies further explore quantitative strategies for the retrieval of aerosol mass profiles from lidar observation. To address the growing need for spatial and temporal aerosol mass data, a synergic retrieval algorithm for simultaneously profiling the aerosol extinction coefficient and mass composition from spaceborne dual-channel lidar data is proposed. By constructing the relationship between mixed aerosol mass profiles and extinction coefficients at different wavelengths by a forward model, additional constraints are induced to improve the accuracy of lidar ratio, which is a critical parameter for the retrieval of aerosol extinction coefficients by solving the lidar equation. Meanwhile, aerosol composition profiles can also be deduced based on the a priori estimation of aerosol compositions and intrinsic optical features of the aerosols. This method is first applied in simulated data with wavelengths at 532 nm and 1064 nm. The simulations are based on the reanalysis data of aerosol mass concentration profiles in Inner Mongolia, China. Compared with the classic Fernald method using empirically estimated lidar ratio, the proposed method improves the accuracy of column-integrated aerosol extinction coefficients (also known as aerosol optical depth, AOD) by 19.58% at 532 nm and 3.57% at 1064 nm. The accuracy for column dust and sulfate aerosols is enhanced by 12.46% and 17.58%, respectively. Further validation with CALIOP observations suggests that the proposed method produces improved extinction results and reliable aerosol composition information. Full article

Here, we consider a nonlinear hydrodynamic model with mixed dispersion–temporal evolution as the scalar version of the generalized shallow-water wave equation, which specifically provides a comprehensive and versatile framework for studying energy propagation in nonlinear fluids of constrained depth. This equation is acknowledged as an integrable model in the analysis of tidal wave dynamics and in simulations of weather variations, tsunami prediction, and irrigation flows. We also investigate a few of its singular and periodic solitary wave solutions by employing various Riccati-based ansatzes. These results highlight the necessity of studying various nonlinear wave phenomena, which may have potential applications in various domains of physics and applied mathematics. These results extend the variety of its solutions and also enrich the existing knowledge about its solutions with various profiles. To improve visual clarity and to facilitate structural understanding, the solution profiles are represented graphically using Maple software (version 2023.2) in 3D, 2D, and contour plots.We also discuss its invariance under infinitesimal transformations, which yields a one-dimensional Hamilton–Jacobi-like equation. Full article

The morphological and structural state of rough solid electrodes usually has a complex effect on the kinetics of an electrochemical process. In order to correctly distinguish the influence of different factors on the rate of an electrode reaction, it is necessary to first separate a purely geometric current rise caused by the surface area increase. At the same time, it is necessary to take into account that surface roughness itself often not only leads to a geometric rise in the electrode area, but also contributes to a change in the kinetic parameters of the electrochemical process. As a consequence, the conclusion regarding an electrocatalytic effect will be reasonable only if the roughness effect is correctly taken into account. The most difficult problem is to establish the role of roughness when experimental electrochemical data are obtained under mixed diffusion–kinetic control of the electrode process. However, the use of appropriate theoretical approaches is required to correctly determine the kinetic characteristics of the electrochemical stage, i.e., of the charge transfer stage. This paper establishes the influence of the morphology and structure of electrodeposited copper coatings on the kinetics of the cathodic reduction of nitrate ion, which occurs in a mixed diffusion–kinetic mode, using the theoretical model of chronoamperometry of an electrochemical process on a rough electrode developed earlier by the authors. Several Cu-electrodes with roughness and structure, the parameters of which vary widely enough, were obtained by cathodic deposition from sulfate solutions of different compositions. The integral (roughness factor) and local (average roughness) characteristics of the surface morphology were determined by methods of underpotential deposition and atomic force microscopy, respectively. Structural investigation of the electrodeposited coatings was carried out by X-ray diffraction to determine their crystallographic structure and average crystallite size. The methods of voltammetry and a rotating disk electrode revealed the mixed kinetics of the electroreduction of ${\mathrm{NO}}_3^{-}$ ions. The kinetic parameters of the charge transfer stage on the copper coatings with a roughness factor of f_r ≤ 3.5 are determined for the first time in this paper by treatment of the experimental current decay curves with the non-linear theoretical equation obtained by the authors for the chronoamperogram of the process on rough electrodes. It was found that the rate constant of the charge transfer stage and the exchange current density of the nitrate ion electroreduction increase by about 50%, with an increase in the average surface roughness from 25 to 120 nm. Considering that this effect is not caused by a purely geometric increase in the true surface area of the electrode, and that the average crystallite size is approximately the same (25 ± 2 nm) for all investigated coatings, it can be concluded that the electrocatalytic activity of copper increases in the reaction of the cathodic reduction of nitrate ions during the transition to copper electrodes with the higher average surface roughness. Taking into account XRD data, the role of the structural and morphological state in the kinetics of the electroreduction of nitrate ions has been established. The smoothest polycrystalline coating was found to be the least electrocatalytically active in this reaction. On the contrary, the roughest coatings with the most prominent plane (220) show the highest activity, which increases with increasing average roughness, possibly due to the growth of defects and excess energy of such curved surfaces. Full article

