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This work deals with fracture mechanisms in quasi-brittle materials, focusing on the characterization of the Fracture Process Zone (FPZ) of specimens under tensile load. Particularly, paper was used as model material. Experiments were conducted on notched and unnotched specimens. Based on an image analysis of these observations, a stochastic finite element model was developed, using both a nonlocal stress-based approach and a discretized random field modeling of the Young's modulus. The proposed methodology allowed characterizing the damage zone and the size of the FPZ, analyzing the influence of the mesostructure, composed of flocs (fiber aggregates where the basis weight is larger than the average one) and antiflocs (complement of flocs). The area of the active FPZ and the normalized stress drop were linked using a surface energy dissipated in the active FPZ. The stress drop, until limiting value, increased with the width of the active FPZ. Finally, a relationship between the surface energy and the nonlocal internal length was established. [ABSTRACT FROM AUTHOR]

Thin-walled tubular deployable composite boom (DCB) has gained significant attention due to its lightweight, simple structure and high packaging efficiency. The experimental and numerical simulation methods were employed in this paper to investigate the folding behavior of the DCB. Using T700/epoxy unidirectional reinforced prepreg as raw material, DCB specimens were prepared by the vacuum bag method. To complete the folding experiments of DCB specimens, a folding mechanism was designed and manufactured. Folding experiments of DCB specimens were conducted and folding moment versus rotational displacement curves were measured. In addition, a Finite Element Model (FEM) was established to predict the folding behavior of the DCB. Different failure criteria were considered in the numerical analysis, including the Tsai‐Hill criterion and maximum stress criterion. Prediction results using the FEM were compared with experimental results, and both sets of results were in good agreement. It is shown that the DCB can achieve the folding function without failure. The research results in this paper are of great significance to the practical engineering application of the DCB. [Display omitted] • Six tubular deployable composite boom specimens and a precise folding mechanism were designed and prepared. • Folding experiments were conducted to measure the folding moment and rotational displacement curves. • A finite element model for predicting the folding behavior of the tubular deployable composite boom was established. [ABSTRACT FROM AUTHOR]

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Faced with the pressure brought by major changes in the shipping industry such as liner alliances and larger ships, more and more ports are inclined to choose cooperation. This paper first explains the reasons for the lack of spontaneous cooperation motives between ports through game theory and then points out that in order to achieve stable cooperation between ports, it may be necessary to use external forces to establish a cooperation mechanism that enables both parties to achieve a win-win situation. Further, the article explores the evolution path of port cooperation and the stability of cooperation through evolutionary game theory and finds that the incremental benefits of port cooperation, the cost of cooperation, the additional revenue of free-riding, the compensation for unilateral cooperation, and the distribution coefficient of incremental benefits are the key factors affecting the stability of port cooperation. Then, with the help of numerical simulation experiments, the influencing factors affecting the evolution path and stability of port cooperation are discussed. Finally, in order to promote port cooperation and improve the stability of cooperation, this paper puts forward corresponding policy implications and management insights for policymakers based on relevant influencing factors. • The article explains the reasons for the lack of spontaneous cooperation motives between ports through classical game theory. • to promote the cooperation among ports, the article analyzes the related determinants affecting the evolutionary paths port cooperation. • The article calculates the equilibrium points of the evolutionary game model, determines the corresponding equilibrium strategies. • Numerical simulation analysis was carried out on the changes of relevant parameters reflecting corresponding influencing factors. [ABSTRACT FROM AUTHOR]

Full-waveform inversion (FWI) is an effective method for imaging subsurface properties using sparsely recorded data. It involves solving a wave propagation problem to estimate model parameters that accurately reproduce the data. Recent trends in FWI have seen a renewed interest in extended methodologies, among which source extension methods leveraging reconstructed wavefields to solve penalty or augmented Lagrangian (AL) formulations have emerged as robust algorithms, even for inaccurate initial models. Despite their demonstrated robustness on synthetic data, challenges remain, such as the lack of a clear physical interpretation and reliance on difficult-to-compute least-squares (LS) wavefields. Moreover, the literature lacks a general and through comparison of these source extension methods with each other and with the standard FWI. This paper is divided into three critical parts. In the first, a novel formulation of these methods is explored within a unified Lagrangian framework. This novel perspective permits the introduction of alternative algorithms that use LS multipliers instead of wavefields. These multiplier-oriented variants appear as regularizations of the standard FWI, are suitable to the time domain, offer tangible physical interpretations, and foster enhanced convergence efficiency. The second part of the paper delves into understanding the underlying mechanisms of these techniques. This is achieved by solving the associated non-linear equations using iterative linearization and inverse scattering methods. The paper provides insight into the role and significance of Lagrange multipliers in enhancing the linearization of the equations. It explains how different methods estimate multipliers or make approximations to increase computing efficiency. Additionally, it presents a new physical understanding of the Lagrange multiplier used in the AL method, highlighting how important it is for improving algorithm performance when compared to penalty methods. In the final section, the paper presents numerical examples that compare different methods within a unified iterative algorithm, utilizing benchmark Marmousi and 2004 BP salt models. [ABSTRACT FROM AUTHOR]

This paper delves into the numerical analysis of the extended Fisher-Kolmogorov (EFK) equation within open bounded convex domains R ⊂ R d , where d ≤ 3. Two distinct finite element schemes are introduced, namely the semi-discrete and fully-discrete finite element approximations. The existence and uniqueness of solutions are established for both the semi-discrete and fully-discrete finite element approximations. Error bounds are investigated across different scenarios, including comparisons between the semi-discrete and exact solutions, as well as between the semi-discrete and fully-discrete solutions, along with the fully-discrete and exact solutions. An effective algorithm has been proposed to solve the nonlinear system resulting from the fully-discrete finite element approximation at each time step. The paper also provides computed numerical error results and showcases a variety of numerical experiments to further illustrate and support the findings. [ABSTRACT FROM AUTHOR]

