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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 investigates an adapted loss function for the estimation of a linear regression with right censored responses. The adapted loss function could be used in composite quantile regression, which is a good method to handle the responses with high censored rate. Under some regular conditions, we establish the consistency and asymptotic normality of the resulting estimator. For estimation of regression parameters, we propose the MMCD algorithm, which generates satisfactory results for the proposed estimator. In addition, the algorithm can also be extended to the fused adaptive lasso penalized method to identify the interquantile commonality. The finite sample performances of the methods are further illustrated by numerical results and the analysis of two real datasets. [ABSTRACT FROM AUTHOR]

Particle morphology is a crucial determining factor in the physicochemical properties of geological materials. Currently, there are still substantial challenges with the characterization and reconstruction of the morphology of irregular particles. Most currently used characterization and reconstruction methods were developed separately, and lack cohesive integration of parameters between the two processes. This limitation hinders the comprehensive characterization of the multiscale geometric features and impedes a clear relation between geometrical features and reconstruction parameters. Therefore, a unified 2D and 3D morphological characterization method for irregular particles is developed in this paper, enabling a systematic morphology quantification across three relative scales. Furthermore, a geometric parameters-driven particle reconstruction approach is proposed, which is the reverse of the quantification process, achieving precise and controllable 2D and 3D irregular morphology reconstruction. The proposed methods achieve, for the first time, an integrated quantification and reconstruction framework of irregular particle morphology, as well as a unified 2D and 3D morphology characterization. Notably, the proposed approach exhibits strong robustness and computational efficiency when performing 2D and 3D particle morphology quantification and precisely controllable virtual particle reconstruction, which are the bases for accurate mechanical analyses and numerical simulations. [ABSTRACT FROM AUTHOR]

Selectively thickening core wall is an effective approach to improve the birefringence of hollow core photonic bandgap fiber (HC-PBGF). However, the variation of core wall thickness has a significant influence on the transmission loss and transmission bandwidth. In this paper, the effects of selectively thickening core wall on birefringence and loss performance of the HC-PBGF are systematically investigated. Numerical analysis results indicate that when the core wall thickness in the y-direction is 2.4 to 3.3 times as that in the x-direction, the birefringence of a 19-cell HC-PBGF can be improved to 10− 4, meanwhile the transmission loss can be controlled below 10 dB/km. The high birefringence (≥ 10− 4), low transmission loss (< 10 dB/km) performance can be maintained in a wide waveband from 1460 to 1610 nm, even under a tight bending radius of 6 mm. The applicability of selectively thickening core wall on improving birefringence is also confirmed in the 7-cell HC-PBGF and 37-cell HC-PBGF, where the birefringence of 7-cell HC-PBGF and 37-cell HC-PBGF can be enhanced to 5.5 × 10− 4 and 5.0 × 10− 5, respectively. Moreover, to further reduce the transmission loss, two modified structures (adding nodes or anti-resonant layer) are discussed. The numerical analysis results demonstrate that the structure by adding nodes on the thickened core wall is more advantageous in terms of reducing transmission loss and expanding transmission bandwidth. [ABSTRACT FROM AUTHOR]

In soft soil layers, piles are frequently loaded laterally by horizontal soil movements. In many cases, the lateral pressure acting on piles due to horizontal soil movements is calculated with empirically or analytically based approaches, respectively. However, most of these design approaches do not consider possible influences on the resulting pile loads. This paper presents the results of model tests and numerical simulations on single piles and pile groups in cohesive soil subjected to lateral loads which were carried out to overcome limitations of available design approaches. Based on extensive small-scale 1 × g-model tests and numerical investigations with the finite element method, influencing factors on the lateral pressure, such as the roughness of the pile–soil interface, the pile size, the pile shape and the pile spacing were identified. A parametric study with the numerical model quantified the most relevant factors influencing the development of lateral pressure on piles due to adjacent surface loads and lead to the development of a simplified analysis approach. [ABSTRACT FROM AUTHOR]

With the development of cloud computing, users are more inclined to outsource complex computing tasks to cloud servers with strong computing capacity, and the cloud returns the final calculation results. However, the cloud is not completely trustworthy, which may leak the data of user and even return incorrect calculations on purpose. Therefore, it is important to verify the results of computing tasks without revealing the privacy of the users. Among all the computing tasks, the polynomial calculation is widely used in information security, linear algebra, signal processing and other fields. Most existing polynomial-based verifiable computation schemes require that the input of the polynomial function must come from a single data source, which means that the data must be signed by a single user. However, the input of the polynomial may come from multiple users in the practical application. In order to solve this problem, the researchers have proposed some schemes for multi-source outsourced data, but these schemes have the common problem of low efficiency. To improve the efficiency, this paper proposes an efficient polynomial-based verifiable computation scheme on multi-source outsourced data. We optimize the polynomials using Horner's method to increase the speed of verification, in which the addition gate and the multiplication gate can be interleaved to represent the polynomial function. In order to adapt to this structure, we design the corresponding homomorphic verification tag, so that the input of the polynomial can come from multiple data sources. We prove the correctness and rationality of the scheme, and carry out numerical analysis and evaluation research to verify the efficiency of the scheme. The experimental indicate that data contributors can sign 1000 new data in merely 2 s, while the verification of a delegated polynomial function with a power of 100 requires only 18 ms. These results confirm that the proposed scheme is better than the existing scheme. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach to analyzing the dynamics of COVID-19 using nonstandard finite difference (NSFD) schemes. Our model incorporates both asymptomatic and symptomatic infected individuals, allowing for a more comprehensive understanding of the epidemic's spread. We introduce an unconditionally stable NSFD system that eliminates the need for traditional Runge–Kutta methods, ensuring dynamical consistency and numerical accuracy. Through rigorous numerical analysis, we evaluate the performance of different NSFD strategies and validate our analytical findings. Our work demonstrates the benefits of using NSFD schemes for modeling infectious diseases, offering advantages in terms of stability and efficiency. We further illustrate the dynamic behavior of COVID-19 under various conditions using numerical simulations. The results from these simulations demonstrate the effectiveness of the proposed approach in capturing the epidemic's complex dynamics. [ABSTRACT FROM AUTHOR]

