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This paper aims to present an associated methodology to evaluate the initial stress of coal-rock masses in steeply inclined coal seams.

On the basis of the real-time monitoring data in the field, the corresponding analytical analysis is carried out in consideration of the characteristics of topography and geology, so as to deduce the value of the initial stress in the study area and also give the analytical model of the initial stress field.

The authors identified feasibility of the initial stress level of coal-rock masses in steeply inclined coal seams, and revealed that exact acquisition on the displacement of surrounding rock was feasible to analyze the initial stress level of coal-rock masses by the back analytical method in the steeply inclined coal seams as a two-dimensional plane problem.

The calculation results including vertical stress, minimum horizontal principal stress and shearing stress were 7.057, 8.085 and 0.057 MPa, respectively. The KJ743 coal mine initial stress monitoring system was used to collect real-time initial stress data, which were used to check the accuracy of the analytical back results. The value of the vertical stress varied from 6.8 to 7.0 MPa, which is slightly smaller than the result of the back calculation. The minimum principal horizontal stress varied from 7.6 to 8.4 MPa, which is similar to the result of the back calculation.

The first compressible flow solution based solely on the locally analytical method is developed. This is accomplished by developing the flow model and locally analytical solution for inviscid subsonic compressible flow. The stream function for irrotational, compressible flow without body forces was chosen as the governing differential equation. To demonstrate the modelling and locally analytical solution, this analysis is then applied to predict the flow in convergent nozzles, both planar and axially symmetric, for different back pressures. Results are presented which demonstrate the effectiveness of this technique.

This paper aims to propose an analytical model for the harmonic content no-load magnetic fields and Back electric motive force (EMF) in double-sided TORUS-type non-slotted axial flux permanent magnet (TORUS-NS AFPM) machines with surface-mounted magnets considering the winding distribution and iron saturation effects.

First, a procedure to calculate the winding distribution with a rectangular cross-section is proposed. The magnetic field distribution and magnetic motive force (MMF) drop due to saturation in iron cores are then exactly extracted in a 2-D analytical model. The consequent influence on air-gap magnetic field and Back EMF are also calculated using a new iterative algorithm. The results are compared with those of the conventional analytical model without saturation, 2-D finite element analysis (FEA) and an experiment on a fabricated prototype machine.

Unlike the conventional method, the new method yields the no-load magnetic field distributions in air-gap and iron cores and Back EMF very exactly such that the results well match to those of the FEA and experiment.

Unlike the conventional winding factor, the winding distribution is considered here along the both axial and circumferential directions, which improves the accuracy level of results for non-slotted structures with relatively large air-gaps. The magnetic field distribution and MMF drop-in iron parts are also calculated as the basis for exact recalculation of air-gap magnetic field and Back EMF. Because of small computational burden beside superior accuracy, the proposed model can be treated as an accurate and fast substitute for FEA to be used during the design procedure or for predicting the other performance characteristics of TORUS-NS AFPM machines.

Discusses the 27 papers in ISEF 1999 Proceedings on the subject of electromagnetisms. States the groups of papers cover such subjects within the discipline as: induction machines; reluctance motors; PM motors; transformers and reactors; and special problems and applications. Debates all of these in great detail and itemizes each with greater in‐depth discussion of the various technical applications and areas. Concludes that the recommendations made should be adhered to.

Using appropriate solution techniques for transformer inrush current transient study is of great prominence owing to the inevitable inclusion of differential equations leading to complicated analysis procedures. This study aims to propose an analytical-numerical method to accurately analyze the three-phase three-limb core-type transformer inrush current in different cases considering the nonlinear behavior of the iron core.

The proposed method focuses on acquiring equations for inrush current and also the magnetic core flux by the application of a simulation-based iterative approach. In this regard, multiple integral equations are solved taking the time intervals into account. Then several derivations and integrations of matrix terms are substituted into the obtained results so as to simplify the solution process.

The method provides notable enhancements in computation time and also excellent qualities of accuracy compared with conventional numerical methods.

The proposed method is simulated for two three-phase transformers via MATLAB software. The obtained simulation results have been also compared with experimental tests.

Actually, the analytical-numerical method is capable of computing higher number of iterations in a shorter time efficiently, while making use of the conventional numerical procedures may not result in expected convergences. The simulation results of the proposed analytical-numerical technique illustrate a close agreement with the experimental test, and hence, verify the method preciousness.

The purpose of this study is to develop a new method of lines for one-dimensional (1D) advection-reaction-diffusion (ADR) equations that is conservative and provides piecewise analytical solutions in space, compare it with other finite-difference discretizations and assess the effects of advection and reaction on both 1D and two-dimensional (2D) problems.

