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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]

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]

The QZ algorithm computes the generalized Schur form of a matrix pencil. It is an iterative algorithm and, at some point, it must decide when to deflate, that is when a generalized eigenvalue has converged and to move on to another one. Choosing a deflation criterion that makes this decision is nontrivial. If it is too strict, the algorithm might waste iterations on already converged eigenvalues. If it is not strict enough, the computed eigenvalues might not have full accuracy. Additionally, the criterion should not be computationally expensive to evaluate. There are two commonly used criteria: the elementwise criterion and the normwise criterion. This paper introduces a new deflation criterion based on the size of and the gap between the eigenvalues. We call this new deflation criterion the strict criterion. This new criterion for QZ is analogous to the criterion derived by Ahues and Tisseur for the QR algorithm. Theoretical arguments and numerical experiments suggest that the strict criterion outperforms the normwise and elementwise criteria in terms of accuracy. We also provide an example where the accuracy of the generalized eigenvalues using the elementwise or the normwise criteria is less than two digits whereas the strict criterion leads to generalized eigenvalues which are almost accurate to the working precision. Additionally, this paper evaluates some commonly used criteria for infinite eigenvalues. [ABSTRACT FROM AUTHOR]

Reinforced concrete flat slab projects usually require openings close to the columns for electrical and hydraulic installations. Since such openings reduce the punching shear of slabs, a comprehensive study is needed. In this paper, numerical models of slabs tested in literature were elaborated upon, using the commercial software in finite elements DIANA. The physical nonlinearity of the materials was considered. After the calibration and validation of the numerical parameters related to concrete and reinforcement, 62 numerical models were created for performing a parametric analysis. The numerical analysis aimed to study the effect of openings close to the columns and verify the punching resistance reduction. In this parametric study, the main variables were the compressive strength of the concrete, the bending reinforcement ratio, the number of openings, and the distance from the openings to the column's face. Finally, the numerical results obtained were compared with the punching strength values provided by the main structural design codes, viz., NBR 6118 (2014), Eurocode 2 (2004), ACI 318 (2019), fib Model Code (2010), and the next generation of Eurocode 2, which are constantly questioned in academic papers regarding their safety. [ABSTRACT FROM AUTHOR]

ABSTRACT The next-generation seismic imaging algorithms will consider multiple scattering as indispensable information, being referred to as Full-Wavefield Migration. In addition, these algorithms will also include autonomous velocity updating in the migration process, being referred to as Joint Migration Inversion. Full-Wavefield Migration and Joint Migration Inversion address the industrial needs to improve images of very complex reservoirs as well as the industrial ambition to produce these images in a more automatic manner (automation in seismic processing). In this vision paper on seismic imaging, Full-Wavefield Migration and Joint Migration Inversion are formulated in terms of a closed-loop estimation algorithm that can be physically explained by an iterative double focusing process (full-wavefield common-focus-point technology). A critical module in this formulation is forward modelling, allowing feedback from migrated output to unmigrated input (closing the loop). For this purpose, a full-wavefield modelling module has been developed, which utilizes an operator description of complex geology. The full-wavefield modelling module is pre-eminently suited to function in the feedback path of a closed-loop migration algorithm. 'The Future of Seismic Imaging' is presented as a coherent trilogy, proposing the migration framework of the future in three consecutive parts. In Part I, it was shown that the proposed full-wavefield modelling module algorithm differs fundamentally from finite-difference modelling because velocities and densities need not be provided. Instead, an operator description of the subsurface is used. In addition, the concept of reverse modelling was introduced. In Part II, it is shown how the theory of Primary Wavefield Migration can be extended to Full-Wavefield Migration by correcting for angle-dependent transmission effects and by utilizing multiple scattering. The potential of the Full-Wavefield Migration algorithm is illustrated with numerical examples. A multidirectional migration strategy is proposed that navigates the Full-Wavefield Migration algorithm through the seismic data cube in different directions. [ABSTRACT FROM AUTHOR]

ABSTRACT The next generation seismic imaging algorithms will consider multiple scattering as indispensable information, referred to as Full Wavefield Migration. In addition, these algorithms will also include autonomous velocity updating in the migration process, referred to as Joint Migration Inversion. Full wavefield migration and joint migration inversion address the industrial needs of improving images of very complex reservoirs as well as the industry ambition of producing these images in a more automatic manner ('automation in seismic processing'). In this vision paper on seismic imaging, full wavefield migration and joint migration inversion are formulated in terms of a closed-loop, estimation algorithm that can be physically explained by an iterative double focusing process (full wavefield Common-Focus-Point technology). A critical module in this formulation is forward modelling, allowing feedback from migrated output to unmigrated input ('closing the loop'). For this purpose a full wavefield modelling module has been developed that utilizes an operator description of complex geology. Full wavefield modelling module is pre-eminently suited to function in the feedback path of a closed-loop migration algorithm. 'The Future of Seismic Imaging' is presented as a coherent trilogy, proposing in three consecutive parts the migration framework of the future. In part I it was shown that the proposed full wavefield modelling module algorithm differs fundamentally from finite difference modelling, as velocities and densities need not be provided. Instead, full wavefield modelling module uses an operator description of the subsurface. In Part II it was shown how the theory of Primary Wavefield Migration can be extended to Full Wavefield Migration by correcting for elastic transmission effects and by utilizing multiple scattering. In Part III it is shown how the full wavefield migration technology can be extended to Joint Migration Inversion, allowing full wavefield migration of blended data without knowledge of the velocity. Velocities are part of the joint migration inversion output, being obtained by an operator-driven parametric inversion process. The potential of the proposed joint migration inversion algorithm is illustrated with numerical examples. [ABSTRACT FROM AUTHOR]