Enhancing information security has become increasingly significant in the digital age. This paper investigates the concept of physical layer security (PLS) within a relay-aided power line communication (PLC) system operating over a multiple-input multiple-output (MIMO) channel based on MK model. Specifically, we examine the transmission of confidential signals between a source and a distant destination while accounting for the presence of multiple eavesdroppers, both colluding and non-colluding. We propose a two-phase jamming scheme that leverages a full-duplex (FD) amplify-and-forward (AF) relay to address this challenge. Our primary objective is to maximize the secrecy rate, which necessitates the optimization of the jamming precoding and transmitting precoding matrices at both the source and the relay while adhering to transmit power constraints. We present a formulation of this problem and demonstrate that it can be efficiently solved using an effective block coordinate descent (BCD) algorithm. Simulation results are conducted to validate the convergence and performance of the proposed algorithm. These findings confirm the effectiveness of our approach. Furthermore, the numerical analysis reveals that our proposed algorithm surpasses traditional schemes that lack jamming to achieve higher secrecy rates. As a result, the proposed algorithm offers the benefit of guaranteeing secure communications in a realistic channel model, even in scenarios involving colluding eavesdroppers. [ABSTRACT FROM AUTHOR]

The occurrence of rockfalls is a prevalent geological hazard, especially in the Three Gorges Reservoir area of the Yangtze River. Analyzing the pre-rockfall evolution process of hazardous rock mass is crucial for stability assessment, risk monitoring, and evaluation. Generally, numerical analysis is conducted to study the rock stability and failure; however, it is primarily based on the two-dimensional calculation of typical cross-sections without considering the shape of the three-dimensional space of the hazardous rock mass, thus leading to distorted results. To address this issue, this paper proposes a methodological approach for the analysis of the stability conditions of a hazardous rock mass. The approach starts with field investigations and an Unmanned aerial vehicle (UAV) photogrammetric survey to gather data. These data are then used to construct a three-dimensional (3D) geological model of rock mass. Finally, a 3D numerical simulation is performed to analyse the potential failure processes of hazardous rock mass. In this study, we focused on the hazardous Diaozui rock mass of the Qutang Gorge in the Three Gorges Reservoir area (China). We constructed a 3D geological model of the rock mass based on the data from the field survey and UAV photogrammetric survey. Using this 3D geological model, we established a 3D numerical analysis model to assess the rockfall hazard. By utilizing the Strength reduction method (SRM) and simulating the collapse process of the hazardous rock mass, we analyzed the instability mechanism and failure evolution process of the Hazardous Diaozui rock mass. The results illustrated the potential failure mode, the key-oriented wedges of the rock mass, and the potential critical failure point for the hazardous rock mass. These findings provide valuable insights for stability assessment, risk monitoring, and evaluation of the hazardous rock mass in the Three Gorges Reservoir area. [ABSTRACT FROM AUTHOR]

This paper investigates a 2-bit all-optical analog-to-digital converter (AO-ADC) using the photonic crystal (PhC) structure. The proposed structure comprises a 27 × 27 grid of silicon rods in air with a refractive index of 3.6. In the design of this converter, a linear demultiplexer and an optical encoder are used. The optical demultiplexer has one input and three outputs. Optical coding has three inputs and two outputs. In general, this converter consists of one input and two outputs, and according to the output light power from the structure and the threshold level of the converter, two logical 0 and 1 states are created in the output. The footprint of the proposed AO-ADC is as small as 118.5 µm2 making it more suitable for use in the optical integrated circuits (OICs) compared to the previous structures. The proposed AO-ADC works at an operating wavelength of 1550 nm with a response time of about 0.6 ps and also works with lower optical intensity. [ABSTRACT FROM AUTHOR]

The Double-Yield (D-Y) model is a widely used method for predicting the mechanical properties of caved rock. However, determining the numerical simulation parameters for this model typically requires extensive trial and error. In this paper, a new approach for parameter inversion of the D-Y model is proposed and applied to a real case study involving repeated mining in multiple coal seams. The proposed framework combines FLAC3D, a finite element numerical simulation software, with a new computational tool developed using MATLAB® App Designer. By applying this framework to the case study, the accuracy and efficiency of parameter determination in the mining area are improved. In addition, a 3D finite element model of multiple coal seams is generated based on the geological information of the case study, and the stress evolution is analyzed. The simulation results are then validated through field measurements, providing valuable reference information for safe and efficient production. Overall, this improved method for parameter inversion of the D-Y model, along with the combined numerical simulation and field measurement approach, enhances the understanding of stress evolution in multiple coal seams and contributes to safer and more efficient mining operations. Highlights: An in-depth analysis was conducted to examine how variations in Double-Yield parameters impact the numerical simulation curve. A breakthrough approach for parameter inversion of the Double-Yield (D-Y) model is introduced, and the computational tool is developed. A 3D finite element model is crafted to analyse the dynamic stress evolution during repeated mining of multiple coal seams. The accuracy of simulation outcomes is bolstered by validation against field measurements of mining-induced stress. [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 this paper, we discuss properties of the singular value decomposition (SVD-decomposition) within the framework of the analysis of the numerical rank in ill-posed problems for determining frequency properties of discrete sequences consisting of trigonometric binomials. The properties of the numerical rank of the SVD-decomposition are indicated. We propose an algorithm for determining the frequencies of trigonometric binomials involved in the original function that forms a discrete sequence; this algorithm is based on estimates of the numerical rank. We obtain a stable criterion for estimating the numerical rank based on the arithmetic-mean estimators of the pseudo-null-space of the trajectory matrix. Also, we present the results of numerical experiments that demonstrate the consistency of the arithmetic-mean estimator of the pseudo-zero-space for the analysis of the spectrum of noisy sequences. [ABSTRACT FROM AUTHOR]

