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The paper presents a mathematical model for the hysteresis phenomenon in a multi-winding single-phase core type transformer. The set of loop differential equations was developed for Kth winding transformer model where the flux linkages of each winding includes a flux common Φ to all windings as function of magneto motive force Θ of all windings. The purpose of this paper is to first determine a hysteresis nonlinearity involved in Φ(Θ) function using modified Preisach theory and second to develop new analytical formula of Preisach distribution function (PDF).

It is assumed in this paper that flux linkage characteristics Ψ(i) of each winding have nonlinear component due to the magnetization characteristic of the steel core and sum of linear components due to the self and mutual leakage fluxes. This nonlinear component of Ψ(i) characteristic can be expressed as a flux common Φ to all windings vs ampere-turns Θ of all windings. The nonlinear flux linkage characteristics Ψ(i) of the tested transformer are calculated from the set of measured terminal voltages and terminal currents. To simulate magnetic behavior of the iron core the feedback scalar Preisach model of hysteresis is proposed which gives more accurate predictions than classical model. For this hysteresis model the PDF and feedback function are needed. The intend of this paper is to find these function as an analytical formulas which are convenient for numerical simulations. For identification of the PDF and feedback function parameters of the considered iron core of tested transformer the Levenberg-Marquardt optimization algorithm was used.

The flux common to all windings is calculated by integrating the induced voltages of the appropriate windings. In this paper the PDF is proposed as a functional series including two dimensional Gauss expressions. In order to proper approximation of hysteresis nonlinearity of the tested iron core the first three terms of functional series of the PDF have been used. In the optimization algorithm only initial and descending limiting hysteresis curves Φ(Θ) were utilized. The feedback function for proposed hysteresis model is assumed as third-order polynomial. The hysteresis model has been successfully validated by comparing the calculated and measured results of Φ(Θ) hysteresis curves. This hysteresis model can be used in transient and steady state simulations of tested transformer taking into account the hysteresis phenomenon. The developed hysteresis model can be also used for analysis of the influence of remnant flux on the operation of tested transformer especially in transient states.

In this paper the feedback Preisach hysteresis model is involved in the flux common to all windings vs ampere-turns of all windings. The new PDF is proposed as functional series including two dimensional Gauss expressions. For tested transformer the three first terms of this functional series may be used for proper approximation of hysteresis nonlinearities.

A number of models of consumer behaviour, or of the influences on consumer behaviour, imply non‐linearity and non‐reversibility. These include the order winning/qualifying criteria model from manufacturing strategy, and the satisfier/dissatisfier and zone of tolerance models from the field of service quality. This paper demonstrates that these models share a commonality with the physical sciences’ hysteresis model, and that hysteresis can be used as a valid and informative model of a number of aspects of consumer behaviour. The application of this pre‐existing model unifies a number of previously disparate and even contradictory elements and suggests a common pattern of behaviour over a wide range of activities. The implications of this for operations strategy, service quality and further research are discussed.

In this paper an outline of the development of methods for the analysis of non‐linear circuits is presented. Non‐inert and inert elements have been discerned and an inertia measure has been proposed. For this purpose, an exponential function with time constant T equal to T_R, T_L, or T_C is formulated for an element of type R, L, or C, respectively. In circuits with the imposed cause, which varies sinusoidally in time with period T_e, the following situations are distinguished and considered: T_e ≫ T; T_e ≪ T; and T_e ≈ T. In the first case, the effect changes in time according to the non‐linear characteristic of the element. In the second case, the respective circuit is referred to as the “quasi‐linear”, because for the sinusoidal cause the effect is also sinusoidal. In the third case, the hysteresis occurs and the effect is a two‐valued function. The hysteresis effect occurs also in resistive elements.

This paper aims to perform a comparative study between capabilities of two numerical schemes from two main branches of numerical methods for solving hyperbolic conservation equations.

The accuracy and performance of a newly developed high‐resolution central scheme vs a higher‐order Godunov‐based method are evaluated in the context of black‐oil reservoir simulations. Both methods are modified enabling study of applications that are not strictly hyperbolic and exhibit local linear degeneracies in their wave structure.

The numerical computations show that while both schemes produce results with virtually the same accuracy, the Godunov method reproduces slightly more accurate results at the expense of calculation of eigen‐structures.

The paper investigates only one dimensional problems, but the idea can be easily extended to multi‐dimensional problems.

The paper shows the strengths and weaknesses of two practical numerical methods.

Such comparative study has not been published elsewhere and in particular, the performance of numerical methods on simulating hysteresis effect in hydrocarbon reservoirs has not been investigated in detail before.

Presents the possibility of utilization of the textile heating element for designing protective clothing. Investigation of the textile heating element has been carried out and it has been found that a conductive woven fabric of specific resistance should not be higher than 4*10−2 (Ω*m). Physical behaviour of the heating element can be described according to Ohm's law. A number of variants of heating packs have been tested by means of thermovision. Attention was paid to the problem of ensuring an appropriate distribution of temperatures on the inner side of clothing and obtaining a possible low temperature on the outside of clothing. A model of the system, body/heated clothing/environment, has been developed, making assumptions related to: the structure and physiology of the body; the structure of clothing and properties of materials; outer climatic conditions. Clothing prototypes were subjected to laboratory tests to verify correctness of the assumptions concerning both the heating system construction and the active clothing designing. The laboratory and functional investigations of active clothing have been positively verified by the developed model. Garments so designed are absolutely safe for the user and protects him efficiently against cooling‐down during his stay in a low temperature environment.