This study examines farmers’ perceptions of how policy support is associated with ecological agriculture adoption and perceived green development outcomes in Xinjiang under China’s Rural Revitalization Strategy. A sequential explanatory mixed-methods design was used, in which the qualitative phase was deliberately connected to the quantitative phase through a shared sampling frame and a construct-aligned interview guide, and the two strands were integrated using a joint display and meta-inferences. In the quantitative phase, survey data from 300 farmers were analyzed using partial least squares structural equation modelling (PLS-SEM) to test the relationships among perceived policy support, ecological agriculture adoption, and green development. In the qualitative phase, semi-structured interviews with 30 participants drawn from the same respondent pool were thematically analyzed to explain, qualify, and contextualize the statistical relationships. The quantitative findings show a strong positive association between perceived policy support and ecological agriculture adoption (β = 0.659, p < 0.001), a strong positive association between ecological agriculture adoption and green development (β = 0.689, p < 0.001), and a smaller but significant direct association between perceived policy support and green development (β = 0.324, p < 0.001). The indirect effect of perceived policy support on green development through ecological agriculture adoption (β = 0.454) indicates partial mediation. The model explains 43.4% of the variance in ecological agriculture adoption and 47.4% of the variance in green development. The integrated joint display shows that technical training, policy clarity, and extension support helped farmers translate policy support into ecological practices, whereas high initial costs, financing constraints, and market uncertainty limited adoption and created uneven outcomes. The integrated findings suggest that policy effectiveness depends not only on the availability of support instruments but also on farmers’ practical capacity, economic security, and confidence in market returns. The study contributes perception-based mixed-method evidence on the policy–adoption–green development nexus in an ecologically vulnerable agricultural region. Full article

In this paper, the Tricomi problem for a second-kind mixed-type equation with a lower-order term is studied in an unbounded domain. The elliptic part of the domain is a vertical half-strip, while the hyperbolic part is bounded by characteristics. Homogeneous Dirichlet conditions are imposed on the walls of the half-strip, gluing conditions are given on the parabolic degeneracy line, and the trace of the desired solution is prescribed on one of the characteristics. The uniqueness of the solution is proved using the extremum principle and the Zaremba–Giraud principle. The existence of the solution is established by Green’s function method: in the elliptic part, Green’s function of the mixed problem is constructed in the form of a rapidly convergent series; in the hyperbolic part, a generalized solution of the Cauchy problem of a special class is used. The functional relations on the degeneracy line lead to a singular integral equation, which is regularized by the Carleman–Vekua method into a Fredholm integral equation of the second kind with a weak singularity. Explicit formulas for the trace of the solution and its normal derivative are obtained. For a specific set of parameters, a numerical visualization of the solution is performed, the gluing conditions are verified, and a physical interpretation of the obtained graphs is given in the context of transonic gas dynamics. The results can be useful for mathematical modeling of flows in Laval nozzles and other problems of mechanics. Full article

