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Obtaining observational constraints on the role of turbulent effects for the solar dynamo is a difficult, yet crucial, task. Without such knowledge, the full picture of the operation mechanism of the solar dynamo cannot be formed. The magnetic helicity spectrum provides important information about the $\alpha$ effect. Here we demonstrate a formalism in spherical geometry to infer magnetic helicity spectra directly from observations of the magnetic field, taking into account the sign change of magnetic helicity across the Sun's equator. Using an angular correlation function of the magnetic field, we develop a method to infer spectra for magnetic energy and helicity. The retrieval of the latter relies on a fundamental definition of helicity in terms of linkage of magnetic flux. We apply the two-scale approach, previously used in Cartesian geometry, to spherical geometry for systems where a sign reversal of helicity is expected across the equator at both small and large scales. We test the method by applying it to an analytical model of a fully helical field, and to magneto-hydrodynamic simulations of a turbulent dynamo. The helicity spectra computed from the vector potential available in the models are in excellent agreement to the spectra computed solely from the magnetic field using our method. In a next test, we use our method to obtain the helicity spectrum from a synoptic magnetic field map corresponding to a Carrington rotation. We observe clear signs of a bihelical spectrum of magnetic helicity. Our formalism makes it possible to infer magnetic helicity in spherical geometry, without the necessity of computing the magnetic vector potential. This has the advantage of being gauge invariant. It has many applications in solar and stellar observations, but can also be used to analyze global magnetoconvection models of stars and compare them with observations., Comment: 10 pages, 6 figures, 3 appendices, submitted to Astronomy and Astrophysics

We study uniqueness of the recovery of a time-dependent magnetic vector-valued potential and an electric scalar-valued potential on a Riemannian manifold from the knowledge of the Dirichlet to Neumann map of a hyperbolic equation. The Cauchy data is observed on time-like parts of the space-time boundary and uniqueness is proved up to the natural gauge for the problem. The proof is based on Gaussian beams and inversion of the light ray transform on Lorentzian manifolds under the assumptions that the Lorentzian manifold is a product of a Riemannian manifold with a time interval and that the geodesic ray transform is invertible on the Riemannian manifold., Comment: 31 pages

Transverse steady-state vibrations of a two-layer plate, consisting of a piezoelectric layer and a layer with piezomagnetic properties, are considered. On the basis of hypotheses about the distribution of mechanical quantities, electric and magnetic potential over the thickness of the plate, the equations and boundary conditions of the applied theory of bending vibrations of the plate are obtained using the variational principle. The first natural vibration frequencies were found, the values of which showed conformity with their calculations in the ACELAN finite element package.

In the paper, we consider a three-dimensional model of fluid-solid interaction when a thermo-electro-magneto-elastic body occupying a bounded region Ω+ is embedded in an inviscid fluid occupying an unbounded domain $\Omega^{-}=^3 \setminus $. In this case, we have a six-dimensional thermo-electro-magneto-elastic field (the displacement vector with three components, electric potential, magnetic potential, and temperature distribution function) in the domain Ω+, while we have a scalar acoustic pressure field in the unbounded domain Ω−. The physical kinematic and dynamic relations are described mathematically by appropriate boundary and transmission conditions. With the help of the potential method and theory of pseudodifferential equations, we prove the uniqueness and existence theorems for the corresponding boundary-transmission problems in appropriate Sobolev-Slobodetskii and Holder continuous function spaces.

An analytical solution to the anti-plane dynamics problem of semi-space rare earth giant magnetostrictive media with circular cavity defects near the horizontal boundary under the action of SH wave is studied. Based on the Helmholtz theorem and the theory of complex function, the elastic-magnetic dynamic equation of magnetostrictive medium is established, and the semi-space incident wave field is written. In addition, based on the theory of complex function and the method of wave function expansion, the expression of the wave function of the scattered displacement field and the corresponding magnetic potential of the scattered wave under the condition of no stress and magnetic insulation of the horizontal boundary are obtained. Then, based on the conditions of free boundary stress, continuous magnetic induction intensity and continuous magnetic potential around the circular cavity, the infinite linear algebraic equations are established. Finally, the analytical expressions of dynamic stress concentration factor and magnetic field intensity concentration factor around circular cavity in semi-space rare earth giant magnetostrictive medium are obtained. Numerical examples show that the analysis results depend on the following parameters: permeability, dimensional-piezomagnetic coefficient, frequency of the incident wave, incident angle, distance between the circular cavity and horizontal boundary. These results have certain reference value for the study of non-destructive testing and failure analysis of rare earth giant magnetostrictive materials.