The aim of this paper is twofold. First, we prove L p estimates for a regularized Green's function in three dimensions. We then establish new estimates for the discrete Green's function and obtain some positivity results. In particular, we prove that the discrete Green's functions with singularity in the interior of the domain cannot be bounded uniformly with respect of the mesh parameter h. Actually, we show that at the singularity the discrete Green's function is of order h - 1 , which is consistent with the behavior of the continuous Green's function. In addition, we also show that the discrete Green's function is positive and decays exponentially away from the singularity. We also provide numerically persistent negative values of the discrete Green's function on Delaunay meshes which then implies a discrete Harnack inequality cannot be established for unstructured finite element discretizations. [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]

Crafting a model possessing high-fidelity state transfer is one of the important topics discussed in the literature because of its wide applications. In this paper, we study a state transfer problem in a central spin model in the presence of external classical modulations to address some aspects of the Epstein effect. Experimental studies behind the Epstein effect demonstrate that a classical modulation/vibration can cause state transfer in a system that was previously thought to be impossible. This is another demonstration of a nontrivial impact of the classical world on the quantum one to be understood yet and our work is a step toward it. Indeed, performed numerical analysis demonstrates that central spin models can be used to obtain high-fidelity state transfer caused mainly by external classical modulations. [ABSTRACT FROM AUTHOR]

This paper presents a numerical analysis of different rheology models during the encapsulation of moulded underfill (MUF) for flip-chip package. Robust computational fluid dynamics of finite volume analysis software; ANSYS FLUENT Workbench 14.5 was utilised in three-dimensional. A remarkable analysis was carried out by considering three distinctions among rheology models, namely Power Law, Cross, and Castro-Macosko. Nevertheless, a unique function has been written for the Castro–Macosko model since it considers the curing effect using user-defined functions. The volume of fluid technique was utilised to track the flow front of epoxy moulding compound (EMC). Beforehand, the flow visualization for the tray cavity has been verified by both experiment and simulation qualitatively, and it has been found to be in good agreement. It also conformed to the rheological properties, i.e., viscosity and shear rate. For MUF encapsulation, the 3D views of the melt front profile during encapsulation were presented. In addition, the viscosity-shear rate and void formation versus rows of multi-flip chips for all models were plotted and discussed. The numerical results have shown that the best rheology model for EMC during encapsulation was the Castro-Macosko model with consideration of curing effect. It was clearly found that the retardation flow occurred since the conversion of EMC took place, i.e., the curing effect. The present numerical analysis is expected to grant a good understanding of epoxy behaviour for engineers and designers in the electronic packaging industry. [ABSTRACT FROM AUTHOR]

In this paper, finite element method is used to calculate the static performance of gas journal bearing, in which rotation speed term is introduced into the stiffness matrix of linear triangular element to realize the performance calculation of the bearing with rotation speed. The results indicate that the average gas film thicknesses corresponding to the maximum load capacity and stiffness, and the minimum attitude angle increase with the growth of orifice diameter. Load capacity and stiffness significantly improved with the increase of rotation speed, eccentricity ratio and supply pressure when the bearing has thin average gas film thickness. Attitude angle increases with the growth of rotation speed, while the growth rate slows down or even decreases at high speed. The most effective way of reducing attitude angle is to increase supply pressure. It can be found that rotation speed affects attitude angle through changing gas pressure difference between two orifices, while other parameters have the same effect by changing gas pressure at orifice outlet. Article Highlights: Analyzing performances of gas journal bearings by solving Reynolds equation with FEM. Solving Reynolds equation with speed term using FEM. Investigating the effect of bearing parameters on attitude angle, stiffness, and load capacity. [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]

Splines are piecewise polynomial functions which are continuously differentiable to some order r. For a fixed integer d the space of splines of degree at most d is a finite dimensional vector space, and a largely open problem in numerical analysis is to determine its dimension. While considerable attention has been given to this problem in the bivariate setting, the literature on trivariate splines is less conclusive. In particular, the dimension of generic trivariate splines is not known even in large degree when r > 1 . In this paper we use a bound we previously derived for splines on vertex stars to compute a new lower bound on the dimension of trivariate splines in large enough degree. We illustrate in several examples that our formula gives the exact dimension of the spline space in large enough degree if vertex positions are generic. In contrast, for splines continuously differentiable of order r > 1 , every lower bound in the literature diverges (often significantly) in large degree from the dimension of the spline space in these examples. We derive the bound using commutative and homological algebra. [ABSTRACT FROM AUTHOR]

This paper presents the results of an analysis of the porous structure of spherical activated carbons obtained from cation-exchange resin beads subjected to ion exchange prior to activation. The study investigated the effects of the type of cation exchange resin, the concentration of potassium cations in the resin beads and the temperature of the activation process on the adsorption properties of the resulting spherical activated carbons. The numerical clustering-based adsorption analysis method and the quenched solid density functional theory were used to analyse the porous structure of spherical activated carbons. Based on original calculations and unique analyses, complex relationships between preparation conditions and the porous structure properties of the obtained spherical activated carbons were demonstrated. The results of the study indicated the need for simultaneous analyses using advanced methods for the analysis of porous structures, i.e., the numerical clustering-based adsorption analysis method and the quenched solid density functional theory. This approach allows a reliable and precise determination of the adsorption properties of the materials analysed, including, among other things, surface heterogeneities, and thus an appropriate selection of production conditions to obtain materials with the expected adsorption properties required for a given industrial process. [ABSTRACT FROM AUTHOR]