During fast-fill, large type IV polymer composite hydrogen storage tanks experience significant temperature gradients associated with both the compression of the gas and a Joule–Thomson effect that can compromise vessel integrity, significantly affecting overall safety. In order to remedy this concern, the current work proposes a novel active mixing approach in which the tank rotates, which leads to enhanced internal convective heat transfer and consequently minimizes temperature gradients. Transient CF simulations were performed using the Redlich–Kwong real-gas equation of state, capturing the high-pressure thermodynamic behavior of hydrogen precisely. The study, based on the 1000 s fast-refueling of a tank of 20.56 m³ internal volume, was carried out to assess the tangential speeds of rotation at 10, 30, and 50 rad/s, respectively. Results also show that thermal performance has a strongly nonlinear dependence on rotational speed. At 10 rad/s, a reasonably even temperature profile develops with a much lower energy cost. The most significant suppression of peak temperatures, and therefore the most efficient cooling, is seen at 30 rad/s. Nevertheless, when the rotation speed further elevates to 50 rad/s, abundant viscous dissipation heating results in an unwanted secondary temperature increase while partially counteracting the benefits brought about by improved mixing. On the whole, the results indicate that an ideal operating window more closely correlated with 30 rads/s is seen to provide the most beneficial compromise between temperature uniformity, maximum temperature limitation, and energy consumption for rapid refueling of large composite hydrogen storage systems. Full article

This study aims to explore and evaluate the factors influencing Gen Z’s intention to choose green tourism destinations in Hanoi, Vietnam. The paper proposes a comprehensive analytical framework by integrating the Stimulus-Organism-Response (S-O-R) model and the Theory of Planned Behavior (TPB). A mixed-method approach was employed, in which quantitative data were collected from 269 Gen Z respondents in Hanoi and analyzed using the Partial Least Squares Structural Equation Modeling (PLS-SEM) technique through SmartPLS. The findings reveal that external environmental stimuli, including green destination image (GDI) and social media influence (SMI), positively affect individuals’ internal psychological states, namely environmental awareness (EA), attitude toward green tourism (ATT), and subjective norms (SM). These psychological states, in turn, exert positive effects and strongly promote Gen Z’s intention to choose green tourism destinations in Hanoi. This study not only contributes to filling the theoretical gap in sustainable tourism consumption behavior in the digital era but also provides practical managerial implications for policymakers and tourism businesses in developing communication strategies and tourism products that align with the preferences and expectations of younger generations. Full article

An ordinary state-based peridynamic (OSPD) approach combined with an interaction integral method is proposed to calculate dynamic stress intensity factors (DSIFs) and simulate crack propagation in two-dimensional cracked brittle solids. Numerical investigations are carried out for mode I and mixed-mode cracked plates under static, quasi-static, and dynamic loading conditions. A local damping scheme is incorporated into the peridynamic equations of motion to achieve convergence in static and quasi-static analyses. The influence of circular holes on DSIFs and crack propagation paths is systematically examined. Quantitative analyses of elastic deformation and quasi-static fracture behavior for mode I and mixed-mode cracks are verified through the uniaxial tension of a slab. The peak values of DSIFs exceed their static counterparts under dynamic loading. Complex dynamic fracture phenomena, including crack branching in both straight and inclined edge cracks, are successfully captured. The results obtained by the OSPD approach are validated through comparisons with theoretical benchmarks and finite element results, demonstrating high accuracy and effectiveness in calculating elastic deformation and stress intensity factors (SIFs), as well as accurately predicting crack propagation paths in quasi-static and dynamic fracture problems in brittle solids. Beyond the benchmark problems, the proposed OSPD approach is particularly well-suited for investigating more complex fracture systems. Full article

This article presents several new analytical results for a modified class of Bernoulli polynomials, namely, the Bernoulli polynomials of the second kind (BPs2). The paper mainly develops new connection and inverse connection formulas between the first and second kinds of Bernoulli polynomials using two different approaches. One of these approaches uses the generating functions for both polynomial families, whereas the other employs the power series representation, along with its inverse formula and certain closed forms of sums. Another principal contribution of the paper is the derivation of new explicit formulas for moments, derivatives, and higher-order derivatives of the BPs2, together with inverse derivative formulas and mixed linearization formulas involving several polynomial families, including Chebyshev-type and generalized Fibonacci polynomials. Furthermore, a collection of new definite integral formulas associated with the BPs2 is established. The obtained formulas provide new operational representations for the BPs2 and may be useful in spectral methods, basis transformations, and the treatment of differential equations involving polynomial approximations. Full article