This paper presents new general mathematical models of normalized hysteresis curves, which define major‐hysteresis‐loop and minor‐hysteresis‐loop trajectories with several degrees of freedom. These mathematical models may be integrated into models of circuits containing nonlinear inductances for application in simulation studies. Also, the models presented can be applied to the description of hysteresis of different physical nature in other areas of science where the hysteresis phenomenon is encountered, for example: dielectric hysteresis, mechanical hysteresis, adsorption hysteresis, optical hysteresis, and so forth.

Hysteresis is one of the main concepts used in Layard, Nickell and Jackman′s book, Unemployment: Macroeconomic Performance and the Labour Market. Attempts to clarify the concept of hysteresis, from its formal representation to its empirical applications. Emphasizes the idea that hysteresis refers back to a given set of formal properties, independently of the phenomenologies within which it is liable to be encountered. In economics, the fields concerned may indeed vary a lot (labour market, foreign trade, etc.). By highlighting all the formal properties of hysteresis, shows how the assimilation of phenomena characterized by a zero eigenvalue for linear systems (or unit‐root systems for discrete‐time processes) is wrong and, moreover, how the imprecise use of the concepts can lead to the particular constraints affecting unit‐root econometrics being overlooked.

The purpose of this paper is to present the differences in results of numerical calculations arising from different simplifications of the rotational magnetization model in typical dynamo sheets.

A comprehensive model of rotational magnetization processes in typical dynamo sheets should take into consideration the magnetic hysteresis and eddy current phenomena and also certain anisotropic properties. The chosen model of the rotational magnetization is briefly presented in this paper. A method of the inclusion of the rotational magnetization model into equations of the magnetic field distribution is described. The correctness of these equations has been verified experimentally. Numerical calculations of the rotational magnetization in two types of dynamo sheets were carried out for several simplifications of the described model.

Results of numerical calculations of the rotational magnetization with the omission of the hysteresis phenomenon or with the omission of eddy currents were compared with results obtained with the use of the comprehensive model of the rotational magnetization.

The paper presents comments and recommendations concerning the omission of both the hysteresis phenomenon and eddy currents in the analysis of the rotational magnetization in dynamo sheets and the impact of these simplifications on numerical calculation results.

The content of the paper refers to very important issues of modeling and calculations of the rotational magnetization in typical dynamo steel sheets.

The purpose of this paper is to elaborate upon the mathematical model of coupled electromagnetic, fluid dynamic and motion phenomena that will allow for investigation of the magnetic hysteresis influence on the axial symmetry magnetorheological fluid (MRF) clutch operation.

To solve the partial differential equations describing magnetic vector and fluid velocity potential distributions in axial symmetry MRF electromechanical transducers the finite‐element methods have been applied. To solve model equations in the time domain, the time stepping method have been adopted. To introduce magnetic hysteresis phenomenon to presented approach the Jiles‐Atherton model have been applied. The physical properties of MRFs have been modeled by means of the Bingham model. Owing to high nonlinearity of the considered problem to solve obtained matrix equations systems the iterative Newton‐Raphson combined with the block over relaxation method have been applied.

The proposed model of coupled phenomena and the elaborated algorithm for solving the nonlinear model equations can be successfully applied in the analysis of transients in the MRF transducers taking fluid dynamics and magnetic hysteresis into account. Comparison of the measured and calculated clutch characteristics proves the model accuracy. Moreover, it has been shown that the residual magnetic flux density of the ferromagnetic core has significant impact on both to yield stresses forming in MRFs as well as the torque in disengagement clutch operation.

Development of the method for analysis of transients electromagnetic and fluid flow phenomena in MRF transducers taking magnetic hysteresis, electric circuits and motion into account. The presented approach is universal and can be successfully applied in other types of MRF electromechanical transducers such as clutch, brakes, rotary and linear dampers.

The purpose of this paper is to present the method which relatively easily allows to approximate the hysteresis loop of the dynamo or transformer steel sheets. The paper also looks into the formulation of an equation allowing determination of distribution of the flux density and eddy currents in cross-section of these sheets.

An exponential function was applied in the presented method relating to the approximation of the hysteresis loop. When the field strength changes its value, then, the flux density are the sum or difference of a function, describing the lower or upper hysteresis curve and some “ransient” component. On the basis of Maxwell’s equations and Amper’s law, one non-linear differential equation was formulated which allows to calculate the flux density and eddy currents in a cross-section of a transformer sheet.

The method which relatively easily allows approximation of the hysteresis loop of ferromagnetic material is presented in the paper. The paper presents the derivation of one non-linear differential equation, allowing calculation of the flux density and eddy currents in the cross-section of the transformer sheets, taking into account the hysteresis phenomenon.

The paper presents the method that can be used in modeling of the hysteresis loops of dynamo or transformer sheets, and the final non-linear differential equation can be applied in calculations of the magnetic field and eddy currents in cross-section of the transformer sheets.

The paper refers to important issues of modeling and calculations of the magnetic and eddy current field distribution in transformer steel sheets.