We show abstract versions for Banach couples of several limiting compact interpolation theorems established by Edmunds and Opic for couples of [ABSTRACT FROM AUTHOR]

The evolution of Artificial Intelligence of Things (AIoT) pushes connectivity from human‐to‐things and things‐to‐things, to AI‐to‐things, has resulted in more complex physical networks and logical associations. This has driven the demand for Internet of Things (IoT) devices with powerful edge data processing capabilities, leading to exponential growth in device quantity and data generation. However, conventional data preprocessing methods, such as data compression and encoding, often require edge devices to allocate computational resources for decoding. Additionally, some lossy compression methods, like JPEG, may result in the loss of important information, which has negative impact on the AI training. To address these challenges, this paper proposes a two‐step attribute reduction approach, targeting devices and dimensions, to reduce the massive amount of data in the AIoT network while avoiding unnecessary utilization of edge device resources for decoding. The device‐oriented and dimension‐oriented attribute reductions identify important devices and dimensions, respectively, to mitigate the multimodal interference caused by the large‐scale devices in the AIoT network and the curse of dimensionality associated with high‐dimensional AIoT data. Numerical results and analysis show that this approach effectively eliminates redundant devices and numerous dimensions in the AIoT network while maintaining the basic data correlation. [ABSTRACT FROM AUTHOR]

This paper presents the findings of a large‐scale experimental study that focus on assessing structural behavior of reinforced concrete (RC) cantilever slabs with carbon/epoxy fiber‐reinforced polymer (CFRP) composite strips using a near‐surface‐mounted (NSM) approach. The NSM/CFRP system evaluated in this study was implemented in strengthening the shoulders of the Slide Canyon Bridge in California, USA. The experimental phase is divided into two main parts: (i) determining the design parameters for NSM, including the bondline strength through pull‐out tests, and (ii) conducting a practical evaluation of the bending behavior of original and retrofitted RC cantilever slabs, each with varying NSM reinforcement and three different development lengths. Results of this study indicated that the use of NSM‐CFRP has a considerable benefit in that it significantly improves ductility and changes the failure mode of the unstrengthened RC slab from the typical brittle shear‐based failure mode to a more ductile flexural‐based failure mode. The large‐scale slab specimens' performances, which had different development lengths, showed little variance, except for the slab specimen with a development length of 457.0 mm that exhibited an appreciable flexural stiffness as compared to other specimens evaluated in this study. In order to simulate the serviceability and ultimate behavior of the RC slab specimens, linear and nonlinear finite element analyses were performed. A satisfactory agreement between numerical and experimental results was achieved especially at load level prior the initiation of large‐size cracks. [ABSTRACT FROM AUTHOR]

Liquid sodium hybrid bearing is mechanical pump shaft bottom key support components, that play a balanced radial force of the impeller by fluid effect, in order to improve the bearing performance, based on the calculation model, simulation analysis, structure improvement and other aspects of analysis, this paper based on the theory of fluid mechanics of bearing finite element model for numerical calculation and analysis of flow field. Under different eccentricities and vibration velocities, the influence of structure improvement on bearing capacity is analysed. The results show that the bearing capacity of the liquid sodium hybrid bearing is mainly the hydrostatic bearing capacity, and the hydrodynamic pressure only plays an auxiliary role. After the improvement of the load‐bearing structure, the load‐bearing capacity is increased by 4%–7.3%. And the leakage is reduced by 27%–38% when the depth of the annular groove is 0.6 mm. [ABSTRACT FROM AUTHOR]

This paper proposes and analyzes an uncoupled and linearized compact finite difference scheme for the generalized dissipative symmetric regularized long‐wave (GDSRLW) equations. The unique solvability and some a priori estimates of the proposed difference scheme are rigorously proved based on the mathematical induction method. To obtain the ‖·‖∞$$ {\left\Vert \cdotp \right\Vert}_{\infty } $$‐norm estimation of numerical solutions, the discrete energy method is used to prove the convergence and stability of the difference scheme. The proposed difference scheme preserves the original energy dissipation property, and the convergence of the scheme is proved to be fourth‐order in space and second‐order in time in the ‖·‖∞$$ {\left\Vert \cdotp \right\Vert}_{\infty } $$‐norm for both u$$ u $$ and ρ$$ \rho $$. Some numerical experiments are given to verify the theoretical analysis and the reliability of the proposed difference scheme. [ABSTRACT FROM AUTHOR]

For all humanity, the sudden outbreak of Corona Virus Disease 2019 has been an important problem. Timely and effective media coverage is considered to be one of the effective approaches to control the spread of epidemic in early stage. In this paper, a Sentiment‐enabled Susceptible‐Exposed‐Infected‐Recovered (SEIR) model is established to reveal the relationship between the propagation of the epidemic and media coverage. The authors take the positive and negative media coverage into consideration when implementing the Sentiment‐enabled SEIR model. This model is constructed by parameterizing the number of current confirmed cases, cumulative cured cases, cumulative deaths, and media coverage. The numerical simulation and sensitivity analysis are conducted based on the Sentiment‐enabled SEIR model. The numerical analysis confirms the rationality of the Sentiment‐enabled SEIR model. The sensitivity analysis shows that positive media coverage acts a pivotal part in reducing the figure for confirmed cases. Negative media coverage has an effect on the figure for confirmed cases is not as significant as that of positive media coverage, but it is not negligible. [ABSTRACT FROM AUTHOR]

