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To compare the numerical solutions in primal and dual meshes of magnetostatic problems solved with the finite integration technique.

The development of the whole set of magnetostatic discrete formulations is proposed. Four formulations are computed: two in terms of fields and two in terms of potentials. Moreover, each computation is carried out on the primal and dual mesh. Two applications are presented and the results are analysed and discussed.

The whole set of magnetostatic formulations gives only two solutions. The solutions do not depend of the formulation, but they depend of the choice of the field discretisation in primal or dual mesh.

The computation is carried out on the dual mesh.

Two sets of dual magnetodynamic and magnetostatic finite element formulations taking thin conducting magnetic shells into account are proposed. The abstraction of the thin region from the computational domain is performed by an appropriate treatment of the surface integral terms arising in the weak formulations. Results are presented for two three‐dimensional test‐problems.

Connection boundary conditions are studied with the finite element method using different types of mixed finite elements, i.e. nodal, edge and facet elements of different shapes and degrees, used in both b‐ and h‐conform formulations. The developed associated tools are first applied to periodicity boundary conditions before being applied to the treatment of the moving band in 2D and 3D. This step by step approach enables their validation before pointing out the effect of the considered elements on the accuracy of the moving band method. A special attention is given to the consistency of these boundary conditions with gauge conditions and source magnetic fields.

Thin conducting sheets are used in many electric and electronic devices. Solving numerically the eddy current problems in presence of these thin conductive sheets requires a very fine mesh which leads to a large system of equations, and it becomes more problematic in case of higher frequencies. The purpose of this paper is to show the numerical pertinence of equivalent models for 3D eddy current problems with a conductive thin layer of small thickness e based on the replacement of the thin layer by its mid-surface with equivalent transmission conditions that satisfy the shielding purpose, and by using an efficient discretization using the boundary element method (BEM) to reduce the computational work.

These models are solved numerically using the BEM and some numerical experiments are performed to assess the accuracy of the proposed models. The results are validated by comparison with an analytical solution and a numerical solution by the commercial software Comsol.

The error between the equivalent models and analytical and numerical solutions confirms the theoretical approach. In addition to this accuracy, the computational work is reduced by considering a discretization method that requires only a surface mesh.

Based on a hybrid formulation, the authors present briefly a formal derivation of impedance transmission conditions for 3D thin layers in eddy current problems where non-conductive materials are considered in the interior and the exterior domain of the sheet. BEM is adopted to discretize the problem as there is no need for volume discretization.

The aim of the present paper is to compare the performances of a finite‐element perturbation technique applied either to the h‐ conform magnetodynamic formulation or to its b‐ conform counterpart in the frame of nondestructive eddy‐current testing problems.

In both complementary perturbation techniques, the computation is split into a computation without defect (unperturbed problem) and a computation of the field distorsion due to its presence (perturbation problem). The unperturbed problem is conventionally solved in the complete domain. The source of the perturbation problem is then determined by the projection of the unperturbed solution in a relatively small region surrounding the defect. The discretisation of this reduced domain is chosen independently of the dimensions of the excitation probe and the specimen under study and is thus well adapted to the size of the defect.

The accuracy of the perturbation model is evidenced by comparing the results of the two counterpart formulations to those achieved in the conventional way for different dimensions of the reduced domain. The size of the reduced domain increases with the size of the defect at hand. This proposed sub‐domain approach eases considerably the meshing process and speeds‐up the computation for different probe positions.

At a discrete level, the impedance change due to the defect is efficiently and accurately computed by integrating only over the defect itself and a layer of elements in the reduced domain that touches its boundary. Therefore, no integration of any flux variation in the coils is required.

The steady laminar quasi-3D fully developed magnetohydrodynamic (MHD) flow of a liquid metal in a curved annular channel is studied in order to determine the effect of the magnetic field on the velocity distribution. The paper aims to discuss this issue.

Due to the fluid motion under the effect of the applied transverse external magnetic field, an additional magnetic field and an electric current density are induced. A hybrid formulation is used for the induced electric current density, implementing for its axial component the Ohm’s law and for its transverse components the Ampere’s law. The suggested formulation (denominated h-formulation) is combined with the extended Continuity Vorticity Pressure numerical variational method for MHD flows.