A conservative method of lines based on the piecewise analytical integration of the two-point boundary value problems that result from the local solution of the advection-diffusion operator subject to the continuity of the dependent variables and their fluxes at the control volume boundaries is presented. The method results in nonlinear first-order, ordinary differential equations in time for the nodal values of the dependent variables at three adjacent grid points and triangular mass and source matrices, reduces to the well-known exponentially fitted techniques for constant coefficients and equally spaced grids and provides continuous solutions in space.

The conservative method of lines presented here results in three-point finite difference equations for the nodal values, implicitly treats the advection and diffusion terms and is unconditionally stable if the reaction terms are implicitly treated. The method is shown to be more accurate than other three-point, exponentially fitted methods for nonlinear problems with interior and/or boundary layers and/or source/reaction terms. The effects of linear advection in 1D reacting flow problems indicates that the wave front steepens as it approaches the downstream boundary, whereas its back corresponds to a translation of the initial conditions; for nonlinear advection, the wave front exhibits steepening but the wave back shows a linear dependence on space. For a system of two nonlinearly coupled, 2D ADR equations, it is shown that a counter-clockwise rotating vortical field stretches the spiral whose tip drifts about the center of the domain, whereas a clock-wise rotating one compresses the wave and thickens its arms.

A new, conservative method of lines that implicitly treats the advection and diffusion terms and provides piecewise-exponential solutions in space is presented and applied to some 1D and 2D advection reactions.

This paper aims to show the proposed energy method for inductance calculation is valid for any number of poles, phases and any winding layout.

A two-dimensional (2-D) analytical energy-based approach is presented to calculate self-inductances and mutual inductances of brushless surface-mounted permanent-magnet machines.

The proposed calculation procedure is valid for brushless permanent-magnet machines with slotted or slotless stator structure. Comparisons between energy method and flux linkage method are presented based on simulation and experimental results. It shows that the energy method has an excellent agreement with the result obtained from finite element method (FEM) and experimental study.

This paper compares energy-based method with flux linkage method and FEM for inductance calculations in slotless and slotted permanent-magnet motors. The relations for inductance calculation are presented which are obtained based on 2-D analytical representation of magnetic field.

The purpose of this paper is the fast and accurate modelling of surface-mounted Axial-Flux Permanent-Magnet (AFPM) machines equipped with cylindrical magnets using quasi-3D approach. Furthermore, the accuracy of the method is improved by using leakage coefficient, saturation coefficient and an appropriate permeance function.

Quasi-3D approach is used for fast and accurate modelling of AFPM machines. Air-gap flux density distribution, induced back EMF, and produced cogging torque are calculated using the proposed method with reasonable accuracy.

The results obtained by quasi-3D approach compared to Finite-Element-Analyses (FEA) shows how accurate, fast and efficient this method is. It is proved that, this method can be successfully applied to evaluate the performance of the AFPM machines.

Effectiveness and accuracy of quasi-3D approach is assessed on different AFPM machines. Furthermore, to increase the accuracy of computations, the effects of the magnetic potential drop at iron parts of the machine are taken into account by using a saturation coefficient. Besides, the influence of the slot opening on the flux density distribution is taken into account by using an appropriate relative permeance function.

The objective of this paper is to develop a semi-analytical finite element method for solving chemical dissolution-front instability problems in fluid-saturated porous media.

The porosity, horizontal and vertical components of the pore-fluid velocity and solute concentration are selected as four fundamental unknown variables for describing chemical dissolution-front instability problems in fluid-saturated porous media. To avoid the use of numerical integration, analytical solutions for the property matrices of a rectangular element are precisely derived in a purely mathematical manner. This means that the proposed finite element method is a kind of semi-analytical method. The column pivot element solver is used to solve the resulting finite element equations of the chemical dissolution-front instability problem.

The direct use of horizontal and vertical components of the pore-fluid velocity as fundamental unknown variables can improve the accuracy of the related numerical solution. The column pivot element solver is useful for solving the finite element equations of a chemical dissolution-front instability problem. The proposed semi-analytical finite element method can produce highly accurate numerical solutions for simulating chemical dissolution-front instability problems in fluid-saturated porous media.

Analytical solutions for the property matrices of a rectangular element are precisely derived for solving chemical dissolution-front instability problems in fluid-saturated porous media. The proposed semi-analytical finite element method provides a useful way for understanding the underlying dynamic mechanisms of the washing land method involved in the contaminated land remediation.

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).