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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.

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.

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.

The purpose of this study is to stabilize the rotating speed of the permanent magnet direct current (PMDC) motor driven by a DC-DC boost converter under mismatched disturbances (i.e.) under varying load circumstances like constant, frictional, fan type, propeller and undefined torques.

This manuscript proposes a higher order sliding mode control to elevate the dynamic behavior of the speed controller and the robustness of the PMDC motor. A second order classical sliding surface and proportional-integral-derivative sliding surface (PIDSS) are designed and compared.

For the boost converter with PMDC motor, both simulation and experimentation are exploited. The prototype is built for an 18 W PMDC motor with field programmable gate arrays. The suggested sliding mode with second order improves the robustness of the arrangement under disturbances with a wide range of control. Both the simulation and experimental setup shows satisfactory results.

According to software-generated mathematical design and experimental findings, PIDSS exhibits excellent performance with respect to settling speed, steady-state error and peak overshoot.

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.

This study aims to address the inherent uncertainties within closed-loop supply chain (CLSC) networks through the application of a multi-objective approach, specifically focusing on the optimization of integrated production and transportation processes. The primary purpose is to enhance decision-making in supply chain management by formulating a robust multi-objective model.

In dealing with uncertainty, this study uses Pythagorean fuzzy numbers (PFNs) to effectively represent and quantify uncertainties associated with various parameters within the CLSC network. The proposed model is solved using Pythagorean hesitant fuzzy programming, presenting a comprehensive and innovative methodology designed explicitly for handling uncertainties inherent in CLSC contexts.

The research findings highlight the effectiveness and reliability of the proposed framework for addressing uncertainties within CLSC networks. Through a comparative analysis with other established approaches, the model demonstrates its robustness, showcasing its potential to make informed and resilient decisions in supply chain management.

This study successfully addressed uncertainty in CLSC networks, providing logistics managers with a robust decision-making framework. Emphasizing the importance of PFNs and Pythagorean hesitant fuzzy programming, the research offered practical insights for optimizing transportation routes and resource allocation. Future research could explore dynamic factors in CLSCs, integrate real-time data and leverage emerging technologies for more agile and sustainable supply chain management.

This research contributes significantly to the field by introducing a novel and comprehensive methodology for managing uncertainty in CLSC networks. The adoption of PFNs and Pythagorean hesitant fuzzy programming offers an original and valuable approach to addressing uncertainties, providing practitioners and decision-makers with insights to make informed and resilient decisions in supply chain management.