This paper employs a numerical approach to investigate the impact of liquidity shocks on European options in modeling markets. To accurately capture the behavior of European options under liquidity shocks, a coupled system of differential equations is employed, consisting of a degenerate parabolic equation and a diffusion-free equation. The primary focus is on developing and analyzing implicit-explicit methods for numerically simulating European option pricing, specifically considering the presence of liquidity shocks while ensuring the positivity of the solution. The paper also includes convergence analysis and establishes the discrete comparison principle for the developed methods. Numerical experiments are conducted using both uniform and nonuniform meshes to validate the theoretical findings, demonstrating the efficiency and accuracy of the proposed methods. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to investigate the tribological benefits of a biomimetic teardrop surface texture inspired by snakeskin compared to conventional surface textures with the help of geometrical and flow parameters using computational fluid dynamics techniques. Design/methodology/approach: The lubricant is assumed to be Newtonian, and the flow is laminar with constant viscosity and isothermal property. The governing equations, continuity and Navier–Stokes equation, are discretised by the finite volume method, and cavitation modelling is included. The discretisation for the momentum equations is carried out using the second-order difference method for the SIMPLEC algorithm of pressure–velocity coupling. Findings: The results indicate that biomimetic teardrop surface texturing performs better than conventional shapes surface textures in improving tribological performance. Furthermore, the parallel texture orientation along with the flow generates a high-pressure distribution relative to other orientations. Surface texture area density also highly influences the load-carrying capacity, which is optimum at 29%. Zigzag pattern arrangement performs better compared to linear pattern arrangement of texturing. Originality/value: The paper proposes that this unique biomimetic teardrop shape can give better tribological performance than conventional shapes. Peer review: The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-02-2024-0053/ [ABSTRACT FROM AUTHOR]

Positive semidefinite kernels on spheres cross time are on demand in spatial statistics, machine learning and numerical analysis, motivated by applications in the climate, environmental and earth sciences. Most of the recent literature has focused on kernels that are isotropic on the sphere and stationary in time, but this assumption is often overly limited in quantifying spatial dependence properly. A broader class of kernels can be obtained by trading isotropy for axial symmetry, i.e., stationarity with respect to longitudes only. This paper challenges theoretical aspects by providing a spectral representation that uniquely characterizes space-time positive semidefinite kernels that are axially symmetric on the sphere and stationary in time. We also address the problem of partial Fourier inversion and show that it is feasible under mild technical conditions. The second part of the paper focuses on constructive methods to build nonseparable kernels having axial symmetry on the sphere and stationarity over time. [ABSTRACT FROM AUTHOR]

• The elastic instability phenomenon in hyperelastic layered materials with the phases exhibiting stiffening behavior is studied • A closed-form expression for the critical stretch of macroscopic instability is derived • An analytical prediction based on Bloch-Floquet analysis for the microscopic instability is exhibited • The critical parameters and transition of instability modes are found to be highly tunable with phase stiffening This paper investigates the elastic instability behavior in soft periodic laminates subjected to finite strains, with a focus on both macroscopic and microscopic instabilities. Considering the deformation-induced phase stiffening, the Gent model with a high bulk-to-shear modulus ratio describes the behavior of incompressible phases. This non-Gaussian statistics-based model captures the non-linear constitutive results from the limited extensibility of polymeric molecular chains. This paper derives an analytical prediction for the onset of macroscopic (or longwave) instability and microscopic instability as functions of material parameters. Moreover, a numerical Bloch-Floquet analysis is imposed on identifying the instability behavior under compression. We consider a wide range of phase combinations and find that the relatively rapid stiffening of the matrix compared to the stiff layer increases the stability of laminates by decreasing the critical stretch ratio. Essentially, properly manipulating the stiffening parameters can produce an absolutely stable region without observed instability. This paper also systematically illustrates the changes in instability and the transition between macro and micro instability in fully Gent laminates, which show higher stability than fully neo-Hookean laminates with larger critical stretch ratios. The critical characteristics of instabilities, such as critical stretch ratios and critical wavenumbers, can be controlled by the choice of stiffening parameters and other material properties, enlarging the tuning of soft laminates for desired buckling patterns in practical applications. [ABSTRACT FROM AUTHOR]

• A model to explore the multiphysics characteristic of semiconductors is presented. • The model determines the thermal and mechanical properties of complex patterns. • Results show a strong correlation between thermal and mechanical properties. • Dielectric bands asymmetrically affect thermal and mechanical behavior. • Machine learning can predict one property from another. As semiconductor performance improves through advanced package designs, it becomes important to consider both thermal and mechanical properties. Better understanding their relationship enhances system design and optimization. This study has introduced a numerical method that takes into account both thermal and mechanical fluxes to construct thermal and mechanical property maps for practical application in semiconductor engineering. Furthermore, this paper investigated the relationship between the two properties using the constructed property maps in commercially available semiconductor packages. Owing to the complexity of packaging design patterns, a coupled isoparametric mapping and machine learning (ML) method was introduced to investigate their effects. The model then determines and investigates the anisotropic equivalent thermal and mechanical properties of the commercialized semiconductor packages with complex pattern designs, according to the package materials, volume fractions of each material, and design patterns. This approach pursues more sophistication and practicality compared to simplified composite structure property evaluation models. Additionally, all processes in the algorithm are automated based on ML methods, making them practically applicable in the semiconductor industry. The study shows that there is a strong correlation between the thermal and mechanical characteristics in the complex package patterns. This relationship was able to form a fairly clear category based on the shape of the dielectric band because the dielectric band had significantly different effects on the thermal and mechanical fluxes. The study discussed the physical implications of the similarities and differences between the two behaviors and validated the results of the equivalent properties through finite element (FE) analysis. Finally, the study cross-validates the relationship by showing that information from one flux behavior can be used to predict the other based on the ML method. Based on the results, this paper can provide a better understanding of thermal and mechanical fluxes in semiconductor package patterns for package design and optimization. [ABSTRACT FROM AUTHOR]

