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This paper aims to investigate the features of three vectorized iterative numerical schemes used to simulate the behavior of modified Burgers equation (MBE).

Two of the schemes comprise differential quadrature and finite difference methods, while the third scheme consists of only differential quadrature for the derivative approximations. Proposed schemes are simulated for well-posed problems of MBE having known the analytic solution. The computational complexity of the schemes is examined through monitoring the time taken to complete the simulation. The results are compared with the analytic solution with the help of discrete error norms. Also, the accuracy of the proposed schemes is compared with that of the existing schemes in the literature. Vectorized MATLAB programs of the schemes are used for all investigations.

It is observed that all the three schemes succeeded in producing a good replication of the exact solution. The results are closer to the analytical solution than the results in the literature. Among the three schemes, the scheme labeled as FDTDQS is found highly accurate and computationally cheaper using fewer grid points. From the vectorized MATLAB programs provided, it is evident that the implementation of the schemes is simple.

This study gives an idea about three numerical schemes for a highly nonlinear problem. This mathematical framework can be adopted to any one-dimensional partial differential equation as well, and the provided program will be helpful to generate more fast and accurate vectorized code in MATLAB.

The purpose of this work is that of providing the guidelines of an efficient implementation of power flow computations using the MATLAB computation environment.

The goal of obtaining high efficiency from MATLAB programs often proves elusive unless special care is taken in exploiting the vectorising capability of MATLAB programming. In the present paper the implementation of Newton‐Raphson power flow in MATLAB is examined with particular emphasis on the way of obtaining a vectorisable code capable of achieving effective numerical performance by exploiting its formulation in terms of complex variables.

Tests on actual networks with up to 1,300 buses are presented. They show that the complex power flow is as efficient as the best implementations of the Newton Raphson power flow using real variables, as long as the operations involved are reordered with the aim of exploiting the vectorisation capabilities of the MATLAB environment.

It is shown that improved numerical efficiency in the MATLAB can be obtained through its formulation in terms of complex variables. The complex Newton‐Raphson load flow, not very common in practical uses, is shown to have many desirable qualities from the point of view of MATLAB programming and is presented in detail.

The aim of the paper is to demonstrate a fast numerical solution for Raman fiber amplifier equations using proposed guess functions and MATLAB intrinsic properties. MATLAB BVP solvers are addressed for the solution.

The guess functions proposed for the solution of RFA equations using MATLAB BVP solvers are derived from Taylor expansion of pump and signal wave near the boundary to specifically obtain convergence for the initial mesh point. The guess functions increase simulation speed significantly. In order to improve the simulation speed further, vectorization and analytical Jacobians are introduced. Comparisons among bvp4c and bvp5c have been made with respect to total pump power, number of signals, vectorization with/without analytical Jacobians, fiber length, relative tolerance and continuation method. The simulations are performed to determine the effect of the run time on the choice of the number of equally spaced mesh points (N) in the initial guess, and thus optimal N values are found.

MATLAB BVP solvers have been proven to be effective for the numerical solution of RFAs with the proposed guess functions. In particular, with vectorizing, run time reduction is between 2.1 and 5.4 times for bvp4c and between 1.6 and 2.1 times for bvp5c and in addition to vectorizing, with the introduction of the analytical Jacobians, the reduction is between 2.4 and 6.2 times for bvp4c and 1.7 and 2.2 times for bvp5c, respectively, depending on the total pump power between 1,000 mW and 2,000 mW and the number of signals. Also, simulation results show that the efficiency of the solution with proposed guess functions is improved more than six times compared with those of previously reported continuation methods. Results show that the proposed guess functions with the vectorization and analytical Jacobians can be used for the performance evaluation of RFAs for the high power systems/long gain fiber span.

The robust improvement of the solution proposed in this paper lies in the fact that the derived guess functions for the RFAs are highly effective in the sense that they assist the solver to converge to the solution for any total pump power value in a wide range from 1 to 3,000 mW and for any fiber lengths ranging 1 to 200 km which are used in practical applications. Hence, it is practicable for the performance evaluation of the existing RFA networks.

The novelty of this method is that, starting with the co‐propagating single pump and signal RFA schema, the authors derived the guess function specifically for the initial mesh points rather than using its analytical approximations. Moreover, the solution is generalized for co‐/counter propagating pumps/signals with the curve fitted coefficient(s).

This paper aims to present a digital image processing (DIP)-based discrete element method (DEM) for the analysis of heterogeneous geomaterials. Taking a soil and rock mixture as an example, the direct shear test is used to illustrate the application of this method. The numerical result is validated by the laboratory experiment and implies its feasibility in the analysis of heterogeneous geomaterials.

This method has two major steps. Based on a modification of the connected-component labeling algorithm, a novel vectorization method, which can transform the digital photos to vectorized geometry automatically, is proposed first. Then, a simple yet effective method for the generation of heterogeneous DEM models is presented using the simulation of simplicity technique.

DIP-DEM method is a feasible approach for the analysis of mechanical behavior of heterogeneous material. For soil and rock mixtures (SRM), the horizantal deformation at peak shear point becomes larger with the normal stress. Compared with pure soil, the rock aggregates mainly improve the friction angle of SRM.

As a universal method taking advantage of both DIP and DEM, this method has broad application prospects in related fields.