The above reference to lodestone is interesting in that it is over 2000 years old. The property of the magnetic field to attract or generate a force is universally known and is used in practical devices, probably more than most of us realize. How many applications of the permanent magnet do you recall? Did you know, for example, that many electric motors use permanent magnets or that the ignition in cars is commonly controlled by a permanent magnet and a Hall-element switch? It is therefore quite useful to identify the properties of the permanent magnet since sooner or later you will encounter it in design. Thus follows the study of magnetic properties of materials. Many materials exhibit magnetic properties, some quite surprising. The permanent magnet is only one of them. Iron, nickel, or chromium oxides on audio tapes, video tapes, or computer disks store information in the form of magnetic field variations. Solid nickel contracts when placed in a magnetic field, while strong magnetic fields cause atoms to tilt about their spin axes, a phenomenon that leads directly to magnetic resonance imaging (MRI). Naturally occurring materials, such as magnetite (Fe3O4), are found in bacteria and in brains of many animals which use this material as a biological compass for navigation in the geomagnetic field. Magnetite and hematite (Fe2O3) are the basis of the lodestone (a naturally occurring, magnetic stone).

On the basis of a generalized interdisciplinary method that consists of a modification of Hamilton–Ostrogradski principle by expanding the Lagrange function with two components that address the functions of dissipation energy and the energy of external conservative forces, a mathematical model is presented of an electromechanical system that consists of the force section of a magneto-levitation non-contact maglev suspension in a prototype traction vehicle. The assumption that magnetic potential hole, generated naturally by means of cryogenic equipment, is present in the levitation suspension, serving to develop the model system. Contrary to other types of magnetic cushion train suspensions, for instance, maglev–Shanghai or Japan–maglev, this suspension does not need a complicated control system, and levitation is possible starting from zero train velocity. As high-temperature superconductivity can be generated, the analysis of levitation systems, including the effect of magnetic potential holes, has become topical. On the basis of the model of a prototype maglev train, dynamic processes are analyzed in the levitation system, including the effect of the magnetic potential hole. A system of ordinary differential equations of the dynamic state is presented in the normal Cauchy form, which allows for their direct integration by both explicit and implicit numerical methods. Here, the results of the computer simulations are shown as figures, which are analyzed.

We present studies of Abrikosov vortex motion across the magnetically charged edges of long thin ferromagnetic stripes placed above or under a thin superconducting film. The magnetic charges at the stripe edges form attractive or repulsive potential wells for vortices. Using a relatively small in-plane magnetic field to polarize the stripe edges and normal-to-plane magnetic field to induce up or down polarized vortices, we tune the attractive or repulsive stripe-vortex interactions. Imaging of the vortex dynamics reveals that the repulsive magnetic potential ${{U}_{m}}^{+}$ acts as a robust vortex pinning barrier, while the attractive ${{U}_{m}}^{\ensuremath{-}}$ has practically no effect on the vortex motion irrespective of the position of the stripes located above or underneath the superconducting film. We analyze the observed asymmetry using equations of the overdamped vortex motion. The formal analytical solution yields an asymmetry, but the numerical modeling with and without noise terms does not confirm it. Instead, we find that the asymmetry is caused by the creation of spontaneous vortices at the maxima of ${U}_{m}$, which depends on the edge polarity and suppress ${{U}_{m}}^{\ensuremath{-}}$. Furthermore, our experiment and time-dependent Ginzburg-Landau simulations demonstrate that magnetic pinning dominates over vortex pinning due to corrugations of the superconducting layer deposited on top of the ferromagnetic stripes.

Power lines are often placed in ground or sea water, which are weakly conductive media. In the paper, a new analytical formula, taking into account the proximity effect in a twin line placed in a weakly conductive medium, is derived, and the effect of the conductive medium is considered. In the first step, one of the wires is replaced by a current filament, and the solution is sought for magnetic vector potential around the filament. In the next step, an analytical formula for eddy currents induced in a long straight conductor of circular cross-section placed near to the current filament in the extensive conductive medium is found by using the method of separation of variables. The correctness of the formula is checked by comparison with the results obtained via other methods like finite and boundary element methods. Then, the effect of various parameters on the eddy current distribution is tested. Next, the proximity effect in a twin symmetrical line is considered, and the effect of the conductivity of the surrounding medium is investigated. The results indicate that the conductive medium weakens the proximity effect, but in typical cases (ground and sea water), the effect is very small.

In this work the magnetic anisotropy phenomenon in ferromagnetic materials was modeled using Orientation Distribution Function (ODF). The ODF is a concept that can be used to model the first magnetization curve of electrical steel sheet along any magnetization direction. The model is inserted in a 2D Finite Element (FE) field calculation software with vector magnetic potential formulation. Aspects related to the inclusion of the model in the formulation and its performance are discussed.