A new cable-damper stopper equipped for Coal-Fired Thermal Power Plants (CFTPPs) was proposed in our previous paper, where a series of shaking table tests were carried out to investigate its seismic performance, so this paper aims to reveal the working mechanism of the stopper from the theoretical and numerical simulation aspects. The stopper is composed of three main components, i.e. a steel cable, a steel block and a viscous damper. First, the nonlinear restraint stiffness of the steel cable to the boiler was derived; second, the critical damping of the stopper, which makes the vibration of the boiler decay exponentially with no oscillation, was derived; third, an iterative method was proposed to globally tune the CFTPP structure, which makes it possible to obtain the optimal parameters of the cable-damper stopper, including the diameter of the steel cable and damping coefficient of the damper. Finally, finite element models were built and time history analyses were conducted to verify the proposed optimization approach. Firstly, the finite element models were proved valid through the comparison between the results of the simulations and the experiments. Then, based on the results of the simulations, the theoretical procedure was validated. The results revealed that the proposed cable-damper stopper reduced the seismic responses of displacements of the top floor and the boiler significantly, about 30.18% and 60.01% respectively compared with their counterparts of CFTPPs without stoppers. [ABSTRACT FROM AUTHOR]

The performance of the Plate Indirect Evaporative Cooler (PIEC) can be effectively improved by incorporating baffles in the dry channel. However, in the dimensional influence of the baffles on PIEC performance there remains a research gap. In order to investigate the impact of baffle dimensions on the wet bulb efficiency, namely the average heat transfer coefficient and the cooling capacity of the PIEC, this paper proposed and verified a three-dimensional numerical model and method based on the species transport model and the Euler wall film model. At the same time, in order to obtain the equilibrium point between the enhanced heat transfer performance and the additional resistance induced by baffles, a comprehensive performance evaluation index is introduced. The results indicate that, under the same conditions, (1) the baffle effect on PIEC performance is significant at a lower inlet air velocity, and the wet bulb efficiency of the PIEC with baffles can be improved by 22.8%; (2) the baffle effect on PIEC performance is negative if its relative length exceeds 60% or the primary air inlet velocity surpasses 4 m/s under the conditions specified in this paper; and (3) the baffle effect on PIEC performance is significant when its channel height is lower and its channel width is larger, and the wet bulb efficiency of the PIEC with baffles can be improved by 29.3%. [ABSTRACT FROM AUTHOR]

The main objective of the present article is to investigate the hydromagnetic particle Reiner-Rivlin fluid flow in an asymmetric (divergent) channel. The non-dimensionalized equations solved by the shooting method. The graphs are intended to examine how different developing parameters affect the thermal and velocity fields. The effects of various parameters on skin friction and the rate of heat transmission along channel walls are investigated using tabular data. The current results are in admirable agreement with the published data. The fluid velocity delineates in the first portion of the channel and rockets up in the second when the inelastic parameter increases. An increase in cross-flow Reynolds number is accompanied by an increasing tendency in particle temperature. Several areas, like metal steam resistors, fiber suspension in paper manufacture, etc., are significantly impacted by the magnetic field's action on Reiner-Rivlin fluid through asymmetric channels. [ABSTRACT FROM AUTHOR]

In this paper, we numerically study the influence of saturable absorber parameters, namely, modulation depth, recovery time, and saturation energy, on the performance of an ultrafast fiber laser that is mode-locked by a hybrid scheme of a saturation absorber (SA) and a nonlinear polarization rotation (NPR). Maps of mode-locked states related to intracavity wave-plates are created to evaluate the operation of hybrid mode-locking under different modulation depths of the SA. Along with the improvement of modulation depth of the SA, the mode-locked pulse results from a combination effect of the SA and NPR. The numerical analysis reveals that the SA parameters can significantly impact the pulse profile, peak power, and operation state. Moreover, they can also impact the selection of NPR mode-locked points, resulting in variation in stable single pulse output. A higher modulation depth can suppress the unstable multiple pulses' operation and convert them into harmonic mode-locked pulses. The obtained results indicate that the selection of appropriate SA parameters can effectively improve the output characteristics of hybrid mode-locked fiber lasers. [ABSTRACT FROM AUTHOR]

Aiming to reduce the impact of substation noise on the lives of surrounding residents, improving the low and middle frequencies acoustic performance of traditional resistive mufflers in indoor substations is significant. The paper is based on the resonance sound absorption mechanism, and for the first time applies multi-frequency resonance noise reduction technology to the research field of indoor substation noise control, proposing a multi-frequency resonant muffling structure. The acoustic performance of the proposed muffler unit is investigated through theoretical and numerical analysis. The measured noise data of the indoor substation is used as sound excitation in the numerical analysis. The results show that at frequencies of 100 Hz, 200 Hz, 300 Hz, 400 Hz, and 500 Hz, the noise in indoor substations is significantly reduced by the multi-frequency resonant muffling structure. The paper provides references for the application of multi-frequency resonant mufflers in the field of noise control of indoor substations. [ABSTRACT FROM AUTHOR]

The rock mechanics parameters are important indicators for risk assessment in tunnel construction. However, rock mechanical parameters estimated by traditional mechanical testing in the field are subject to considerable uncertainties due to limitations testing technology, which can directly lead to unreliable risk assessment results. Deformation data for parametric back analysis is a reliable and efficient method for estimating mechanical parameters of rock masses. Deformation monitoring data used for parameter back analysis is an efficient and reliable method for estimating rock mechanical parameters, but the current research generally suffers from inaccurate constitutive models, confusing selection of input data, and failure to consider the intrinsic correlation of mechanical parameters. In this paper, a deformation-based back analysis method for rock mechanical parameters was proposed by XGBoost with RC. Taking the Changning Tunnel in Yunnan Province, China, as an example, the construction process of the back analysis model was described in detail. To improve the reliability of the sample data, the Ubiquitous-Joint constitutive model was used and a more characteristic deformed data selection method was proposed. Furthermore, the performance of the back analysis model was improved through Bayesian Optimization of hyperparameters and order filtering of Regressor Chain, and the intrinsic correlation of the parameters was effectively considered through the Regressor Chain. The results showed that applying the rock mechanics parameters obtained from the back analysis model to numerical simulation can effectively predict deformation during tunnel construction, and the error rate of deformation prediction was within 10%, which demonstrates the reliability of the method in this paper. This method can be extended to other heavily fractured tunnels. Highlights: Summarized the technical process of back analysis of mechanics parameters based on machine learning, analyzed the current research status, and put forward the existing problems. Through the spatial–temporal effect analysis of deformation of rock mass, a reasonable selection method of the surrounding rock deformation index in the sample data is proposed. The performance of the back analysis model of rock mechanics parameters is effectively improved by hyperparameter optimization of Bayesian and order filtering of Regressor Chains. [ABSTRACT FROM AUTHOR]