In this paper, we propose an approach for describing wave propagation in finite-size microstructured metamaterials using a reduced relaxed micromorphic model. This method introduces an additional kinematic field with respect to the classical Cauchy continua, allowing to capture the effects of the underlying microstructure with a homogeneous model. We show that the reduced relaxed micromorphic model is not only effective for studying infinite-size metamaterials, but also efficient for numerical simulations and analysis on specimens of finite size. This makes it an essential tool for designing and optimizing metamaterials structures with specific wave propagation properties. The proposed model's efficiency is assessed through numerical simulations for finite-size benchmark problems, and shows a good agreement for a wide range of frequencies. The possibility of producing the same macroscopic metamaterial with different but equivalent unit cell "cuts" is also analyzed, showing that, even close to the boundary, the reduced relaxed micromorphic model is capable of giving accurate responses for the considered loading and boundary conditions. [ABSTRACT FROM AUTHOR]

In this paper, we study the phase tranisions in the extended holographic thermodynamics of Born–Infeld AdS black holes. The extended gravitational thermodynamics of black holes is related to the thermodynamics of the dual field theory by varying both cosmological constant and Newton's constant. With topological analysis and numerical calculation, we find that the reentrant large-small-large black hole phase transition still exists in D = 4 . Interestingly, a similar reentrant phase transition is also observed in the dual field theory, between the high-, low- and high-entropy thermal states. For higher dimension D > 4 , only the van der Waals like phase transition is observed, both in the bulk and the dual field theory. [ABSTRACT FROM AUTHOR]

In this paper, we provide a numerical solution for the nonlinear tempered fractional integrodifferential equation in three dimensions. We use the trapezoidal convolution rule with backward differences (BDF2) for temporal discretization, and develop an alternating direction implicit difference scheme for spatial discretization. A novel fast approximation is applied to tackle the nonlinear term. The stability and convergence analysis of the numerical scheme are analyzed. Furthermore, some numerical experiments are provided to confirm the theoretical results. [ABSTRACT FROM AUTHOR]

This paper gives a highly efficient technique to analyse the fractional BBM-Burger equation and fractional Diffusion-Wave equation. These equations are used to model various real-life phenomena like acoustic gravity waves, diffusion theory, anomalous diffusive systems, and wave propagation phenomena. A modified technique, which is the combination of the Homotopy perturbation method and Laplace transform, is used for getting the numerical solution. The Lyapunov function is used to investigate asymptotic stability, and the maximum absolute error for the proposed technique is also examined. The efficiency of the proposed technique is shown by computing the root mean square (RMS), L 2 , and L ∞ errors and comparing the results with the other techniques. [ABSTRACT FROM AUTHOR]

Because of the increased mobility of vehicle users, it might be difficult to keep communication services in vehicle networks effective and dependable. Huge hurdles have been presented to vehicular networks as a result of the meteoric rise in the amount of data, which comes with the needs of high dependability and low latency. The deployment of access point servers at geographic locations that are closer to the vehicles in order to provide real-time service to applications that are based on the vehicles is one possible option. However, there is a limited amount of cache store space, and there is also a lack of a tractable access mode allocation method. As a result of these factors, it is very difficult to strike a compromise between the network transmission performance and fronthaul savings. Because the signal-to-interference-ratio (SIR) can be enhanced with switching mode in vehicular infrastructure, it may be possible to achieve higher levels of dependability. To serve all of the vehicles, the conventional allocation in vehicular network may not be sufficient on its own for two reasons: (1) the number of vehicles exceeds the number of paths, and (2) a vehicle may be located outside of the coverage path. Therefore, the implementation of switching mode allocation in vehicular communication is very necessary in order to increase the number of vehicles that can be supplied. In this paper, allocation using V2I, V2V, and V2X modes have been analyzed to provide dependable coverage for vehicles. These methods are used for communicating with other vehicles. In this paper, the numerical analysis has been performed such that SIR is optimized. In switching mode allocation, it has been shown that establishing a variable SIR threshold is helpful in achieving a path coverage that can be relied upon. It has been shown beyond a reasonable doubt that the coverage probability is likewise directly dependent on SIR thresholds. The theoretical analysis is verified, and it is confirmed that the suggested method is capable of achieving significant performance improvement in terms of coverage probability and data rate. [ABSTRACT FROM AUTHOR]

Reservoir computing (RC) is a popular class of recurrent neural networks (RNNs) with untrained dynamics. Recently, advancements on deep RC architectures have shown a great impact in time-series applications, showing a convenient trade-off between predictive performance and required training complexity. In this paper, we go more in depth into the analysis of untrained RNNs by studying the quality of recurrent dynamics developed by the layers of deep RC neural networks. We do so by assessing the richness of the neural representations in the different levels of the architecture, using measures originating from the fields of dynamical systems, numerical analysis and information theory. Our experiments, on both synthetic and real-world datasets, show that depth—as an architectural factor of RNNs design—has a natural effect on the quality of RNN dynamics (even without learning of the internal connections). The interplay between depth and the values of RC scaling hyper-parameters, especially the scaling of inter-layer connections, is crucial to design rich untrained recurrent neural systems. [ABSTRACT FROM AUTHOR]

This paper presents an enhanced version of the standard shooting method that enables problems with two unknown parameters to be solved. A novel approach is applied to the analysis of the natural vibrations of Euler-Bernoulli beams. The proposed algorithm, named as two-parameter multiple shooting method, is a new powerful numerical tool for calculating the natural frequencies and modes of multi-segment prismatic and non-prismatic beams with different boundary conditions. The impact of the axial force and additional point masses is also taken into account. Due to the fact that the method is based directly on the fourth-order ordinary differential equation, the structures do not have to be divided into many small elements to obtain an accurate enough solution, even though the geometry is very complex. To verify the proposed method, three different examples are considered, i.e., a three-segment non-prismatic beam, a prismatic column subject to non-uniformly distributed compressive loads, and a two-segment beam with an additional point mass. Numerical analyses are carried out with the software MATHEMATICA. The results are compared with the solutions computed by the commercial finite element program SOFiSTiK. Good agreement is achieved, which confirms the correctness and high effectiveness of the formulated algorithm. [ABSTRACT FROM AUTHOR]