This paper presents an accurate 6/4 switched reluctance machine (SRM) model based on an improved conformal mapping (CM) method. Subdomain method is used to solve the vector magnetic potential of the transformed simple region, and electromagnetic torque is calculated. The developed method is verified by comparing its results with those obtained from the finite element method (FEM).

This paper proposes a method to compute the coupling factor of single and multi-layered coils having a square, hexagonal, or circular geometry, placed center to center to each other, such that there is no lateral or angular misalignment, and only vertical misalignments are of interest. Existing methods involve using 2D / 3D electromagnetic solvers, elliptical integrals, Bessel function, magnetic vector potential, or a combination of these methods. All these methods increase computational complexity and are not in a compact form. The calculation of the coupling factor requires the computation of mutual inductance and the self-inductance of the coils. The self-inductance of single-layered coils is calculated using Modified Wheeler's eq. and the self-inductance for multi-layered coils is calculated using a combination of Modified Wheeler's eq. (for the inductance of each layer) and elliptical integrals (for mutual inductance between layers). The mutual inductance of single and multi-layered coils is derived based on the series expansion of Neumann's eq. with an addition of a factor to reduce the maximum error from 37% to 6.64%. A side length transformation eq. is derived and proposed for equivalent coil transformation from a hexagonal coil to a circular coil or vice versa. The method proposed here requires only geometric quantities of the coils for the computation of mutual inductance. Simulation and experimental results showed excellent agreement with the proposed model of separation distances greater than the inner radius of the transmitter (Tx) or receiver (Rx) coil (whichever has a smaller inner radius). For simulation results, an error of up to 5% was seen for single-layered coils and an error of up to 6.64% was seen for multi-layered coils. For experimental results, the error was under 5% for double-layered air coils and 8.1% for single-layered coils with a ferrite core at separation distances greater than the inner radius of the coils. Hence, the coupling factor can be computed accurately with the proposed model at separation distances greater than the inner radius of Tx or Rx coil.

Magnetic shields that use both active and passive components to enable the generation of a tailored low-field environment are required for many applications in science, engineering, and medical imaging. Until now, accurate field nulling, or field generation, has only been possible over a small fraction of the overall volume of the shield. This is due to the interaction between the active field-generating components and the surrounding high-permeability passive shielding material. In this paper, we formulate the interaction between an arbitrary static current flow on a cylinder and an exterior closed high-permeability cylinder. We modify the Green's function for the magnetic vector potential and match boundary conditions on the shield's interior surface to calculate the total magnetic field generated by the system. We cast this formulation into an inverse optimization problem to design active--passive magnetic field shaping systems that accurately generate any physical static magnetic field in the interior of a closed cylindrical passive shield. We illustrate this method by designing hybrid systems that generate a range of magnetic field profiles to high accuracy over large interior volumes, and simulate them in real-world shields whose passive components have finite permeability, thickness, and axial entry holes. Our optimization procedure can be adapted to design active--passive magnetic field shaping systems that accurately generate any physical user-specified static magnetic field in the interior of a closed cylindrical shield of any length, enabling the development and miniaturization of systems that require accurate magnetic shielding and control., 22 pages, 9 figures, 1 table

This paper investigates the mechanical cutting effect on the performance of induction motors. Numerical modeling of cutting effect is described in this paper. The approach inverts the degradation of the permeability model for inclusion of it into magnetic vector potential formula by Newton method. The effect of cutting on iron losses is implemented in finite element simulation. The simulation results are compared with experimental results of prototype IE4 efficiency induction motors rated at 2.2 kW. One of them was manufactured with annealed electrical steel lamination to highlight the cutting effect on the performance of the motor. The notable effect of cutting was measured in increased stator current; however, negligible differences were found in measured iron losses. The presented model in this paper follows the measurements.