In this paper, a semi‐discrete rotational velocity‐correction projection method is proposed to solve the Kelvin–Voigt viscoelastic fluid equations. In this method, the rotational velocity‐correction projection method can preserve the divergence free of the velocity u$$ u $$, and the nonlinear equation was linearized. Then, the unconditional stability and optimal convergence order will be provided by the numerical analysis. Finally, our analysis are confirmed by some numerical results, and the algorithm is effective. [ABSTRACT FROM AUTHOR]

In this paper, a second‐order accurate scheme is considered for the temporal discretization of the abstract Volterra integrodifferential equation with a weakly singular kernel. The time discrete scheme is constructed by the Crank–Nicolson method for approximating the time derivative and product integration (PI) rule for approximating the integral term. The proposed scheme employs a graded mesh for time to compensate for the singular behavior of the exact solution at t=0$$ t=0 $$. Under the suitable assumptions, the stability and convergence are established by the energy argument, and the error is of order k2$$ {k}^2 $$, where k$$ k $$ is the parameter for the time grids. Numerical experiments validate the theoretical estimate. [ABSTRACT FROM AUTHOR]

Summary: In the paper, a nonlinear analysis of RC phase‐shift oscillator with operational amplifier is done. Using Kirchhoff's laws, a nonlinear system of three differential equations that describes the behavior of the oscillator is obtained. This system is analyzed using the Poincaré–Andronov–Hopf bifurcation theory. The basic principles of the Poincaré–Andronov–Hopf bifurcation theory are presented in advance, including the Center Manifold Theory and the Theory of Normal Forms. It was found that, under certain conditions, the oscillator system has a limit cycle, which means that the oscillator under consideration generates periodic oscillations. The period, amplitude, and stability of the generated periodic oscillations are determined theoretically. The obtained analytical results are confirmed by a numerical analysis of the nonlinear system of differential equations performed by MATLAB. [ABSTRACT FROM AUTHOR]

This work is motivated by the fact that the reliability of electrical connectors influenced by their mechanical behavior and fatigue life directly affects the working performance of the whole equipment system. In this paper, theoretical analyses of insertion force, maximum stress, and fatigue life in an aviation electrical connector are presented and the corresponding mathematical models are firstly derived. Then, to numerically investigate its mechanical behavior and fatigue life, a simplified 3D FE model is developed by using ABAQUS and FE‐SAFE software and verified by experiments and theoretical analysis. Finally, the distribution and evolution characteristics of contact forces, stress and fatigue life considering the influences of reed thickness and slot width are quantitatively analyzed in details. The results indicate that the insertion force first increases and then stabilizes at the level of 0.16 N as the pin head is fully inserted into the jack, which shows an opposite to the evolution of extraction force. Moreover, the maximum value of stress and the minimum value of fatigue life are all located at the root of the jack reed. Besides, unlike the small effect of slot width, the Fimax and σmax values obviously increase and the Nf value decreases with the increment of reed thickness. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish a precise illustration for the structure of the nonconstant steady states for a Beddington–DeAngelis and Tanner predator–prey reaction–diffusion system with prey‐taxis. We treat the nonlinear prey‐taxis as a bifurcation parameter to analyze the bifurcation structure of the system. Furthermore, the exported global bifurcation theorem, under a rather natural condition, offers the existence of nonconstant steady states. In the proof, a priori estimates of steady states will play an important role. The local stability analysis with a numerical simulation and bifurcation analysis are given. Finally, some conclusions including biological meanings are performed to summarize our main analytic results and future investigations. [ABSTRACT FROM AUTHOR]

Condition‐based maintenance has been studied for managing the degradation of components in a system. However, components in different positions may undergo different workload, leading to imbalanced components degradation. Component reallocation is an effective method to balance the degradation of components in different positions with different degradation rates. Thus, this paper investigates the joint optimization of condition‐based maintenance and condition‐based reallocation for a non‐repairable system with multiple identical and functionally‐exchangeable components that undergo different continuous degradation processes due to different workload. We model this problem through Markov decision process, which is solved by a dynamic programming algorithm, and the objective is to provide the optimal maintenance and reallocation actions exactly for each system state, that is, the joint optimal policy, to minimize the discounted long‐run total cost. Especially, our joint policy is on component‐level and proved to be optimal. Finally, the numerical analysis shows the structural insights and effectiveness of the proposed joint policy, for which the sensitivity analysis on the degradation parameters, setup cost, reallocation cost, and downtime cost is performed. We also propose a new reallocation strategy and show the results and computation time for systems with different scales, which indicates that our model can handle systems with reasonable size. [ABSTRACT FROM AUTHOR]