Layered rock slope exists widely. Because of its special slope structure, it is prone to bending deformation and toppling failure, which is a serious threat to engineering construction and safety operation. At present, the research of layered rock slope still has great innovation potential. During the construction of Wudongde Hydropower Station on Jinsha River, safety and stability problems such as slope geological structure development, face rock unloading and relaxation, and even slip and large deformation were encountered. Through field exploration, it is found that the rock and soil stratification of the slope on both sides of Wudongde Hydropower Station is highly obvious. At present, there is a lack of research on-site long-term displacement monitoring of layered rock high-steep slope, especially for layered slope in complex hydrogeology and construction environment. In order to strengthen the research on the deformation and stability of layered rock slope, this paper analyzes the measured displacement data of Wudongde hydropower station slope, and establishes three-dimensional geological finite element model with the help of numerical simulation software. The stability of the slope is calculated by combining the finite difference method and the strength reduction method. Finally, the evolution mechanism of the deformation of the layered rock slope is explained according to the geological structure characteristics. The main conclusions of this paper are as follows: the layered slope in the dam reservoir area is prone to deformation under the combined action of long-term construction disturbance and fissure water seepage, and the construction disturbance has a strong influence on the artificial excavation area below 1070 m, and the maximum rock mass deformation and surface displacement in the artificial excavation area of the slope reach 92.2 mm and 312.5 mm, respectively. However, the influence of construction disturbance on the natural mountain above 1070 m is limited, the valley deformation of the natural mountain on the left bank of the reservoir area is higher than that on the right bank, and the cumulative deformation is still less than 20 mm. The influence of seepage on the displacement of the area with higher elevation at the top of the slope is more obvious, and the influence of excavation and other disturbances on the displacement of the artificial excavation area with lower elevation is more obvious. The deformation of the river valley in the water cushion pond behind the dam increases slowly, and the change trend of the field deformation data is mostly consistent with that of the numerical calculation. The horizontal shrinkage of the mountains on both sides shows a contraction trend on the whole, and the maximum horizontal shrinkage calculated by numerical simulation is close to 20 mm, which is located at the elevation of 990 m. [ABSTRACT FROM AUTHOR]

In city-integrated energy systems containing electric–thermal multi-energy sources, the uncertainty of renewable energy sources and the fluctuation of loads challenge the safe, efficient, economic and stable operation of the integrated energy systems. This paper introduces a novel approach for the operation of a carbon capture plant/CHP with PV accommodation within a city-integrated energy system. The proposed strategy aims to maximize the utilization of photovoltaic (PV) power generation and carbon capture equipment, addressing issues related to small-scale CHP climbing constraints and short-term output regulation. Additionally, this paper presents a multi-timescale optimal scheduling strategy, which effectively addresses deviations caused by PV fluctuations and load changes. This was achieved through a detailed analysis of the CHP climbing constraints, carbon capture equipment operation and real-time characteristics of PV power generation. This paper introduces a fully distributed neural dynamics-based optimization algorithm designed to address multi-timescale optimization challenges. Utilizing rolling cycles, this algorithm computes both day-ahead and real-time scheduling outcomes for urban integrated energy systems. Theoretical analyses and numerical simulations were conducted to validate the precision and efficacy of the proposed model and algorithm. These analyses quantitatively evaluate the scheduling performance of PV power generation and carbon capture CHP systems across various timescales. [ABSTRACT FROM AUTHOR]

Introduction: This paper presents a scoping review of empirical Germanlanguage research concerning the professionalization of Physical Education Teachers (PETs) and Physical Education Teacher Education (PETE). This paper provides detailed insight into research activities in the field and gives recommendations for further research. It points out possible thematic, methodical and theoretical commonalities and divergences between German-speaking and international/Anglophone discourses, as well as shared challenges for future research. Methods: Using a scoping review methodology, the original framework was adjusted and extended to fit the needs of a transparent and substantiated inductive approach to thematic mapping. Based on a definition of research on PETE, we formulated inclusion and exclusion criteria and manually searched articles in six periodical Germanlanguage journals and conference proceedings. 160 empirical articles from the period 2010 to 2018 were selected. First, they were analyzed and charted in two stages. In a descriptive analysis following a deductive approach, the research field was mapped along with the categories chronological–numerical development, methods, samples, participants, authorship, and theoretical frameworks. In a thematic synthesis process following an inductive paradigm, a two-dimensional categorization system was developed along which the articles were charted. This system not only enables reporting about numerical findings but also provides information about the nature and interrelation of research domains and topics. Second, Anglophone literature reviews and handbook articles served as a point of reference to compare and discuss results from the German language to the Anglophone discourse. Special attention was given to thematic comparisons concerning similar and differing research trends and challenges. Results: The review shows research foci and identifiable gaps in accordance with present developments in educational policy as well as a significant increase in numerical output in the evaluated time period. While research on particular phases and moments of PETE gathered substantial insights, results especially regarding the understanding of long-term, biographical, professional developments of PETs are lacking in both research fields. To better understand long-term educational developments of PETs and how they are influenced remains the main challenge for future research. While German-language and Anglophone research cultures both come from their own historical, theoretical and methodological traditions, several attempts to open discourses concerning theoretical frameworks, methodological developments and research foci were revealed. One example is the development of qualitative methods to research implicit orientations and constructs, which originate from a shared qualitative history. This can potentially lead to a better understanding of educational processes and how these implicit constructs effect teaching. Discussion and conclusion: With finding and outlining commonalities and divergences between German-language and Anglophone research, this review provides a basis and status quo outlining possibilities for further research, cooperation and exchange. Moreover, similar trends and challenges were identified on a meta-level. Especially concerning theoretical backgrounds and methodical developments, the different research communities can further mutually improve each other and should enhance interaction and exchange. The results outline several possibilities for mutual enrichment. [ABSTRACT FROM AUTHOR]

