Purpose: Flux-switching permanent magnet (FSPM) machines are double salient machines with a high energy density suitable for e-mobility. For a fast design process, machine specialists need easy-to-use motor models. For the FSPM model, analytical methods cost high efforts to create and to improve them. Numerical methods such as the finite element method (FEM) have been extensively studied in the literature with little emphasis given to their alternatives.Methods: This research shows the implementation of the Schwarz-Christoffel (SC) MAPPING for the FSPM. With this numerical method, the double salient motor geometry is transformed into a simpler geometry to reduce the model complexity. For the electromagnetic analysis, SC MAPPING is implemented both as a stand-alone method and as an integrated method with the tooth contour method and the orthogonal field diagram method.Results: Findings are presented in a comparative analysis for all created models including the finite element method.Results show a very good agreement among the presented models.Conclusions: The results obtained in this paper show that SC MAPPING is a good alternative to the FEM. With the provided step-by-step explanation on how to implement SC MAPPING, the method can be expanded to other electrical machine classes.

Elastic solutions applicable to single underground openings usually suffer from geometry related simplification. Most tunnel shapes possess two axes of symmetry while a wide range of geometries used in tunneling practice involve only one symmetry axis. D-shape or horse-shoe shape tunnels and others with arched roof and floor are examples of the later category (one symmetry axis). In the present paper, with the use of CONFORMAL MAPPING, two methods were developed to determine the appropriate MAPPING functions on which an analytical elastic solution for a tunnel with one vertical axis of symmetry is based. These CONFORMAL MAPPING functions turn complicated geometries into a unit circle for the sake of simplification. These two approaches were introduced into a computer program used for an arbitrary tunnel cross section. Results showed that the second approach has more accuracy and is able to produce any shape, since it uses a nonlinear structure in its constitutive equations. Besides, the values for different coefficients have been presented for a variety of tunnel geometry curvature, as well as acceptable variation for the coefficients to represent tunnels with conventional shapes.

In this paper, we introduce the notion of T-CONFORMAL transformations and T-CONFORMAL maps between Riemannian manifolds. Here, T stands for a smooth (1,1)-tensor field defined on the domain of these maps. We start by defining what it means for a map to be T-CONFORMAL and also dwell on some basic properties of such type maps. We next specialize our discussion to the situation when the map T satisfies the condition ∇T = 0. Accordingly, we prove Liouville's theorem for T-CONFORMAL maps between space forms Rn(c) as an application under the condition ∇T = 0. The proof relies upon properties of T-CONFORMAL maps proved earlier. Broadly, the paper seeks to provide a general understanding of CONFORMAL MAPPINGs in the presence of a tensor field T and show how classical results such as Liouville's theorem apply.

The target of this paper is to study N(k)-contact metric manifolds with some types of CONFORMAL vector , elds like ,-holomorphic planar CONFORMAL vector , elds and Ricci biCONFORMAL vector , elds. We also characterize N(k)-contact metric manifolds allowing CONFORMAL Ricci almost soliton. Obtained results are supported by examples.

The flow field, velocity and pressure coefficient distribution of some 2-D ideal flows are presented. CONFORMAL MAPPING is used to simulate two-dimensional ideal flow for a variety of complex internal and external configurations, based on the numerical integration of Schwarz-Christoffel transformation. The advantages of this method are simplicity and high accuracy. The method presented in this paper has been applied to flow problems for which established experimental results are available in the literature. The close agreement between the predictions of simulation program and experimental results shows that the present method is applicable to any 2-D ideal flow regardless of the system of coordinates.