Nanofluids are used to achieve maximum thermal performance with the smallest concentration of nanoparticles and stable suspension in conventional fluids. The effectiveness of nanofluids in convection processes is significantly influenced by their increased thermophysical characteristics. However, this technology is not ended here; binary and ternary nanofluids are now used to improve the efficiency of regular fluids. Therefore, this paper aims to analyze the natural convection Newtonian ternary nanofluid flow in a vertical channel. The tri‐hybridized nanoparticles of zinc oxide ZnO, Aluminum oxide Al2O3, and titanium oxide TiO2 is dissolved in base fluid distilled water (DW) to form a homogenous suspension. The impact of thermal radiation, joule heating, and viscous dissipation are also assumed. The classical Newtonian ternary nanofluid model has been generalized by using fractal‐fractional derivative (FFD) operator. The generalized model has been discretized by using the Crank–Nicolson scheme and then solved by using computational software. To analyze the behavior of fluid flow and heat distribution in fluid, the obtained solution was computed numerically and then plotted in response to different physical parameters. It is noted from the figure that when the volume fraction ϕ reaches to 0.04 (4% of the base fluid), the ternary nanofluid flow shows a significant amount of enhancement in heat transfer rate as compared to binary and unary nanofluid flows. This enhancement in the rate of heat transfer leads to improve the thermophysical characteristics such as viscosity, thermal expansion, and heat capacity etc. of the base fluid. It is also worth mentioning here that the thermal field is also enhance with the higher values of Eckert number Ec$Ec$, radiation parameter Rd$Rd$, and joule heating parameter Jh${J_h}$. [ABSTRACT FROM AUTHOR]

Arnold, L. J. & Roberts, R. G. 2011: Paper I - Optically stimulated luminescence (OSL) dating of perennially frozen deposits in north−central Siberia: OSL characteristics of quartz grains and methodological considerations regarding their suitability for dating. Boreas, Vol. 40, pp. 389-416. 10.1111/j.1502-3885.2011.00209.x. ISSN 0300−9483. Optically stimulated luminescence (OSL) dating of coarse-grained quartz is increasingly being used as the main chronological tool in late Quaternary palaeoenvironmental reconstructions of Siberia. However, relatively little information has been published on the suitability of OSL dating for the various types of perennially frozen sediments found in this region. Here we provide a systematic examination of the quartz luminescence characteristics of 21 perennially frozen samples from the Taimyr Peninsula and adjacent coastal lowlands of north-central Siberia, and discuss their implications for the reliability of single-grain and multi-grain OSL chronologies in such contexts. The results of this study suggest that the quartz luminescence characteristics of these samples are, in principle, favourable for OSL dating but, in practice, require that a series of validation checks are made of the chosen experimental conditions. If these tests are satisfied, then reliable OSL chronologies should be obtained for sedimentary deposits in this region. Importantly, however, the single-grain and multi-grain aliquot equivalent dose (D) distribution characteristics for our samples reveal that there are advantages in targeting certain types of depositional settings for OSL dating studies of Siberian sediments. We also show that samples from the same depositional settings, and even from the same sites, do not necessarily display similar D distribution characteristics. The latter complication favours the use of single-grain analysis to unravel the bleaching and burial histories of young (mid- to late Holocene) sediments in these Arctic environments. [ABSTRACT FROM AUTHOR]

This paper introduces a new scheme for the numerical computation involving shock waves. The essence of the scheme is to adaptively implement a conjugate low-pass filter to effectively remove the accumulated numerical errors produced by a set of high-pass filters. The advantages of using such an adaptive algorithm are its controllable accuracy, relatively low cost and easy implementation. Numerical examples in one and two space dimensions are presented to illustrate the proposed scheme. Copyright © 2003 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Summary This paper discusses visualization methods for discriminant analysis. It does not address numerical methods for classification per se, but rather focuses on graphical methods that can be viewed as pre-processors, aiding the analyst's understanding of the data and the choice of a final classifier. The methods are adaptations of recent results in dimension reduction for regression, including sliced inverse regression and sliced average variance estimation. A permutation test is suggested as a means of determining dimension, and examples are given throughout the discussion. [ABSTRACT FROM AUTHOR]

The focus of this paper is on the solution of Maxwell's equations for time-harmonic fields on triangular, possibly non-orthogonal meshes. The method described was first introduced in References 1 and 2 for eigenvalue problems arising in the design of accelerator components and dielectric loaded waveguides. It is based on the well-known Finite Integration Technique (FIT) which is a proven consistent discretization method for the computation of electromagnetic fields. The FIT-discretization on non-orthogonal 2D grids has close relations to the Nédélec elements or edge elements in the Finite Element Method. Revisiting FIT on triangular grids this paper intends to stimulate thorough studies of the latter subject which is well worth further investigations. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

For the simulation of acoustic-structure interaction problems, the coupled field equations must be solved. The structure is commonly discretized using finite elements, whereas for the acoustic field the boundary element method (BEM) is favorable. A mortar BEM-FEM coupling algorithm is developed that allows the combination of non-conforming meshes. The high flexibility for the choice of discretizations offers a high efficiency, since specialized shape functions and adaptive mesh refinement can be used in the subdomains. The mortar coupling algorithm yields a saddle point problem that is solved using a preconditioned inexact Uzawa algorithm. The iterative solver enables the use of the fast multipole BEM and thus coupled simulations on large boundary element models. [ABSTRACT FROM AUTHOR]

Inspired by the concept of frequency‐independent antennas in the electromagnetics, which theoretically exhibit a frequency‐independent bandwidth, this paper extends the concept to acoustics by adopting a log‐spiral and its modified shape to introduce a class of metamaterials called frequency‐independent sound‐absorbing metamaterials. Without the requirement of multiple resonators, these metamaterials achieve an ultra‐broadband absorption spanning from 550 Hz for a wide range of incident angles up to 80°, using a single unit cell structure owing to Fabry–Pérot resonance, viscous boundary losses, and thermoviscous loss of the foam. Numerical and experimental analyses are provided to demonstrate the working principles of the proposed structures. Their performance is compared with archimedean spiral, and the influence of air and porous material parameters on the performance of the metamaterial is discussed in detail for normal and oblique incident waves. The underlying principle is discussed in detail, highlighting the distinctions between the proposed structures and state‐of‐the‐art broadband metamaterials. The proposed structures represent a pioneering advancement in the field by offering compact and ultra‐broadband sound‐absorbing metamaterials that are suitable for practical applications. [ABSTRACT FROM AUTHOR]