This paper introduces a novel approach for analyzing efficient numerical solution of a class of singularly perturbed parabolic convection-diffusion PDEs having a finite jump discontinuity mostly in the source function at the interior of the spatial domain. These PDEs often appear in mathematical modeling of the semiconductor devices; and solutions of such problems usually exhibit a weak interior layer at one side of the point of discontinuity along with a boundary layer at one side of the spatial domain. The prime objectives of this paper are to overcome the theoretical challenge related to the monotonocity of the finite difference operator which utilizes one-sided second-order difference operators at the interface point; and also to establish higher-order numerical approximation in space, regardless of smaller and larger values of the parameter ε. Proving discrete maximum principle of the proposed difference operator is found to be challenging task on the standard Shishkin mesh adapted to both boundary and weak interior layers. We overcome this difficulty by constructing a special non-uniform mesh, called modified layer-adapted mesh; and hereby establish the stability as well as the parameter-uniform error estimate in the discrete supremum norm. Finally, the theoretical estimate is verified with numerical results for test examples with and without the exact solution. Moreover, numerical results are obtained for the semilinear PDEs and also compared with the implicit upwind scheme to exhibit the efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The authors present numerical analysis of singularly perturbed parabolic problems. The previous papers in this direction focussed on the convection-diffusion problems with regular type of boundary layers. It is very difficult and almost impossible as stated in the literature, e.g, in Chapter 14 of 'Fitted numerical methods for singular perturbation problems: error estimates in the maximum norm for linear problems in one and two dimensions' (1996) by Miller, John JH and O'Riordan, Eugene and Shishkin, Grigorii I, to capture singularities due to parabolic layers and develop a robust scheme for reaction-diffusion problems with general values of space shifts. The work is in progress now and this is the first paper in this direction. In this work, we are investigating such problems and develop a robust numerical scheme using Mickens's non-standard finite difference scheme and special mesh. Furthermore, numerical examples have been presented to verify the theoretical findings. [ABSTRACT FROM AUTHOR]

The paper deals with numerical analysis of the effect of stress state and loading direction with respect to the rolling direction on damage and fracture behavior of anisotropic metals. The continuum damage model has been enhanced to take into account the influence of production-induced anisotropies and loading direction on damage criteria and on evolution equations of damage strains. Constitutive parameters are determined using experimental results taken from tests with uni- and biaxially loaded specimens. The focus of the paper is on three-dimensional micro-mechanical numerical analyses of micro-defect-containing representative volume elements covering a wide range of stress states. These calculations lead to more insight in the different damage and failure processes on the micro-scale and their influence on the macroscopic damage laws. With the obtained numerical results it is possible to detect general trends, to propose governing equations for the damage criteria, to develop evolution equations for the damage strains, and to identify constitutive parameters of the anisotropic material model. It is shown that the anisotropic behavior and the loading direction with respect to the principal axes of anisotropy affect the evolution of damage mechanisms on the micro-level as well as the corresponding damage strains. [ABSTRACT FROM AUTHOR]

In this research paper, the authors wish to examine the effects of couple stress on hybrid nanofluid considering magnetohydrodynamic three-dimensional transient flow between two parallel plates. Stretching of the lower plate causes fluid flow in the channel. The fluid flow model is shown in mathematical form using a set of coupled nonlinear partial differential equations, which are then translated into coupled nonlinear ordinary differential equations using the proper transformation. The authors used the spectral quasi linearization method (SQLM), an effective numerical technique, to solve the updated equations and study the effects of various flow parameters on fluid temperature and velocity. The Nusselt number and skin friction coefficients were also investigated from an engineering standpoint. The generated solutions are verified using the residual analysis. Statistical analysis is performed on the skin-friction coefficients and the Nusselt number using quadratic regression models. [ABSTRACT FROM AUTHOR]

This paper is devoted to a study of a history-dependent mixed hemivariational-variational inequality arising in contact mechanics. The contact problem concerns the deformation of a viscoelastic body with long memory, subject to a general friction law on one part of the boundary and a frictionless Signorini condition on another part of the boundary. The solution existence and uniqueness of the history-dependent mixed hemivariational-variational inequality based on a Lagrange multiplier approach are proved. Then, a fully discrete scheme is introduced and studied. The trapezoidal rule is used to approximate the integral in the history-dependent operator. For the spatial discretization, the linear finite elements are used to discretize the displacement field, and dual basis functions are used in the approximation of the Lagrange multiplier. Optimal order error estimates are derived for the displacement and the Lagrange multiplier under appropriate solution regularity assumptions. Numerical results are presented to illustrate the theoretical prediction of the convergence orders. [ABSTRACT FROM AUTHOR]

The formation of ice on the surface of the metallic casing of high-end equipment poses a potential threat to its operational safety and stability. One important factor that contributes to bonding failure at the ice-metal interface is stress concentration. This paper aims to investigate the effect of stress concentration on the bonding failure behavior at the ice-metal interface through numerical analysis. First, the forms of bonding failure are categorized. Afterwards, the stress distribution state at the corners of the ice-metal interface is determined by the interfacial stress singularity. Finally, numerical analysis is carried out to investigate the thermal stress distribution law at the corners of the interface during the cooling process of the ice-metal bonding, so as to elucidate the induced mechanism of the interfacial stress state on the bonding failure. This study can provide some reference and guidelines for the study of bonding failure at the ice-metal interface. [ABSTRACT FROM AUTHOR]

This paper deals with the approximations of the functions by generalized Durrmeyer operators of Szász–Mirakjan, which are linear positive operators. Several approximation results are presented well, and we estimate the approximation properties along with the order of approximation and the convergence theorem of the proposed operators. For an explicit explanation of the operators, we determine the properties using the weight function. A quantitative approach is discussed for the operators; quantitative Voronovskaya type and Grüss type theorems are established, showing the operators' more efficient work. We investigate the A$$ A $$‐statistical convergence properties for the said operators, including the rate of approximation in a statistical sense. An important property for the rate of convergence of the operators is obtained in terms of the function with a derivative of the bounded variation. At last, the graphical representations and numerical analysis are discussed and shown to support our theoretical findings. [ABSTRACT FROM AUTHOR]

This paper presents numerical analysis of the discrete fundamental solution of the discrete Laplace operator on a rectangular lattice. Additionally, to provide estimates in interior and exterior domains, two different regularisations of the discrete fundamental solution are considered. Estimates for the absolute difference and lp‐estimates are constructed for both regularisations. Thus, this work extends the classical results in the discrete potential theory to the case of a rectangular lattice and serves as a basis for future convergence analysis of the method of discrete potentials on rectangular lattices. [ABSTRACT FROM AUTHOR]