In this paper, in view of the existing mechanical sand cleaning technology, circulating sand flushing technology, and negative pressure sand cleaning technology, which cannot establish circulation, the pump lift is limited, the sand cleaning efficiency is low, and many other problems when cleaning the sand in deep wells that are prone to leakage, a new type of sand cleaning system that can realize the local circulation and storage of sand fluid at the bottom of the well is designed. The critical problem to be solved in this design is how to simultaneously meet the dual requirements of local circulation and storage, that is, how to coordinate the contradiction between gravel carrying and settlement. Therefore, studying the mechanism of sand transport and settlement in the new type of sand cleaning cylinder is necessary. The discrete phase model of the sand liquid flowing in the sand cleaning cylinder was established using EDEM-FLUENT. The numerical simulation and analysis of the movement law of sand grains, the trajectory line clouds of sand grains, and the variation law of sand settling rate, sand mass flow rate, and sand-carrying liquid flow rate under different working parameters were obtained. The conclusion shows that when the mass flow rate of sand particles is 0.5–0.8 kg/s, and the flow rate of sand-carrying liquid is 0.5– 1 m/s, the grit removal effect of the sand cleaning cylinder is better. In order to verify the sand cleaning effect of this new sand cleaning system and the accuracy of the numerical analysis model, the ground simulation test platform of the sand cleaning cylinder was built, and simulated sand cleaning tests were carried out under different sand particle sizes and different sand-carrying fluid flow rates. The test results show that the new sand cleaning system clears sand well. Comparing the numerical simulation results with the experimental results, the two have the same variation pattern, which verifies the feasibility of this new sand cleaning system and the correctness of the numerical analysis model. The study provides a new sand cleaning system solution, which solves the problem that existing sand cleaning techniques cannot quickly and efficiently clean up sunken sand from leaking oil and gas wells and provides a basis for the selection of field operating parameters for the new sand cleaning system. [ABSTRACT FROM AUTHOR]

In the development of horizontal wells, it is necessary to use tractors to transport logging tools. However, the current wheel tractors have relatively small traction force. To solve this problem, the wheel tractor with a novel design method of driving wheel was designed. Considering the adhesion effect and the furrow effect at the same time, the mechanical model between the driving wheel and the casing was established. Based on this, the factors affecting the friction coefficient between the casing and the driving wheel were obtained. The simulation model between the casing and the driving wheel was established. The boundary conditions and loads were set. According to numerical simulation analysis, it is found that the optimal parameters are the addendum angle of 105°, the tooth inclination angle of 120°, the bottom length of 4 mm and the embedded depth of 0.2 mm. The optimal coefficient friction between the driving wheel and the casing is 1.0476. According to the optimal parameters of the teeth of the driving wheel, a new type of driving wheel was designed. The experiment was carried out in a wheel tractor prototype. According to the unit prototype experiment, the crawling speed of the wheel tractor is 640 m/h and the maximum traction force of a single section can reach 1450 N. This verifies that this design method can indeed provide greater traction for the wheel tractor. This paper lays a theoretical foundation for wheel tractors to design the driving wheel. This is of great significance to improve the efficiency of downhole operations such as plug drilling and promote the development of long horizontal wells. [ABSTRACT FROM AUTHOR]

Applying the gradient discretisation method (GDM), the paper develops a comprehensive numerical analysis for nonlinear equations called the reaction–diffusion model. Using only three properties, this analysis provides convergence results for several conforming and non-conforming numerical schemes that align with the GDM. As an application of this analysis, the hybrid mimetic mixed (HMM) method for the reaction–diffusion model is designed, and its convergence is established. Numerical experiments using the HMM method are presented to facilitate the study of the creation of spiral waves in the Barkley model and the ways in which the waves behave when interacting with the boundaries of their generating medium. [ABSTRACT FROM AUTHOR]

This paper describes a numerical simulation within the framework of a two-dimensional shallow water model of interaction of a solitary wave with a steady rectangular semi-submerged structure. The results of this study are compared with the results of calculations based on a model of irrotational three-dimensional flows, and it is shown that the simulation accuracy at small incident wave amplitudes is satisfactory. It is also revealed that, the solitary wave diffraction on the cylinder surface is neglected when using a one-dimensional shallow water model, then the maximum values of wave runup on the edge of the cylinder and the force loads on it become overestimated. [ABSTRACT FROM AUTHOR]

With the increase in the pace of development, the demand for tunnels has increased in recent years. Analysing the stability of a tunnel in a fractured rock mass is a very challenging and cumbersome activity. The tunnel stability depends on the strength of the rock, joints bolt strength, in-situ stresses, and their orientation. This paper focuses on constructing tunnels in fractured/jointed rock mass. Three different software namely Rocscience Phase2 (finite element based), FLAC3D (finite volume based) and PFC3D (distinct element based), were used to analyse the performance and stability under static and dynamic loading conditions. The geomaterial properties used for the analysis were taken from data obtained after laboratory testing and based on available literature. The effect of joint orientation and bolt length was analysed using Phase 2 assuming plain strain conditions. The effect of earthquake and performance of fully grouted, energy absorbing and deformation-controlled bolts under seismic loading conditions were compared using FLAC3D. While the 3D distinct element analysis of geometry was performed using PFC3D to evaluate the effect of joints and their orientation. The performance of the different types of bolts was also analysed numerically. The behaviour of bolts can be customised using the 'fish'function. The results indicate that analysis must incorporate the fusion of various numerical simulation techniques like finite element-, finite volume- and distinct element-based methods for more reliable results. [ABSTRACT FROM AUTHOR]