This paper proposes an L1/LDG algorithm for a time–space fractional convection equation on a bounded rectangular domain Ω⊂ℝ2$$ \Omega \subset {\mathrm{\mathbb{R}}}^2 $$. Here, the temporal partial derivative is in the sense of Caputo with order α∈(0,1)$$ \alpha \in \left(0,1\right) $$, and the spatial partial derivatives are of Riesz type with orders β,γ∈(0,1)$$ \beta, \gamma \in \left(0,1\right) $$ in x$$ x $$‐ and y$$ y $$‐directions, respectively. L1 approximation is utilized to evaluate the temporal Caputo derivative, while the local discontinuous Galerkin (LDG) method is adopted to deal with the spatial Riesz derivative. The rigorous numerical stability analysis and error estimate are presented which are supported by illustrative numerical examples. [ABSTRACT FROM AUTHOR]

The Klein–Gordon–Schrödinger equations describe a classical model of interaction of nucleon field with meson field in physics, how to design the energy conservative and stable schemes is an important issue. This paper aims to develop a linearized energy‐preserve, unconditionally stable and efficient scheme for Klein–Gordon–Schrödinger equations. Some auxiliary variables are utilized to circumvent the imaginary functions of Klein–Gordon–Schrödinger equations, and transform the original system into its real formulation. Based on the invariant energy quadratization approach, an equivalent system is deduced by introducing a Lagrange multiplier. Then the efficient and unconditionally stable scheme is designed to discretize the deduced equivalent system. A numerical analysis of the proposed scheme is presented to illustrate its uniquely solvability and convergence. Numerical examples are provided to validate accuracy, energy and mass conservation laws, and stability of our proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we consider leap‐frog finite element methods with EQ1rot$$ {\mathrm{EQ}}_1^{\mathrm{rot}} $$ element for the nonlinear Schrödinger equation with wave operator. We propose that both the continuous and discrete systems can keep mass and energy conservation. In addition, we focus on the unconditional superconvergence analysis of the numerical scheme, the key of which is the time‐space error splitting technique. The spatial error is derived τ$$ \tau $$ independently with order O(h2+hτ)$$ O\left({h}^2+ h\tau \right) $$ in H1$$ {H}^1 $$‐norm, where h$$ h $$ and τ$$ \tau $$ denote the space and time step size. Then the unconditional optimal L2$$ {L}^2 $$ error and superclose result with order O(h2+τ2)$$ O\left({h}^2+{\tau}^2\right) $$ are deduced, and the unconditional optimal H1$$ {H}^1 $$ error is obtained with order O(h+τ2)$$ O\left(h+{\tau}^2\right) $$ by using interpolation theory. The final unconditional superconvergence result with order O(h2+τ2)$$ O\left({h}^2+{\tau}^2\right) $$ is derived by the interpolation postprocessing technique. Furthermore, we apply the proposed leap‐frog finite element methods to solve the logarithmic Schrödinger equation with wave operator by introducing a regularized system with a small regularization parameter 0<ϵ≪1$$ 0<\epsilon \ll 1 $$. The detailed theoretical conclusions, including the mass and energy conservation laws of the continuous regularized and discrete regularized systems and the convergence and superconvergence results, are presented as prolongation of the previous work. At last, some numerical experiments are given to confirm our theoretical analysis. [ABSTRACT FROM AUTHOR]

A linear motor that uses a finite length Halbach array as its magnetic field causes a thrust force ripple owing to end effects. In this paper, the theoretical and numerical analysis methods of the Halbach array are investigated. The results of the electromagnetic field analysis are compared to confirm the validity of the theoretical and numerical solutions. Moreover, we focus on the magnetic pole period and coil arrangement of the finite length Halbach field type linear motor to eliminate the influence of the end effects, and report the relationship with the end effects. [ABSTRACT FROM AUTHOR]

A second‐order accurate, linear numerical method is analyzed for the Landau–Lifshitz equation with large damping parameters. This equation describes the dynamics of magnetization, with a non‐convexity constraint of unit length of the magnetization. The numerical method is based on the second‐order backward differentiation formula in time, combined with an implicit treatment for the linear diffusion term from the harmonic mapping part and explicit extrapolation for the nonlinear terms. Afterward, a projection step is applied to normalize the numerical solution at a point‐wise level. This numerical scheme has shown extensive advantages in the practical computations for the physical model with large damping parameters, which comes from the fact that only a linear system with constant coefficients (independent of both time and the updated magnetization) needs to be solved at each time step, and has greatly improved the numerical efficiency. Meanwhile, a theoretical analysis for this linear numerical scheme has not been available. In this paper, we provide a rigorous error estimate of the numerical scheme, in the discrete ℓ∞(0,T;ℓ2)∩ℓ2(0,T;Hh1)$$ {\ell}&amp;#x0005E;{\infty}\left(0,T;{\ell}&amp;#x0005E;2\right)\cap {\ell}&amp;#x0005E;2\left(0,T;{H}_h&amp;#x0005E;1\right) $$ norm, under suitable regularity assumptions and reasonable ratio between the time step size and the spatial mesh size. In particular, the projection operation is nonlinear, and a stability estimate for the projection step turns out to be highly challenging. Such a stability estimate is derived in details, which will play an essential role in the convergence analysis for the numerical scheme, if the damping parameter is greater than 3. [ABSTRACT FROM AUTHOR]