Micro-mixers and piezoelectric pumps have been studied as independent parts, which achieves only single mixing or pumping functions. A new valveless piezoelectric mixing pump (VPMP) driven by a sinusoidal signal is proposed in this paper to achieve a structure with both pumping and mixing functions. It accomplishes this by placing obstacles in the pump chamber and in the flow channel then adding active mixing. Because it is small in size, has a simple structure and is easy to control, it can be used in micro mixing applications. In this study, numerical simulation analysis using the Fluent software tests if the new VPMP has good mixing and pumping performance, and analyzes the effect of the obstacles. Simultaneously, the results of numerical simulation are verified with experiments. It was proven that the flow rate of the VPMP can reach 12.26 mL/min, and that the liquid can achieve uniform mixing. Moreover, the obstacle placed in the pump chamber has a more obvious impact on the mixing capability, and the obstacle placed in the channel has a more obvious impact on the flow rate. In addition, with the increase of the amplitude of driving signal, the flow rate of the VPMP increased correspondingly. With the increase of the frequency, the flow rate first increased and then decreased. The capability of mixing increased with an increase of working frequency. The experimental results showed that the VPMP can achieve good pumping and mixing performance, and that one structure can possess both mixing and pumping functions. [ABSTRACT FROM AUTHOR]

Regarding the damage incurred by aluminum alloy latticed shells under fire loads, a crucial aspect in assessing structural integrity is examining the residual bearing capacity of aluminum alloy gusset (AAG) joints. Consequently, this paper conducted experimental and numerical analyses on the post-fire flexural behavior of AAG joints. Initially, twelve AAG joints underwent post-fire tests, revealing that the failure patterns differed between thin-plate joints (exhibiting block tearing of gusset plates) and thick-plate joints (exhibiting member buckling). Notably, the initial stiffness approximately remained constant, while a trilinear relationship emerged between the ultimate flexural bearing capacity and the maximum post-fire temperature. Subsequently, finite element (FE) analysis was carried out, and the accuracy of FE models was verified by comparing the FE results with the test results. A comprehensive parametric analysis, considering various plate thicknesses, post-fire temperatures, and aluminum alloy brands, was then conducted. Ultimately, employing statistical regression, theoretical equations were formulated to estimate both bending stiffness and bearing capacity for AAG joints after exposure to fire. [ABSTRACT FROM AUTHOR]

In the era of open innovation, it is of great significance to analyse strategic trade-offs for enterprises' technology acquisition between external and internal. This paper considers the relative pay-offs amongst two manufacturers' selection for their respective scarce technology of the Internet of Things, using game theory models and numerical analysis. In addition to self-innovation relying on internal resources, enterprises can obtain technology from external sources, including technology imported from a third party or cross-licensing with its competitor. Unlike empirical analysis, this study focuses on the strategic firms' interactions at the micro-level study and operational considerations, such as the factors influencing the mode of enterprise technology acquisition, firm competition and cooperation behaviour mechanism, and the selection of innovation initiators. The findings provide implications for competitive enterprises in high-tech industries to acquire complementary technologies by identifying what conditions lead to win-win outcomes. In particular, firms can adjust their licensing levels under certain conditions to adapt to the disparities in each other's development capabilities, thus achieving cross-licensing agreements. [ABSTRACT FROM AUTHOR]

This article presents a novel approach using the Fibonacci wavelet collocation method (FWCM) for the numerical solution of Emden-Fowler-type equations. The Emden-Fowler equations are a class of nonlinear differential equations that arise in various fields of science and engineering, particularly in astrophysics and fluid dynamics. Due to their nonlinear and singular nature, the conventional approaches to solving these equations encounter difficulties. This method is particularly effective in handling problems with singularities, as it adapts naturally to the local behaviour of the solution. Here, we introduced the Fibonacci wavelet collocation method as a powerful numerical technique for tackling Emden-Fowler-type equations. The Fibonacci wavelet basis functions possess remarkable properties, including compact support, making them well-suited for approximating solutions to differential equations. The main advantage of this approach lies in its ability to reduce the computational complexity associated with solving Emden-Fowler equations, resulting in accurate and efficient solutions. Comparative analyses with other established numerical methods reveal its superior accuracy and convergence rate performance. Further, several examples demonstrate the method's flexibility when dealing with different singularity levels. This paper contributes to numerical analysis by introducing the Fibonacci wavelet method as a robust tool for solving Emden-Fowler-type equations. [ABSTRACT FROM AUTHOR]

We consider a one-dimensional singularly perturbed 4th order problem with the additional feature of a shift term. An expansion into a smooth term, boundary layers and an inner layer yields a formal solution decomposition, and together with a stability result we have estimates for the subsequent numerical analysis. With classical layer adapted meshes we present a numerical method that achieves supercloseness and optimal convergence orders in the associated energy norm. We also consider coarser meshes in view of the weak layers. Some numerical examples conclude the paper and support the theory. [ABSTRACT FROM AUTHOR]

In this paper, we study a Cauchy problem of fractional diffusion equation concerning fractional Laplacian. We prove the existence and uniqueness of solution to the problem under investigation in Hölder space. Then we apply the Monte Carlo method to solving this Cauchy problem. For the problem with free force term, we derive an unbiased scheme which only produces the statistic error. For the problem with inhomogeneous force term, we establish the simple and high-order jump-adapted schemes by approximating the trajectory of symmetric stable process. The error estimates of these two jump-adapted schemes are given based on the Hölder regularity of the solution. Numerical experiments including even one hundred dimensional case confirm the theoretical analysis and show the numerical efficiency. [ABSTRACT FROM AUTHOR]

In this paper, we first investigate the well-posedness and regularity of mild solution to a stochastic active fluids model driven by the additive noise. A fully-discrete scheme is proposed for solving the given model, which is based on the finite element method for spatial discretization and the backward Euler method for temporal discretization. By overcoming the difficulty of error analysis caused by the discrete Laplacian operator, we obtain the convergence results of the developed scheme. Finally, some numerical examples are provided to validate the theoretical results and we also simulate the motion states of the active fluids. [ABSTRACT FROM AUTHOR]