Horizontal drains (HDs) are commonly deployed at open pit mines to depressurize the pit walls and thereby improve pit wall stability. If successful, depressurization maintains current pit wall angles and improves stripping ratios, which directly influences mine economics. HDs are commonly designed using empirical approaches that have been developed based on experience at other mines and are often aided by 2D and 3D analysis using groundwater models at sites with complex geological and structural settings. Specialized techniques for simulating HDs in these models became available nearly 20 years ago with the introduction of discrete feature elements in FEFLOW, a proprietary groundwater modelling package. More recently, introduction of unstructured grids allowed direct representation of HDs and their sequencing in MODFLOW, a publicly available modelling package that is widely used at mine sites. This paper provides an example of how HD design can be aided by 3D numerical analysis that utilizes these new MODFLOW simulation capabilities. [ABSTRACT FROM AUTHOR]

Analytical techniques used for estimating thermoelastic damping by incorporating both mechanical and thermal interactions between surfaces and the rest of the bulk are intricate and challenging due to the limited understanding of the damping mechanisms in extra-thin films subjected to forced vibrations. This paper proposes a modified model to analytically calculate the thermoelastic damping of ultrathin elastic films due to surface effects and analyzes the thermoelastic damping variation with different factors through numerical experiments on two materials. The model considers surface stresses derived from the elastic surface theory using Kirchhoff's kinetic hypothesis and determines thermoelastic damping by considering thermal dissipation and elastic potential energy. The results show that surface effects significantly influence the thermoelastic damping of the film, and the specific behavior of a thin film's thermoelastic damping with respect to film thickness is impacted by various factors, including material property, the variation range of film thickness, and the forced vibration frequency. This study provides insights into the thermoelastic damping behavior of thin films and has important implications for the development of nanoscale oscillators in MEMS or NEMS systems. [ABSTRACT FROM AUTHOR]

Dynamical systems that evolve continuously over time are ubiquitous throughout science and engineering. Machine learning (ML) provides data-driven approaches to model and predict the dynamics of such systems. A core issue with this approach is that ML models are typically trained on discrete data, using ML methodologies that are not aware of underlying continuity properties. This results in models that often do not capture any underlying continuous dynamics—either of the system of interest, or indeed of any related system. To address this challenge, we develop a convergence test based on numerical analysis theory. Our test verifies whether a model has learned a function that accurately approximates an underlying continuous dynamics. Models that fail this test fail to capture relevant dynamics, rendering them of limited utility for many scientific prediction tasks; while models that pass this test enable both better interpolation and better extrapolation in multiple ways. Our results illustrate how principled numerical analysis methods can be coupled with existing ML training/testing methodologies to validate models for science and engineering applications. Many challenging problems in science and engineering rely on the study of dynamical systems that evolve continuously in time, and yet this feature proves difficult to be captured reliably using modern machine learning (ML) models. This paper develops a convergence test based on numerical analysis and illustrates how this methodology can be combined with existing ML techniques to validate models for science and engineering applications. [ABSTRACT FROM AUTHOR]

There is a fault in the region of Niteroi city, Rio de Janeiro, Brazil, and weathering has formed different soil layers in terms of granulometry, resistance, and stiffness, which are regularly spread throughout the soil mass. These reasonably continuous reliquiae soil layers showed thicknesses varying from a few millimetres to few centimetres. For the weak soil layers, laboratory tests indicated the presence of high activity clay minerals and low shear resistance parameters. The present paper numerically assesses the impact of those relatively weak layers and the excavation execution procedure on the performance of anchored walls. The direction of those layers was orthogonal to the wall face, and the dip was unfavourable to the excavation. The numerical modelling was firstly validated against data from an instrumented structure excavated in gneiss residual soil located in Niteroi city, Rio de Janeiro, Brazil. The results of the parametric study show that the weak layers plastify during the excavation with low lateral movements and the presence of those weak layers leads to an increase of the uphill settlements (about six times), lateral facing displacements (about four times), distortions (about 12 times), and anchor loads (about 1.4 times). This research calls attention to the importance of reliable site investigation for determination of the soil profile and its correct modelling in order to have a safe and cost-effective project. [ABSTRACT FROM AUTHOR]

This paper presents a high-order computational scheme for numerical solution of a time-fractional diffusion equation (TFDE). This scheme is discretized in time by means of L1-scheme and discretized in space using a compact finite difference method. Stability analysis of the method is discussed. Further, convergence analysis of the present numerical scheme is established and we show that this scheme is of O (Δ t 2 - α + Δ x 4) convergence, where α ∈ (0 , 1) is the order of fractional derivative (FD) appearing in the governing equation and Δ t and Δ x are the step sizes in temporal and spatial direction, respectively. Three numerical examples are considered to illustrate the accuracy and performance of the method. In order to show the advantage of the proposed method we compare our results with those obtained by finite element method and B-spline method. Comparison reveals that the proposed method is fast convergent and highly accurate. Moreover, the effect of α on the numerical solution of TFDE is investigated. The CPU time of the present method is provided. [ABSTRACT FROM AUTHOR]

The best polynomial approximation and the Chebyshev approximation are both important in numerical analysis. In tradition, the best approximation is regarded as better than the Chebyshev approximation, because it is usually considered in the uniform norm. However, it is not always superior to the latter, as noticed by Trefethen (Math. Today 47:184–188, 2011) for the function f (x) = | x - 0.25 | . Recently, Wang (arxiv, 2106.03456, 2021) observed a similar phenomenon for a function with an algebraic singularity and proved it in theory. In this paper, we find that for functions with logarithmic endpoint singularities, the pointwise errors of the Chebyshev approximation are smaller than those of the best approximations of the same degree, except only at the narrow boundary layer. The pointwise error for the Chebyshev series truncated at the degree n is O (n - κ) ( κ = min { 2 γ + 1 , 2 δ + 1 } ), but increases as O (n - (κ - 1)) at the endpoint singularities. Theorems are given to explain this effect. [ABSTRACT FROM AUTHOR]