The inflammatory phase is an important event in the skin wound healing process. The deposition of granulation tissue in the wound bed and the rebuilding of the vascular network occur as inflammation diminishes. An angiogenic component in the formation of granulation tissue is the secretion of vascular endothelial growth factor, which assists in the chemotaxis, proliferation, and replication of fibroblasts. In this paper, we develop a mathematical model of skin wound healing angiogenic factors based on inflammatory cells (macrophages and neutrophils) and mediators (interleukin 6 and interleukin 10). We highlight the importance of this process in vascular endothelial growth factor release and in the formation of new capillary tips. We used a mathematical model of partial differential equations based on the reaction‐diffusion‐advection equations. In order to calibrate the parameters, we considered an in vivo model composed by four treatments: hydroalcoholic extract and oil‐resin of Copaifera langsdorffii at 10% concentration, collagenase, and Lanette cream. Using the laboratory data for the wound edge, our mathematical model estimated the values of vascular endothelial growth factor concentration, and tips density in the center of the wound with a maximum error of 2.9%, and predicted healing time required for each treatment. The region of viability for the parameters, in the proposed model, was found through numerical simulations from the Interleukin 6 and 10 dysregulation and we obtained that, among the parameters analyzed, the greatest influencer in the dynamics of the system is the one, which represents the production of Interleukin 10 during phagocytosis. [ABSTRACT FROM AUTHOR]

Bratu‐type equation has wide applications in physics, finance, and other fields. Also, fractional analysis has been a popular topic recently. It is difficult to find the analytical solution once we add the fractional operator on the left side of the equation. In this work, we apply explicit and implicit finite difference methods to solve the fractional Bratu equation. From the numerical examples, we will see that the explicit solution is not accurate, and the implicit solution based on Newton's method is efficient in some sense. Some theoretical results are mentioned in the paper. [ABSTRACT FROM AUTHOR]

The linear elasticity problem has important applications in structural analysis and engineering design. It is shown that the classical Crouzeix–Raviart finite element method is unstable to solve the linear elasticity eigenvalue problem with the pure traction boundary condition. In this paper, first we propose a new scheme with the stabilization terms. Then we prove the a priori error estimates for approximate eigenpairs. Finally, we carry out numerical experiments using the stabilized scheme. Theoretical analysis and numerical results show that this scheme is locking free and efficient. [ABSTRACT FROM AUTHOR]

Recently, a novel approach has been proposed to produce ultrashort, fully coherent high-repetition-rate EUVand X-ray radiation by combining an energy recovery linac (ERL) with the angular-dispersion-induced microbunching methodology. It is critical to maintain microbunching when the beam passes through bending magnets between the undulators, which results in difficulties supporting multiple beamlines. In this paper, the design of a multiplexed emitting system consisting of multi-bend achromats, matching sections and radiators to facilitate the multi-beamline operation is presented. Theoretical analysis and numerical simulations have been carried out and the results show that the microbunching and beam quality can be well maintained after four times of bending. Five radiation pulses with a central wavelength of 13.5 nm and peak power at theMW level have been produced by the same electron beam via this multiplexed emitting system. The proposed method holds potential in the multi-beamline operation of ERL- or storage-ring-based coherent light sources. [ABSTRACT FROM AUTHOR]

The Metro Tunnel Project in Melbourne, Australia, involves the construction of 9 kms of twin rail tunnels and five new underground stations, including the State Library and Town Hall in the City Centre. The stations aim to provide spacious areas measuring around 260 m in length, 30 m in width, and 23 m in height. To address ground conditions, load behaviour, and land constraints, the stations are being built as trinocular form caverns, with a sequential excavation of the central (cavern) tunnel followed by the outer (platform) tunnels. Advanced 3D numerical analyses guided the design of the primary support and permanent linings, with temporary steel columns incorporated into permanent linings for efficiency. Close collaboration and an observational design approach facilitated efficient construction methods and work sequencing. The paper presents insights into the successful design, construction, and verification approaches on aspects of the project. [ABSTRACT FROM AUTHOR]

This paper deals with experimental and numerical analysis of the ductile damage and fracture behavior undergoing biaxial non‐proportional shear reverse loading conditions. In the numerical analysis, an anisotropic cyclic plastic‐damage constitutive model is considered to characterize the damage and fracture behavior. Additionally, the change in the hardening rate is observed after shear reverse loading. Thus, a newly modified non‐hardening strain region method is introduced to capture the change in the hardening ratio between isotropic and kinematic hardening. Furthermore, the damage surface is assumed to translate in the direction of the damage strain increment. Hence, a softening law based on the damage strain is proposed. The modified constitutive model predicts macroscopic force‐displacement and microscopic evolution of plastic and damage behaviors under shear reverse loading with a tensile preload. Through digital image correlation technique and scanning electron microscopy, numerical results can be validated by experimental ones. Furthermore, scanning electron microscopy pictures also reveal different damage and fracture mechanisms on the micro‐level. [ABSTRACT FROM AUTHOR]