This paper presents a numerical analysis, using the rigorous-coupled-wave-analysis method, of microwave and far-IR radiation scattering on thin conductive films of nanometer thickness under the condition of total internal reflection. Transmittance, reflection, and absorption studies have shown the possibility of overcoming the 50% absorption limit with frequency-independent behavior; the absorption above the critical angle reaches values greater than 90%. In addition, the influence of such thin metal-dielectric structure on the Goos–Hänchen shift is considered. At maximum absorption, calculations showed its absence in both TE and TM polarizations. The numerical analysis was carried out for a plane wave and for a 500 cm diameter beam. [ABSTRACT FROM AUTHOR]

The relationship between convexity and symmetry is widely recognized. In fuzzy theory, both concepts exhibit similar behavior. It is crucial to remember that real and interval-valued mappings are special instances of fuzzy-number-valued mappings ( F - N - V - M s ), as fuzzy theory relies on the unit interval, which is crucial to resolving problems with interval analysis and fuzzy number theory. In this paper, a new harmonic convexities class of fuzzy numbers has been introduced via up and down relation. We show several Hermite–Hadamard ( H ⋅ H ) and Fejér-type inequalities by the implementation of fuzzy Aumann integrals using the newly defined class of convexities. Some nontrivial examples are also presented to validate the main outcomes. [ABSTRACT FROM AUTHOR]

Physical experiments in classrooms have many benefits for student learning, including increased student interest, participation and knowledge retention. While experiments are common in engineering and physics classes, they are seldom used in first-year calculus, where the focus is on solving problems analytically and, occasionally, numerically. In this paper, we detail a three-pronged lesson introducing differential equations using analytical, numerical and experimental approaches in a large first-year differential calculus course. Presenting the three approaches in succession allows students to evaluate advantages and disadvantages. The lesson incorporates software and programming and provides opportunities for active, experiential, team-based learning. [ABSTRACT FROM AUTHOR]

The report of the 20th National Congress of the Communist Party of China pointed out that it is necessary to accelerate the construction of digital China, and actively develop equipment intelligence, digitalization, and high‐end equipment manufacturing. With the construction of a new round of digital China, the safety of digital technology and high‐end equipment is particularly important for power grid. Transformer is an important link of power grid operation. The destructive thermal failure of transformer has become a hot research issue in the power industry. At the same time, there are more and more power electronic equipment in the power grid, which makes the regulation and control more and more complicated. Taking a 1000 kVA oil‐immersed transformer as an example, the magnetic, current, and thermal multi field coupling numerical analysis method is first used to simulate and analyse the operation status of the transformer. By comparing the simulation results with the monitoring data results, the error of the results is controlled within 5%. Finally, the multi‐state characteristic parameters of the transformer are monitored through sensors, and the numerical simulation analysis results are integrated with the state monitoring results to build a transformer thermal life loss assessment system. The method in this paper can evaluate and analyse the running state of transformer in real time, which is of great significance for the power company to formulate the treatment measures. [ABSTRACT FROM AUTHOR]

Formerly the geometry was based on shapes, but since the last centuries this founding mathematical science deals with transformations, projections, and mappings. Projective geometry identifies a line with a single point, like the perspective on the horizon line and, due to this fact, it requires a restructuring of the real mathematical and numerical analysis. In particular, the problem of interpolating data must be refocused. In this paper, we define a linear structure along with a metric on a projective space, and prove that the space thus constructed is complete. Then, we consider an iterated function system giving rise to a fractal interpolation function of a set of data. [ABSTRACT FROM AUTHOR]

This paper presents the development of a framework for the parametric design of tunnels using geographic information system (GIS) mapping and building information modelling (BIM). According to the framework, a parametric representation of each system component (e.g., layers of rock mass, size of excavation, topography, fault geometry, primary lining, secondary lining, rock bolts, etc.) can be incorporated in the GIS model with high levels of detail and used for the automatic generation of numerical models for the design of tunnel construction. This parametric evaluation allows the designer to consider several levels of detail for each component, for the efficient design and process optimization in conventional tunneling. Information between parametric analysis and numerical simulations can be freely exchanged with significantly reduced computational effort while results can be exported into BIM. It is anticipated that the proposed framework could lead to a comprehensive, yet efficient analysis of complex conventional tunneling project using parametric evaluations at the early design stages. [ABSTRACT FROM AUTHOR]

Utilizing broadband low Earth orbit satellite signals in an opportunistic manner for navigation is becoming increasingly popular. This paper deals with a particularly useful approach for navigation based on satellite signals of opportunity, which uses carrier Doppler-shift observables. We provide analytically derived and simplified formulas for the Jacobian involved in the numerical computation of the navigation solution and derive a global navigation satellite system-like dilution-of-precision metric that can be used to assess accuracy. A numerical study provides preliminary computational results. [ABSTRACT FROM AUTHOR]

In the process of lower coal roadway support under double gobs in close coal seams, there are problems such as the whole destruction of the lower coal seam and the intermediate strata, the thin roof of the lower coal roadway with the smaller support space, the upper rock of the lower coal roadway without anchor bearing layer, the roof falling, the anchor cable offing, and so on. On the basis of the engineering background of No. 11103 haulage roadway in Fenxi coal mine, the research methods of theoretical modeling analysis, numerical simulation analysis and field engineering test are comprehensively adopted. In this paper, the layout of the roadway with floor insertion in the lower coal seam, the distribution characteristics of surrounding rock deviatoric stress, the control principle of broken surrounding rock and the coupling support method of shed–cable–prop are systematically studied. The study shows that many measures are needed to ensure the stability of the surrounding rock in the strong mining roadway of the lower coal seam. The lower coal seam roadway section was modified from the original rectangular section to adopt an arched section to counteract the broken roof. The staggered position of the lower coal seam roadway layout was modified from the original coal roadway position to a coal–rock roadway, so as to avoid the area of high deviatoric stress in the coal pillar and the area of crushed coal body, and to leave an effective support space for the roof. The support scheme of the lower coal seam roadway was improved to use anchor cable and single prop to support the weak section of U‐type steel shed with local coupling, and realize unequal force coupling by adjusting the size of the force at different coupling points. In the field monitoring the deformation of the roadway is small, and the support effect is good. [ABSTRACT FROM AUTHOR]