This work aims to investigate the problem glucose and hemoglobin detection in blood samples and other liquids, by using a novel SPR sensors. Our designs is based on Kretschmann configuration, incorporating multi-layers of silver (Ag), titanium dioxide (TiO2), black phosphorus (BP) and gold (Au). Simulations based on transfer matrix method were carried out to compute reflectance of each device. The Impact of Ag, BP and TiO2 on the sensitivity performance are demonstrated. The maximum sensitivity attained is 682.34 deg/RIU with other performance parameters computed, minimum reflection (Rmin) of 0.14 % , detection accuracy of 0.290 deg−1, and quality factor of 171.698 RIU−1. Our proposed devices are expected to plays an active role for recognizing biological or chemical entities in liquids. Numerical results obtained in this paper exhibited high sensitivity in comparison with previously reported studies. [ABSTRACT FROM AUTHOR]

In various industrial applications, especially those that focus on heat transfer, curved ducts present an interesting equipment. The flow behavior inside curved ducts is more complex compared to straight ducts, particularly in the presence of nanofluids. Hence, the present paper reports a numerical investigation of a nanofluid two-phase flow according to the Buongiorno model in a curved duct with abruptly expanded cross section. It deals with a toroidal duct with a circular cross-section abruptly expanded through which an Alumina-water nanofluid flows. The nanofluid penetrates the duct with a constant initial velocity at a cold constant temperature. Moreover, the lateral surface of the expanded part of the duct is maintained at a hot temperature, however, the rest of the duct boundaries are assumed to be adiabatic. The aim of the present study is to visualize the impact of the phenomenon of inertia (10 ⩽ Re ⩽ 200), mass diffusion (0.1 ⩽ Le ⩽ 100) and alumina nanoparticles concentration (0 ⩽ φ0 ⩽ 0.1) on the hydrodynamic, thermal and mass behavior of the nanofluid inside the expanded curved ducts under Brownian and thermophoretic diffusions. The nanofluid flow is governed by the mathematical model of Buongiorno including the mass, momentum, energy and nanoparticles equations and solved by the Galerkin finite element method. The numerical results have indicated that, in addition to the presence of Dean's vortices, the enlarged configuration of the current duct leads to the emergence of vortices resulting from flow reattachment. Moreover, the heat transfer rate increases with higher Reynolds numbers. Furthermore, the addition of alumina nanoparticles enhances the heat transfer with a percentage of 15% compared to pure water. Additionally, there is a relative decrease in the heat transfer rate due to nanoparticles' thermophoretic migration. On the other hand, the increase in the Lewis number does not significantly influence this heat transfer rate, although it does promote a more homogeneous distribution of nanoparticles. [ABSTRACT FROM AUTHOR]

Because of the increased mobility of vehicle users, it might be difficult to keep communication services in vehicle networks effective and dependable. Huge hurdles have been presented to vehicular networks as a result of the meteoric rise in the amount of data, which comes with the needs of high dependability and low latency. The deployment of access point servers at geographic locations that are closer to the vehicles in order to provide real-time service to applications that are based on the vehicles is one possible option. However, there is a limited amount of cache store space, and there is also a lack of a tractable access mode allocation method. As a result of these factors, it is very difficult to strike a compromise between the network transmission performance and fronthaul savings. Because the signal-to-interference-ratio (SIR) can be enhanced with switching mode in vehicular infrastructure, it may be possible to achieve higher levels of dependability. To serve all of the vehicles, the conventional allocation in vehicular network may not be sufficient on its own for two reasons: (1) the number of vehicles exceeds the number of paths, and (2) a vehicle may be located outside of the coverage path. Therefore, the implementation of switching mode allocation in vehicular communication is very necessary in order to increase the number of vehicles that can be supplied. In this paper, allocation using V2I, V2V, and V2X modes have been analyzed to provide dependable coverage for vehicles. These methods are used for communicating with other vehicles. In this paper, the numerical analysis has been performed such that SIR is optimized. In switching mode allocation, it has been shown that establishing a variable SIR threshold is helpful in achieving a path coverage that can be relied upon. It has been shown beyond a reasonable doubt that the coverage probability is likewise directly dependent on SIR thresholds. The theoretical analysis is verified, and it is confirmed that the suggested method is capable of achieving significant performance improvement in terms of coverage probability and data rate. [ABSTRACT FROM AUTHOR]

The performance of a permissioned blockchain, namely, Hyperledger Fabric, is modeled and analyzed in a quantitative manner in this paper. Various types of nodes contribute to the performance of Hyperledger Fabric, and each of those is modeled and tracked along the operational flow of the permissioned blockchain. There are nodes for endorsement, ordering, and commitment to realize the due decentralized network operations. A quantitative model for each type of nodes has been proposed in Ke and Park (Performance study on various Hyperledger Fabric node types and transaction flow, IEEE BCCA, 2021) along with numerical analysis. Each type of the nodes is characterized in terms of transaction/block queue size and waiting time, and the transaction/block arrival rates and the transaction/block service rates are considered for simulation purposes. The analysis is extended beyond the analysis in Ke and Park (Performance study on various Hyperledger Fabric node types and transaction flow, IEEE BCCA, 2021) in this paper to particularly demonstrate how the arrival rates and the service rates co-influence the performance and how the number of channels impacts the performance, in order to ultimately facilitate a more dynamic way of optimization, taking the co-relation across different types of nodes into account. The major contribution of this paper to the field of computer science by creating a series of queuing models to evaluate the performance of different types of nodes: Chaincode Execution and Endorsement, Block Creation and Delivery, Transaction Validation and Block Committing, and Transaction Processing. [ABSTRACT FROM AUTHOR]

