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The main aim of the current paper is to find a numerical plan for hydraulic fracturing problem with application in extracting natural gases and oil.

First, time discretization is accomplished via Crank-Nicolson and semi-implicit techniques. At the second step, a high-order finite element method using quadratic triangular elements is proposed to derive the spatial discretization. The efficiency and time consuming of both obtained schemes will be investigated. In addition to the popular uniform mesh refinement strategy, an adaptive mesh refinement strategy will be employed to reduce computational costs.

Numerical results show a good agreement between the two schemes as well as the efficiency of the employed techniques to capture acceptable patterns of the model. In central single-crack mode, the experimental results demonstrate that maximal values of displacements in x- and y- directions are 0.1 and 0.08, respectively. They occur around both ends of the line and sides directly next to the line where pressure takes impact. Moreover, the pressure of injected fluid almost gained its initial value, i.e. 3,000 inside and close to the notch. Further, the results for non-central single-crack mode and bifurcated crack mode are depicted. In central single-crack mode and square computational area with a uniform mesh, computational times corresponding to the numerical schemes based on the high order finite element method for spatial discretization and Crank-Nicolson as well as semi-implicit techniques for temporal discretizations are 207.19s and 97.47s, respectively, with 2,048 elements, final time T = 0.2 and time step size τ = 0.01. Also, the simulations effectively illustrate a further decrease in computational time when the method is equipped with an adaptive mesh refinement strategy. The computational cost is reduced to 4.23s when the governed model is solved with the numerical scheme based on the adaptive high order finite element method and semi-implicit technique for spatial and temporal discretizations, respectively. Similarly, in other samples, the reduction of computational cost has been shown.

This is the first time that the high-order finite element method is employed to solve the model investigated in the current paper.

Considering the impact of the Free Trade Zone (FTZ) policy on forecasting the port cargo throughput, this paper constructs a fractional grey multivariate forecasting model to improve the prediction accuracy of port cargo throughput and realize the coordinated development of FTZ policymaking and port construction.

Considering the effects of data randomization, this paper proposes a novel self-adaptive grey multivariate prediction model, namely FDCGM(1,N). First, fractional-order accumulative generation operation (AGO) is introduced, which integrates the policy impact effect. Second, the heuristic grey wolf optimization (GWO) algorithm is used to determine the optimal nonlinear parameters. Finally, the novel model is then applied to port scale simulation and forecasting in Tianjin and Fujian where FTZs are situated and compared with three other grey models and two machine learning models.

In the Tianjin and Fujian cases, the new model outperforms the other comparison models, with the least mean absolute percentage error (MAPE) values of 6.07% and 4.16% in the simulation phase, and 6.70% and 1.63% in the forecasting phase, respectively. The results of the comparative analysis find that after the constitution of the FTZs, Tianjin’s port cargo throughput has shown a slow growth trend, and Fujian’s port cargo throughput has exhibited rapid growth. Further, the port cargo throughput of Tianjin and Fujian will maintain a growing trend in the next four years.

The new multivariable grey model can effectively reduce the impact of data randomness on forecasting. Meanwhile, FTZ policy has regional heterogeneity in port development, and the government can take different measures to improve the development of ports.

Under the background of FTZ policy, the new multivariable model can be used to achieve accurate prediction, which is conducive to determining the direction of port development and planning the port layout.

The purpose of this paper is to present a new approach to optimizing the design of 3D magnetic circuits. This approach is based on topology optimization, where derivative calculations are performed using the continuous adjoint method. Thus, the continuous adjoint method for magnetostatics has to be developed in 3D and has to be combined with penalization, filtering and homotopy approaches to provide an efficient optimization code.

To provide this new topology optimization code, this study starts from 2D magnetostatic results to perform the sensitivity analysis, and this approach is extended to 3D. From this sensitivity analysis, the continuous adjoint method is derived to compute the gradient of an objective function of a 3D topological optimization design problem. From this result, this design problem is discretized and can then be solved by finite element software. Thus, by adding the solid isotropic material with penalization (SIMP) penalization approach and developing a homotopy-based optimization algorithm, an interesting means for designing 3D magnetic circuits is provided.

In this paper, the 3D continuous adjoint method for magnetostatic problems involving an objective least-squares function is presented. Based on 2D results, new theoretical results for developing sensitivity analysis in 3D taking into account different parameters including the ferromagnetic material, the current density and the magnetization are provided. Then, by discretizing, filtering and penalizing using SIMP approaches, a topology optimization code has been derived to address only the ferromagnetic material parameters. Based on this efficient gradient computation method, a homotopy-based optimization algorithm for solving large-scale 3D design problems is developed.

In this paper, an approach based on topology optimization to solve 3D magnetostatic design problems when an objective least-squares function is involved is proposed. This approach is based on the continuous adjoint method derived for 3D magnetostatic design problems. The effectiveness of this topology optimization code is demonstrated by solving the design of a 3D magnetic circuit with up to 100,000 design variables.

This study aims to discuss the mathematical modelling of a compliance-assisted flapping mechanism and morphable structures for an UAV.