Results are obtained for different values of curvature ratios and Hartmann numbers. It is proved that as the strength of the magnetic field increases, two side regions of velocity jets are formulated in the right and in the left half sides of the inner cylinder in a direction parallel to the external magnetic field. The magnitude of the axial velocity at each region is determined by the balance of the centrifugal and the electromagnetic forces. The results help to better understand the MHD flow in toroidal ducts.

The results aim to help to a better understanding of the MHD flow in curved ducts.

In the applications of FEM. a compromise between the accuracy and the computation cost is often required, especially when 3D cases are concerned Adaptive mesh refinement is a good answer to this demand.

In this paper, we present a brief study on various paradigms to tackle complexity or in other words manage uncertainty in the context of understanding science, society and nature. Fuzzy real numbers, fuzzy logic, possibility theory, probability theory, Dempster‐Shafer theory, artificial neural nets, neuro‐fuzzy, fractals and multifractals, etc. are some of the paradigms to help us to understand complex systems. We present a very detailed discussion on the mathematical theory of fuzzy dynamical system (FDS), which is the most fundamental theory from the point of view of evolution of any fuzzy system. We have made considerable extension of FDS in this paper, which has great practical value in studying some of the very complex systems in society and nature. The theories of fuzzy controllers, fuzzy pattern recognition and fuzzy computer vision are but some of the most prominent subclasses of FDS. We enunciate the concept of fuzzy differential inclusion (not equation) and fuzzy attractor. We attempt to present this theoretical framework to give an interpretation of cyclogenesis in atmospheric cybernetics as a case study. We also have presented a Dempster‐Shafer's evidence theoretic analysis and a classical probability theoretic analysis (from general system theoretic outlook) of carcinogenesis as other interesting case studies of bio‐cybernetics.

The purpose of this paper is to design a model‐based robust controller for autonomous hovering of a small‐scale helicopter.

The model is developed using prediction error minimization (PEM) system identification method implemented to flight data. Based on the extracted linear model, an H_∞ controller is synthesized for robustness against parametric uncertainties and disturbances.

The proposed techniques for modelling provide a linear state‐space model which correlates well with the recorded flight data. The synthesized H_∞ controller demonstrates an effective performance which rejects both sinusoidal and step input disturbances. The controller enables the attitude angle follow the reference target while keeping the attitude rate constant about zero for hover flight condition.

The synthesized controller is effective for hovering and low‐speed flight condition.

This work provides an efficient hovering/low‐speed autonomous helicopter flight control required in many civilian UAV applications such as aerial surveillance and photography.

The paper addresses the challenges of controlling a small‐scale helicopter during hover with inherent modelling uncertainties and disturbances.

Use of hydrotreated, hydrocracked and catalytically dewaxed base oils in hydraulic and industrial applications is increasing on a global scale. The hydrogenation and dewaxing processes involved in the manufacture of these products can result in base oils of exceptionally low aromatic content and sulphur level and raised viscosity index (VI). The aromatic content, sulphur level and VI are parameters used by the American Petroleum Institute (API) to categorize the base oils as Group II or Group III. The performance of additives in these Groups II and III base stocks differs from that in Group I base stocks. In addition, different processes used by different manufacturers will not only create different base stock oxidative stability and solvency from that of Group I base stocks, it will also create differences between Group II base stocks and between Groups II and III base stocks. Several different base stocks have been examined using methods including mass spectrometry and aniline point. Variations in properties, such as aromatic content, cycloparaffinic content and aniline point, appear to relate to differences in oxidation stability and solvency. With the improved response of Groups II/III base stocks to antioxidants, a performance level of 10,000 hours or greater in the ASTM D 943 is common. This necessitates addition of specific antioxidants which result in extended oxidation performance but lead in some cases to the formation of insoluble degradation products in Group II/III base stocks, and more so in Group I base stocks. Phenolic‐ containing and phenolic‐free antioxidant systems have been identified that allow for extended oxidation stability in a wide range of Group II base stocks without sludge formation in either Group I, II or III base stocks.