Earlier work using the time dependent Poynting theorem has shown that the complete description of power in a multimodal radiation field requires the use of three numbers; two are sufficient only with a single modal field. Where three numbers are required it is not possible to correctly represent power as a complex number. In the common notation the third number is a suppressed phase angle; when multiple power fields are combined to form a single one it is essential to account for the suppressed phase angles. The differences in power calculations using the time and frequency domain power theorems are manifest in determination of the energy flow that remains local to the source, oscillating between the near field and source, which does not form part of the far field power. In this paper we numerically model, using commonly accepted frequency and time domain techniques, the simplest antenna design that clearly illustrates the differences between time and frequency domain representations of reactive power. We calculate and contrast the instantaneous and the steady-state far field and local powers emitted from two identical, perpendicularly oriented electrically small TM dipoles as a function of relative phase between the two dipoles. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The analysis of structures which contain thin wires or narrow microstrips using the FDTD method and without resorting to a very fine mesh, has been an area of intensive research for many years. Despite this activity, however, the problem is still not definitively solved. In this paper the problem is attacked by investigating the properties of the FDTD mesh when the material parameters of a single cell, or a small group of cells, are altered. From this, formulae are derived by which these parameters may be chosen in order to accurately represent a conductor of small cross-section. Results are presented which show that accurate results for wire and microstrip transmission lines can be achieved with little or no computational overhead and without the problems of late time instability or spurious field divergence. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In recent years, the finite-difference time-domain (FDTD) method has been used to simulate a wide range of frequency dependent media. The accuracy of these simulations often depends on how accurately the complex dielectric constant is simulated in the sampled time domain used by FDTD. This paper describes the process of modelling the complex dielectric constant as a digital filtering problem and uses Z transforms to convert the frequency domain expression to a sampled time domain expression. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Frequency domain transfer functions of microwave systems are usually calculated either directly in the frequency domain or in the time domain in combination with a Fourier analysis. The computation of loss-free linear devices based on eigenfields (resonant fields) offers an alternative to obtaining broadband frequency characteristics with a high accuracy. Such methods are very effective for problems with multiple narrow resonances as many points in frequency domain have to be calculated to sample the maximas, or time domain computations have to deal with long transients. We describe a method of this type and then an improvement that leads directly to transfer functions, which are very accurate even if only modes in the chosen frequency range are taken into account. Generalized macroscopic parameters are introduced as input and output quantities, which are related to conventional quantities such as discrete currents and voltages, wave parameters, or even beam currents and voltages (as defined in accelerator physics for beams of ultra-relativistic charged particles). When the generalized input/output parameters are causal they are related to each other and to state parameters of the eletromagnetic fields by a differential equation with time independent system matrices. The input/output transfer matrix in the frequency domain is an impedance matrix, which is derived from the system matrices of the discretization as well as from a series expansion using eigensolutions. The number of eigenmodes is typically three times the number of meshpoints, but good approximations can be achieved even with a much smaller set of eigenvalues around the frequency range of interest. Another approach to characterizing the system response is based on the output/input relation described by an admittance matrix. Combining both approaches, the error of the approximations can be estimated and significantly reduced. The application of the method is shown for several examples. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A new approach using FIT-formulation (Finite Integration Technique) (T. Weiland, Electron. Commun., 31, 116–120 (1977); Int. J. Numer. Model., 9, 295–319 (1996)) for simulating waveguide propagation of optical pulses is presented. FIT-methods are widespread in use for broadband linear simulations. In recent years, several attempts have been made to describe different dispersive material-characteristics such as Drude, Debye or Lorentz dispersion. Today advanced FDTD-formulations (Finite Difference Time Domain) also consider non-linear effects (P. M. Goorjian and A. Taflove, IEEE Opt. Lett., 17(3), 180–182 (1992); D. M. Sullivan, IEEE Trans. Microwave Theory Techniques, 43(3), 676–682 (1995)). In the following presented method third-order non-linear effects were described, which can be observed in isotropic media in frequency ranges of optical pulses, by updating material polarization terms using classical descriptions of Lorentz dispersion, Raman scattering and the Kerr effect. The basic idea is transforming these description formulas into sets of linear differential equations and solving them with the help of the general exponential solution. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The simulation of slowly varying electromagnetic fields is possible for very large, realistic problems with finite-difference implicit time-domain (FDiTD) and frequency-domain (FDFD) formulations on the basis of the consistent Finite-Integration Technique (FIT). Magneto-quasistatic time-domain formulations combined with implicit time marching schemes require the repeated solution of real-valued symmetric systems. The solution of driven frequency domain problems usually consists in the solution of one non-Hermitean system. Preconditioned conjugate gradient-type methods are well-suited for this task. They allow the efficient solution even for consistent singular or near-singular systems, which typically arise from formulations for slowly varying electromagnetic fields using the Maxwell-Grid-Equations of the FI-Method. Numerical results for TEAM workshop 11 benchmark problem and for a large practical problem, a shading ring sensor, show that the presented algorithms are capable of solving realistic problems for large numbers of unknowns in acceptable calculation times on contemporary medium sized workstations. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper proposes a multiaxial macroelement for bridge abutments that can be included in the global structural model of a bridge to carry out nonlinear dynamic analyses with very much smaller computational effort than can be achieved using continuum representations of embankment and foundation soil behaviour. The proposed macroelement derives a constitutive force–displacement relationship within a rigorous thermodynamic framework and includes important features of non‐linearity and directional coupling in characterizing the interactions of the abutment with the soil. In a dynamic analysis, the frequency‐dependent response of the system is simulated through the combination of the macroelement with appropriate participating masses. The calibration procedure of the macroelement is based on the assessment of its ultimate capacity and of its response at small displacements, and it is shown that these ingredients can be derived through standardised procedures. In the paper, the macroelement response is validated against the results of fully coupled continuum numerical analyses for a reference soil–abutment system, under both static and seismic loading conditions. We show that the two models achieve similar predictions of maximum and permanent abutment deformations (less than 10–14% difference, respectively) for a suite of three‐axis seismic loading events. [ABSTRACT FROM AUTHOR]