A compliance-assisted flapping wing was designed and modelled mathematically, and signals for the corresponding curves were calculated. The actual wing tip trace of a hummingbird was taken, and variables a, b, h and k were calculated from the image. This data was given to the mathematical model for plotting the graph, and the curve was compared with the input curve. The wing frame and mechanism for control surfaces using morphing is modelled along with single pivoted spine for centre of gravity augmentation and flight orientation control.

The model efficiently approximates the 2D path of the wing using line segments using the muscle and compliance mechanism.

Using a compliance-assisted flapping mechanism offers practical advantages. It allows us to synchronize the flapping frequency with the input signal frequency, ensuring efficient operation. Additionally, the authors can enhance the torque output by using multiple muscle strands, resulting in a substantial increase in the system’s torque-to-weight ratio. This approach proves to be more favourable when compared to conventional methods involving motors or servos, ultimately offering a more efficient and robust solution for practical application.

This model focuses on creating a flexible and tunable mechanism that can at least trace four types of wing traces from the same design, for shifting from one mode of flight to another.

Conventional ornithopter flapping mechanisms are gear or servo driven and cannot trace a wing tip, but some can trace complicated curves, but only one at a time. This model can trace multiple curves using the same hardware, allowing the user to program the curve based on their needs or bird. The authors may vary the shape of the wing tip trace to switch between forward flight, hovering, backward flying, etc., which is not conceivable with any traditional flapping mechanism.

In order to solve the decision-making problem that the attributive weight and attributive value are both interval grey numbers, this paper tries to construct a multi-attribute grey decision-making model based on generalized greyness of interval grey number.

Firstly, according to the nature of the generalized gresness of interval grey number, the generalized weighted greyness distance between interval grey numbers is given, and the transformation relationship between greyness distance and real number distance is analyzed. Then according to the objective function that the square sum of generalized weighted greyness distances from the decision scheme to the best scheme and the worst scheme is the minimum, a multi-attribute grey decision-making model is constructed, and the simplified form of the model is given. Finally, the grey decision-making model proposed in this paper is applied to the evaluation of technological innovation capability of 6 provinces in China to verify the effectiveness of the model.

The results show that the grey decision-making model proposed in this paper has a strict mathematical foundation, clear physical meaning, simple calculation and easy programming. The application example shows that the grey decision model in this paper is feasible and effective. The research results not only enrich the grey system theory, but also provide a new way for the decision-making problem that the attributive weights and attributive values are interval grey numbers.

The decision-making model proposed in this paper does not need to seek the optimal solution of the attributive weight and the attributive value, and can save the decision-making labor and capital investment. The model in this paper is also suitable for the decision-making problem that deals with the coexistence of interval grey numbers and real numbers.

The paper succeeds in realizing the multi-attribute grey decision-making model based on generalized gresness and its simplified forms, which provide a new method for grey decision analysis.

Considering the financial service providers’ (FSPs) information asymmetry in evaluating the supplier and their distinct quit probabilities, we want to examine the supplier’s preference of the financing schemes if both the bank and the online platform exist and how the buyer sets the contract terms in the two financing schemes.

We establish a Stackelberg game model to capture the interactions among three parties, i.e. a supplier, a capital-sufficient buyer and an FSP (either a bank or an online platform), within a first-time contract.

In the non-FSPs’ quit case, the buyer’s profit is higher under the bank loan scenario, while the supplier’s profit performs adversely. The supply chain’s profit is heavily dependent on the buyer’s profit difference between the two financing schemes. Moreover, we find that the supplier borrows the money to exactly cover the production cost. The equilibrium solutions of the FSPs’ quit case and of the capital-sufficient supplier’s case are also derived.

First, we assign different risk profiles to different FSPs in our setting so that modeling a previously ignored but practically significant problem. Second, we innovatively take the FSP’s quit probability into account in our model. Third, we elucidate how these factors can influence the relative efficiency of the two types of financing schemes and the settings of the contract, which further complements and extends the current SCF research.

The purpose of this paper is to evaluate the efficiency of a series network system with undesirable and unreturnable simultaneously.

The research was conducted by applying data envelopment analysis (DEA) approach to measure the efficiency score of a system and substages with an undesirable output of the second and third stages separately. For each case, new production technology was introduced, and based on them, novel DEA models were proposed.

One of the most important issues in the development of a country is the banking industry. In this study, 51 branches of commercial banks as a three-stage system with undesirable and unreturnable outputs in the second stage are considered. Then, the efficiency of each branch and substages is measured by using proposed models.

The efficiency of a three-stage network in the presence of undesirable and unreturnable outputs was assessed. In this model, Kousmanen’s technology was used.

Examines the trend to use standalone civil forfeiture procedures as an alternative to criminal processes for removing the proceeds of crime, outlining the distinction in most legal systems between criminal and civil. Explains why civil recovery is preferred: the standard of proof is lower, requiring to be only beyond a reasonable doubt. Discusses whether these civil recovery proceedings breach the basic presumption of innocence in all rights‐based legal systems, and whether they breach the double jeopardy rule at least in spirit. Indicates the need for research into whether civil recovery is in fact effective in impacting on criminal organisations and the factors likely to influence its effectiveness.