Purpose: This study investigates the multifaceted dynamics of institutional sustainability (IS) within the higher education sectors of Saudi Arabia and Egypt. It examines the direct influence of cultural, technological, and economic factors, alongside change management techniques (CMT), on the sustainability of universities in these two nations. Methodology: Employing a comparative, mixed-methods approach, the research collected data from 427 university staff members across Saudi Arabia and Egypt. Structural Equation Modeling (PLS-SEM) was utilized for data analysis, complemented by Multiple Group Analysis (MGA) to explore variations across different demographics, including gender, geographical location, and institution type (public vs. private). Findings: The study reveals that Change Management Techniques (CMT), cultural norms, technological infrastructure, and economic factors all significantly and directly influence institutional sustainability. Effective CMT is crucial for successful technological integration and mitigating staff resistance. Cultural norms, particularly in high power distance and collectivist societies, profoundly impact the adoption of innovations. A robust technological infrastructure is foundational for operational efficiency and educational outcomes, while strategic economic planning and diversified funding streams are vital for long-term stability and growth. Originality: This research offers actionable insights for policymakers and academic leaders by providing a nuanced understanding of how to build resilient, sustainable, and technologically advanced educational institutions in the Middle East. It emphasizes the necessity of context-specific strategies that acknowledge the unique regional socio-cultural and economic realities of Saudi Arabia and Egypt, bridging the gap between global sustainability paradigms and local implementation challenges. Full article

High-order implicit-explicit (IMEX) schemes are effective for stiff parabolic partial differential equations when temporal regularity is compatible with the active multistep stencil. In moving-interface problems, a fixed Eulerian node may undergo a rapid transition as a diffuse interface crosses the grid, allowing stored multistep history to mix incompatible local regimes. This paper develops a conditional hybrid Deep Neural Galerkin-IMEX (DNG-IMEX) framework for this order-degradation mechanism. A classical IMEX-BDF3 backbone is retained on smooth intervals, whereas flagged event windows are treated by a localized neural/subcycle bridge followed by restart-consistent history reconstruction. The formulation separates the weak parabolic setting from the additional smoothness used for pointwise interface kinematics and proves a Sobolev-level transport estimate, a weak energy estimate, and a conditional propagation result under explicit flagged/restart defect bounds. Numerical tests on a manufactured Allen–Cahn benchmark show that event-aligned restarting suppresses the dominant history-contamination defect. A benchmark diagnostic realization localizes corrections with available event information and improves the baseline when event windows are resolved and the detector remains selective. Interface-thickness and cost tests indicate that sharper interfaces require stronger event resolution and that the present correction pipeline has non-negligible overhead. These findings support selective interface-aware enhancement of classical IMEX time integration. Full article

The optimal reconfiguration of electrical distribution feeders is a fundamental strategy for reducing active power losses and improving voltage profiles, yet it remains a challenging mixed-integer nonlinear programming (MINLP) problem due to the combinatorial explosion of radial topologies and the nonlinearities introduced by power flow equations. This paper proposes a novel master–slave methodology that integrates a Chu and Beasley genetic algorithm (CBGA) with a minimum spanning tree (MST)-based repair mechanism to address these challenges. In the master stage, the CBGA explores the binary space of switching decisions via steady-state population management, duplicate elimination, and stagnation restart policies. A key contribution lies in the MST-based repair procedure, which ensures that every individual generated by crossover and mutation is projected onto a feasible radial and connected configuration, effectively confining the search to the constrained solution space without recourse to penalty functions. A systematic weight-design rule preserves the Hamming distance between infeasible offspring and repaired solutions, minimizing the distortion of genetic information. The slave stage evaluates each candidate topology using a successive approximations power flow solver, assessing electrical feasibility and computing active power losses. The proposed methodology is validated on multiple test feeders, ranging from small 9- and 24-bus networks to large-scale benchmarks including 33-, 69-, 84-, 136-, and 415-bus systems. A comparison against the deterministic sequential switch opening method (SSOM) and a specialized tabu search demonstrates that the CBGA-MST consistently matches the best-known optima in the literature, achieving loss reductions of up to 9.63% compared to SSOM on the 415-bus system. A statistical analysis over 100 independent runs confirms the algorithm’s robustness, with zero standard deviation for networks of up to 69 buses and a standard deviation of only 2.99 kW (0.51%) for the 415-bus system. The findings confirm that the proposed approach offers superior scalability, robustness, and solution quality, positioning it as a practical and effective tool for distribution system operators seeking to enhance network efficiency under peak load conditions. Full article