This paper discusses continuum models for simulating earthquake sequences on faults governed by rate-and-state dependent friction. Through detailed numerical analysis of a conventional strike-slip fault, new observations regarding the use of various continuum earthquake models are presented. We update a recently proposed plasticity-based model using a consistently linearized formulation, show its agreement with discrete fault models for fault thicknesses of hundreds of meters, and demonstrate mesh objectivity for slip-related variables. To obtain a fully regularized fault width description with an internal length scale, we study the performance and mesh convergence of a plasticity-based model complemented by a Kelvin viscosity term and the phase-field approach to cohesive fracture. The Kelvin viscoplasticity-based model can introduce an internal length scale and a mesh-objective response. However, on grid sizes down to meters, this only holds for very high Kelvin viscosities that inhibit seismic slip rates, which renders this approach impractical for simulating earthquake sequences. On the other hand, our phase-field implementation for earthquake sequences provides a numerically robust framework that agrees with a discrete reference solution, is mesh objective, and reaches seismic slip rates. The model, unsurprisingly, requires highly refined grids around the fault zones to reproduce results close to a discrete model. Following this line, the effect of an internal length scale parameter on the phase-field predictions and mesh convergence are discussed. [ABSTRACT FROM AUTHOR]

This paper deals with the design and analysis of a robust numerical scheme based on an improvised quartic B-spline collocation (IQBSC) method for a class of nonlinear derivative dependent singular boundary value problems (DDSBVP). The convergence analysis of the method is studied by means of Green's function approach. It should be pointed out that the numerical order of convergence of standard quartic B-spline collocation (SQBC) scheme for second-order boundary value problems (BVPs) is four, however, our proposed IQBSC method is shown to be sixth order convergence. To illustrate the applicability and accuracy of the method, we consider eight test problems. The obtained results are compared to those from some existing numerical schemes in order to show the advantage of present method. It is shown that the rate of convergence of present numerical scheme is higher than that of some of existing numerical methods. The CPU time of the present numerical method is provided. [ABSTRACT FROM AUTHOR]

Techniques must be used to improve the thermal conductivity of paraffin phase change materials (PCM) for augmenting the passive thermal management of PV. In this paper, transient three-dimensional numerical simulations of PV-PCM systems with square and circular cross-sectional fins have been carried out to analyse the effect of fins and inclination θ on the performance. Finned PV-PCM systems with multiple fin numbers are considered. The parameters, such as the average temperature and efficiency of the module, are simulated and compared. Results show that the system with square fins gives better thermal regulation over cylindrical ones for all inclinations and fin numbers. The system with 16 square fins at θ = 45 ∘ is found with minimum PV temperature and maximum efficiency. Maximum temperature reductions of 57.56 °C and 56.8 °C and efficiency enhancements of 43.47% and 42.89% are achieved for horizontal systems with 16 square and cylindrical fins, respectively, over PV alone system. The effect of fin length is also simulated, and the maximum PV temperature reductions of 56.8 °C and 45.96 °C are obtained for full-length configurations with inclinations of 0 ∘ and 45 ∘ , respectively. The peak velocity of melted PCM is simulated, and a maximum peak velocity of 4.88 mm s−1 is obtained for the unfinned PV-PCM system with θ = 45 ∘. [ABSTRACT FROM AUTHOR]

Carbon doping in GaN-on-Silicon (Si) epitaxial layers is an essential way to reduce leakage current and improve breakdown voltage. However, complicated occupy forms caused by carbon lead to hard analysis leakage/breakdown mechanisms of GaN-on-Si epitaxial layers. In this paper, we demonstrate the space charge distribution and intensity in GaN-on-Si epitaxial layers from 0 to 448 V by simulation. Depending on further monitoring of the trapped charge density of CN and CGa in carbon-doped GaN at 0.1 μm, 0.2 μm, 1.8 μm and 1.9 μm from unintentionally doped GaN/carbon-doped GaN interface, we discuss the relationship between space charge and plateau, breakdown at CN concentrations from 6 × 1016 cm−3 to 6 × 1018 cm−3. The results show that CN in different positions of carbon-doped GaN exhibits significantly different capture and release behaviors. By utilizing the capture and release behavior differences of CN at different positions in carbon-doped GaN, the blocking effect of space charge at unintentionally doped GaN/carbon-doped GaN interface on electron conduction was demonstrated. The study would help to understand the behavior of CN and CGa in GaN-on-Si epitaxial layers and more accurate control of CN and CGa concentration at different positions in carbon-doped GaN to improve GaN-on-Si device performance. [ABSTRACT FROM AUTHOR]

This paper presents the lateral pile-soil response occurring in coral and silica sand foundations through comparative numerical studies. In this study, the Hypoplastic constitutive model was implemented into Abaqus software to simulate the stress–strain relationship of coral sand and silica sand with the same particle gradation. The validation of numerical model was verified by centrifuge test results. Afterward, forty-eight numerical analyses were employed to assess the influence of pile diameter, embedment length, loading eccentricity, and relative density on the lateral response of piles in two kinds of sands. The load–displacement response, pile deflection, bending moment, and p-y curves were compared and analyzed in detail. The results showed that, with the increase in displacement level and relative density, the load responses of piles in coral sand gradually became greater than that in silica sand, the p-y curves in coral sand were also significantly higher than that in silica sand, and the bending moment and deflection profile of pile in silica sand were larger than that in coral sand. The difference in pile response between the two kinds of sands became more significant as the density and load level increased. Finally, a multi-parameter modified p-y model for coral sand was proposed, and its applicability and rationality were validated. [ABSTRACT FROM AUTHOR]

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]