The purpose of this paper is to show some techniques to perform line contingency screening efficiently.

Computation efficiency and speed are mandatory requirements of contingency screening, especially when multiple outages need to be considered. The classical bounding principle, i.e. the idea that the effects of an outage are restricted to the area where the outage occurs, becomes increasingly difficult to apply to multiple contingencies. In the present work a comprehensive strategy, based on a systematic elimination of non-dangerous outages, is shown to be easily applicable to both single and double contingencies.

Tests show the efficiency of the proposed methods with reference to test systems and to an actual network with up to 800 buses.

The bounding approach is the basis of most efficient contingency screening methods based on the linear dc load flow model. In the present work the method is re-considered to improve computational efficiency. The symmetry of the dc Jacobian and the sparse inverse technique are suitably exploited in the evaluation of line outage distribution factors; this also allows a combination of single and double line contingency screening into a single procedure.

This paper is concerned with the application of radial basis function networks (RBFNs) as interpolation functions for all boundary values in the boundary element method (BEM) for the numerical solution of heat transfer problems. The quality of the estimate of boundary integrals is greatly affected by the type of functions used to interpolate the temperature, its normal derivative and the geometry along the boundary from the nodal values. In this paper, instead of conventional Lagrange polynomials, interpolation functions representing these variables are based on the “universal approximator” RBFNs, resulting in much better estimates. The proposed method is verified on problems with different variations of temperature on the boundary from linear level to higher orders. Numerical results obtained show that the BEM with indirect RBFN (IRBFN) interpolation performs much better than the one with linear or quadratic elements in terms of accuracy and convergence rate. For example, for the solution of Laplace's equation in 2D, the BEM can achieve the norm of error of the boundary solution of O(10⁻⁵) by using IRBFN interpolation while quadratic BEM can achieve a norm only of O(10⁻²) with the same boundary points employed. The IRBFN‐BEM also appears to have achieved a higher efficiency. Furthermore, the convergence rates are of O(h^1.38) and O(h^4.78) for the quadratic BEM and the IRBFN‐based BEM, respectively, where h is the nodal spacing.

For this discussion, assume there are n sample observations of the dependent variable y at unique locations. In spatial samples, often each observation is uniquely associated with a particular location or region, so that observations and regions are equivalent. Spatial dependence arises when an observation at one location, say y i is dependent on “neighboring” observations y j, y j∈ϒi. We use ϒi to denote the set of observations that are “neighboring” to observation i, where some metric is used to define the set of observations that are spatially connected to observation i. For general definitions of the sets ϒi,i=1,…,n, typically at least one observation exhibits simultaneous dependence, so that an observation y j, also depends on y i. That is, the set ϒj contains the observation y i, creating simultaneous dependence among observations. This situation constitutes a difference between time series analysis and spatial analysis. In time series, temporal dependence relations could be such that a “one-period-behind relation” exists, ruling out simultaneous dependence among observations. The time series one-observation-behind relation could arise if spatial observations were located along a line and the dependence of each observation were strictly on the observation located to the left. However, this is not in general true of spatial samples, requiring construction of estimation and inference methods that accommodate the more plausible case of simultaneous dependence among observations.

Adaptive grippers are versatile end effectors that mechanically adapt their shapes to the objects they seize, allowing for soft and delicate grasps while still allowing for strong contact forces if needed and therefore they are well suited for industrial applications. The purpose of this paper is to present a software‐oriented approach to design optimal architectures of linkage‐driven adaptive (often a.k.a underactuated) fingers with three degrees of freedom.

The user of the software presented in this paper can design planar underactuated fingers following defined constraints. The software uses an algorithm able to compute the internal and contact forces generated, respectively, in and by the finger, it is also capable of automating the design of non‐straight links to eliminate mechanical interferences, and includes results from a topological synthesis to generate all possible architectures. The mechanisms are evaluated for many criteria such as the volume of their workspaces, stability, force isotropy, stiffness of their grasps, and compactness.

This article introduces 11 new designs of underactuated fingers for four different usages, and many of these variants are good candidates for a physical realization. One of the interesting results of this work is the recurrence of S3 variants coupled with torque amplifiers or closely resembling designs using many unrelated performance criteria.

This paper is the first, to the best of the authors' knowledge, to investigate the systematic design of underactuated fingers driven by linkages considering not one but dozens of mechanical architectures.

This paper proposes a Bayesian procedure to investigate the purchasing power parity (PPP) utilizing an exponential smooth transition vector error correction model (VECM). Employing a simple Gibbs sampler, we jointly estimate the cointegrating relationship along with the nonlinearities caused by the departures from the long-run equilibrium. By allowing for nonlinear regime changes, we provide strong evidence that PPP holds between the US and each of the remaining G7 countries. The model we employed implies that the dynamics of the PPP deviations can be rather complex, which is attested to by the impulse response analysis.

This article reviews the quantitative marketing literature on artificial intelligence (AI) through an economics lens. We apply the framework in Prediction Machines: The Simple Economics of Artificial Intelligence to systematically categorize 96 research papers on AI in marketing academia into five levels of impact, which are prediction, decision, tool, strategy, and society. For each paper, we further identify each individual component of a task, the research question, the AI model used, and the broad decision type. Overall, we find there are fewer marketing papers focusing on strategy and society, and accordingly, we discuss future research opportunities in those areas.