From the literature it is known that orthogonal polynomials as the Jacobi polynomials can be expressed by hypergeometric series. In this paper, the authors derive several contiguous relations for terminating multivariate hypergeometric series. With these contiguous relations one can prove several recursion formulas of those series. This theoretical result allows to compute integrals over products of Jacobi polynomials in a very efficient recursive way. Moreover, the authors present an application to numerical analysis where it can be used in algorithms which compute the approximate solution of boundary value problem of partial differential equations by means of the finite elements method. With the aid of the contiguous relations, the approximate solution can be computed much faster than using numerical integration. A numerical example illustrates this effect. [ABSTRACT FROM AUTHOR]

This paper presents a stochastic analysis of the size effect on the nominal strength of quasibrittle structures with a large preexisting notch. This type of scaling behavior has been extensively studied within a deterministic framework. Little attention is paid to stochastic analysis, which is essential for reliability-based analysis and design of engineering structures. Stochastic finite element simulations are performed to study the failure of geometrically similar beams of different sizes. The numerical analysis uses a continuum damage model, in which the tensile strength and fracture energy are modeled by homogeneous random fields. Different correlation lengths are considered as a parametric study. The analysis yields the size effects on the mean and coefficient of variation (CoV) of the nominal structural strength. It is shown that the size effect on the mean strength agrees well with the Bazant size effect model. The simulation predicts a strong size effect on the CoV of the nominal strength. Small-, intermediate-, and large-size asymptotes are derived analytically for the scaling behavior of the strength CoV. Based on these asymptotes, an approximate scaling equation is proposed for the CoV of nominal strength. The effect of the correlation length on the simulated failure behavior is discussed. [ABSTRACT FROM AUTHOR]

In this paper, an analysis of performance acceleration of an external laser source (ELS) model based polymer fiber gratings (PFGs) by reducing the turn-on delay time (TDelay) is successfully investigated numerically by optimizing model parameters. In contrast to all previous studies that relied either on approximate or experimental equations, the analysis was based on an exact numerical formula. The analysis is based on the investigation of the effect of diode injected current (Iin j), temperature (T), recombination rate coefficients (i.e. Anr, B, and C), and optical feedback (OFB) level. Results have demonstrated that by optimizing model parameters the Delay can be controlled and reduced effectively. [ABSTRACT FROM AUTHOR]

This paper deals with the mathematical analysis of Tuberculosis by using fractal fractional operator. Mycobacterium TB is the bacteria that causes tuberculosis. This airborne illness mostly impacts the lungs but may extend to other body organs. When the infected individual coughs, sneezes or speaks, the bacterium gets released into the air and travels from one person to another. Five classes have been formulated to study the dynamics of this disease: susceptible class, infected of DS, infected of MDR, isolated class, and recovered class. To study the suggested fractal fractional model’s wellposedness associated with existence results, and boundedness of solutions. Further, the invariant region of the considered model, positive solutions, equilibrium point, and reproduction number. One would typically employ a fractional calculus approach to obtain numerical solutions for the fractional order Tuberculosis model using the Adams-Bashforth-Moulton method. The fractional order derivatives in the model can be approximated using appropriate numerical schemes designed for fractional order differential equations. [ABSTRACT FROM AUTHOR]

As a basic parameter of rock, the rock bridge angle plays an important role in maintaining the stability of rock masses. To study the size effect of rock bridge angle on the uniaxial compressive strength of rocks, this paper adopts the principle of regression analysis and combines numerical simulation to carry out relevant research. The research results indicate that: (1) the uniaxial compressive strength decreases with the increase of the rock bridge angle, showing a power function relationship; (2) The uniaxial compressive strength decreases with the increase of rock size and tends to stabilize when the rock size is greater than 350 mm, showing a significant size effect. (3) The fluctuation coefficient of compressive strength increases with the increase of rock bridge angle and decreases with the increase of rock size; When the rock size is 350 mm, the fluctuation coefficient is less than 5%; (4) The characteristic compressive strength and characteristic size both increase with the increase of the rock bridge angle. [ABSTRACT FROM AUTHOR]

The time fractional Schrödinger equation contributes to our understanding of complex quantum systems, anomalous diffusion processes, and the application of fractional calculus in physics and cubic B-spline is a versatile tool in numerical analysis and computer graphics. This paper introduces a numerical method for solving the time fractional Schrödinger equation using B-spline functions and the Atangana-Baleanu fractional derivative. The proposed method employs a finite difference scheme to discretize the fractional derivative in time, while a θ-weighted scheme is used to discretize the space directions. The efficiency of the method is demonstrated through numerical results, and error norms are examined at various values of the non-integer parameter, temporal directions, and spatial directions. [ABSTRACT FROM AUTHOR]

Underwater acoustic vector sensors (UAVSs) are increasingly utilized for remote passive sonar detection, but the accuracy of direction-of-arrival (DOA) estimation remains a challenging problem, particularly under low signal-to-noise ratio (SNR) conditions and complex background noise. In this paper, a comprehensive theoretical analysis is conducted on UAVS signal preprocessing subjected to gain-phase uncertainties for average acoustic intensity measurement (AAIM) and complex acoustic intensity measurement (CAIM)-based vector DOA estimation, aiming to explain the theoretical restrictions of intensity-based vector acoustic preprocessing approaches. On this basis, a generalized vector acoustic preprocessing optimization model is established in which the principle can be described as "maximizing the denoising performance under the constraints of an equivalent amplitude-gain response and phase-bias response". A novel vector acoustic preprocessing method named linear matched stochastic resonance (LMSR) is proposed within the framework of matched stochastic resonance theory, which can naturally guarantee the linear gain-phase restrictions, as well achieving effective denoising performance. Numerical analyses demonstrate the superior vector DOA estimation performance of our proposed LMSR-AAIM and LMSR-CAIM methods in comparison to classical intensity-based AAIM and CAIM methods, especially under low-SNR conditions and non-Gaussian impulsive noise circumstances. Experimental verification conducted in the South China Sea further verifies its the effectiveness for practical application. This work can lay a solid foundation to break through the challenges of underwater remote vector acoustic DOA estimation under low-SNR conditions and complex ocean ambient noise and can provide important guidance for future research work. [ABSTRACT FROM AUTHOR]