This paper presents a 4th-order accurate implicit multistage finite-difference time-domain (IMS-FDTD) method. The analysis of the stability shows that this IMS-FDTD method is unconditionally stable. In addition, its numerical-dispersion relation is derived and the analysis shows that its performance is better than those of conventional unconditionally-stable implicit FDTD methods and is even better than those of some conditionally-stable explicit FDTD methods, such as the Fang(2, 4)-FDTD method. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 1383–1385, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21646 [ABSTRACT FROM AUTHOR]

This paper presents the design and numerical optimization of oil‐lubricated spiral grooved thrust bearing (SGTB) for its application at high speed and axial loading conditions. A numerical model is developed using nonlinear incompressible Reynold's equation and is solved using the finite volume method (FVM) to determine the static characteristics over the bearing surface. Further, the influence of groove parameters such as spiral angle, groove angle, film thickness ratio, number of grooves and speed on the static characteristics of the bearing has been investigated. The result shows that the designed oil‐lubricated SGTB can operate at high‐speed conditions and withstand high axial load. Further, the characteristic data sets acquired from the numerical analysis are trained using an artificial neural network (ANN), and their performance is evaluated through the computation of the regression coefficient. Then adaptive neuro‐fuzzy interface system (ANFIS) surface plot is obtained to determine the optimum bearing parameters. [ABSTRACT FROM AUTHOR]

In recent years, the propagation of ultrasonic guided waves (UGW) along the structure to inspect has amply proven to be an excellent strategy for the health monitoring of isotropic and composite structures (SHM—structural health monitoring). For the proper development of the SHM system, the finite element method (FEM) must be mentioned, since the possibility to study the UGW in very complex structures, even characterized by different materials. Successfully locating any possible damage and identifying its severity are key factors in SHM, thus allowing to reduce the design costs. Numerically, the damage can be modeled with several approaches but it is still not clear which is the best solution to accurately reproduce the UGW mechanisms in a faulty structure. The objective of this paper is to study the various effects that different severities of damage can have on UGW propagation. For the scope, various numerical approaches are considered and the results are compared. [ABSTRACT FROM AUTHOR]

In this paper, we present a mathematical model that analyzes cancer treatment via radiotherapy and proposes ways to control its progression. To identify preventive measures for cancer in its early stages, scientists have studied both risk factors and protective factors. In our model, we consider the disease‐free equilibrium points, namely, the trivial equilibrium (TE), healthy cell absenteeism equilibrium (HCAE), cancer cell absenteeism equilibrium (CCAE), and cancer cell incidence equilibrium (CCIE). We use nonlinear analysis techniques and the spectral radius method to study the stability and instability of systems. Since the reproduction number plays a critical role in stability analysis, we use the spectral radius method to evaluate it. We have also added a control function to the model to enhance it by including interactions between healthy and cancer cells. Optimization techniques are used to identify the limitations and needs of the problem and derive the best solutions to control the tumor. We conduct sensitivity analysis with respect to various parameters to study the model's robustness. To validate our methods and results, we provide simulations and numerical analysis. [ABSTRACT FROM AUTHOR]

Design approach against failure of the earth support using the finite element method The application of the finite element method (FEM) in geotechnical engineering has been established in the last decades for the prediction of deformations in the serviceability limit state (SLS). In practice, stability analyses in the ultimate limit state (ULS) are only partially performed using the FEM and are currently still state of the art. The next generation of Eurocode 7 is intended to regulate numerical methods with regard to their application in the ULS. However, the handling of the additionally required analysis of the German National Annex and DIN 1054 is still unsolved. In this paper, an approach for the numerical analysis of the earth support is presented. Following the well‐established strength reduction method, the weight of the soil γ and the cohesion c' ${{c}^{{ {\prime}}}}$ on the earth resistance side are reduced until failure occurs. On the basis of this, the analysis in ULS is carried out by defining a safety factor for the existing embedment depth of the retaining wall. This is followed by a comparison with the analytical free earth support method, identifying system reserves using the FEM. [ABSTRACT FROM AUTHOR]

Reinforcement of the Rhine bridge Maxau – accompanying measurements, effects and efficacy Due to the steadily increasing traffic volume, fatigue damages occurred on the orthotropic steel deck of the Maxau Rhine Bridge, necessitating a deck reinforcement. In order to reinforce the bridge for traffic loads in future, a layer of high‐strength concrete (HPC) was applied on the orthotropic deck plate. A team of engineers from the Karlsruhe Institute of Technology (KIT) conducted measurements during the reinforcement project. This paper presents the corresponding measurement results, discusses the effects achieved by the reinforcement project, and draws conclusions on its effectiveness. Numerical analyses indicate a decrease in fatigue loads on the orthotropic steel deck, confirming an improved load distribution, which was also determined by the measurements. [ABSTRACT FROM AUTHOR]