Purpose. The purpose of this work is formulation of similarity conditions for plane magnetic fields at a sharp skin-effect continued in non-conducting and non-magnetic medium from different axes bounding plane surfaces of conductors. Methodology. Classic formulation of Cauchy problem for magnetic vector potential Laplace equations, mathematic physics methods and basics similarity theory are used. Two problems are considered: the problem of initial field continuation from one axis and the problem of similar field continuation form other axis on which magnetic flux density or electrical field strength in unknown. Results. Necessary and sufficient similarity conditions of plane pulsed or high-frequency magnetic fields continued from different axes of rectangular coordinates are formulated. For the given odd and even magnetic flux density distributions on axis of initial field corresponding the distributions on axis and solution of continued similar field problem are obtained. Originality. It is proved that for similarity of examined fields the proportion of corresponding vector field projections represented by dimensionless numbers in similar points of axes is necessary and sufficient., Цель. Целью работы является формулировка условий подобия плоскопараллельных магнитных полей при резком поверхностном эффекте, которые продолжаются в непроводящую и немагнитную среду с различных осей прямоугольных координат, ограничивающих плоские поверхности проводников. Методика. Использованы классическая формулировка задачи Коши для уравнения Лапласа относительно векторного потенциала магнитного поля, методы математической физики и основные положения теории подобия. Рассмотрены две соответствующие задачи: задача продолжения исходного поля с одной оси и задача продолжения подобного поля с другой оси, распределение индукции магнитного поля на которой неизвестно. Результаты. Сформулированы необходимые и достаточные условия подобия плоскопараллельных импульсных или высокочастотных магнитных полей, продолжаемых с различных осей прямоугольных координат. Для заданных нечетного и четного распределений индукции на оси исходного магнитного поля определены соответствующие распределения на оси, а также решены задачи продолжения подобного поля. Научная новизна. Доказано, что для подобия рассмотренных полей необходима и достаточна пропорциональность представленных в критериальной форме соответствующих проекций векторов этих полей в сходственных точках осей.

The lift-off spacing distance between the eddy current sensor and test piece will influence the detected signals and accuracy of the measurement. Various techniques including novel sensor designs, features (lift-off point of intersection, lift-off invariance phenomenon), and algorithms have been proposed for the compensation of error caused by the lift-off effect using the eddy current sensor. However, few of these have directly measured the lift-off spacing distance, particularly for the distance up to 15 mm. In this paper, a lift-off tolerant pancake sensor has been designed. By analysing the sensitive region of the magnetic vector potential change (due to the test piece), the receiver of the sensor is designed as a circular spiral pancake coil with a large mean radius and span length (the difference between inner and outer radius). Experiments on the inductance measurement of three different non-magnetic samples have been carried out using both the designed pancake sensor and the previous triple-helix sensor. From the experiment result, the detected signal of the designed sensor has been proved much larger than that of the triple-helix sensor. Besides, simplified algorithms have been proposed for the measurement of the lift-off spacing and thickness of non-magnetic samples when using the proposed pancake sensor. Results show that the lift-off spacing and thickness can be measured with a small error of 0.14 mm (absolute error under 209.66 kHz), and 1.35 % (relative error, under low working frequencies of 142, 238, and 338 Hz) for the lift-off spacing from 1 to 15 mm.

This paper proposes an accurate analytical calculation method for rotor eddy current loss of high-speed machines with the shield layer and retaining sleeve. The calculation model includes six subdomains, such as permanent magnet, shield layer, retaining sleeve, air gap, slot opening, winding. Considering the eddy current reaction of the permanent magnet, shield layer, and retaining sleeve, the vector magnetic potential equation derivation model for each subdomain is established, and the eddy current loss of the permanent magnet and shield layer caused by current harmonics and slot openings is accurately calculated. The model is used to study the factors affecting the rotor eddy current loss, including carrier ratio, modulation ratio, slot opening length, and thickness of permanent magnet and protective retaining sleeve. The results of model analysis and calculation are compared with the results of finite element and machine experiments to verify the correctness and regularity of model analysis and calculation.

In this paper, the magnetic vector potential (MVP) equations are solved for a 5.5-kW radial-flux induction machine (RFIM) in five subdomains. The proposed modeling technique considers a uniform distribution of the current density in the rectangular slots of both rotor and stator. The RFIM is represented using a 2D model in the cylindrical coordinate system. The magnetic flux distribution in each region which is used to calculate the core losses and the machine inductances for the steady state analysis of the machine. T-equivalent circuit (T-EC) is considered to study the machine performance parameters. The rotor and stator resistances are calculated based on the geometry of the machine. The results demonstrate the accuracy of the model in prediction of the airgap flux density. The comparison of the machine performance parameters with the 2D FEA results demonstrate the reliability of the analytical model in the prediction of the machine behavior at the rated condition. Refereed/Peer-reviewed

In this paper, three Halbach array structures are compared for the design of an in-wheel permanent magnet machine for land speed racing. A finite-element model (FEM) based multi-objective optimization is used to explore the potential of all three structures to achieve high torque-weight ratio, low torque ripple, and low losses. The comparison shows that the 3-segment structure has similar performances with the 4-segment structure and lower torque ripple. To better understand the optimization results, the winding function and mutual harmonics exclusion theory were used to analyze their performances. It was found that, although the magnetic potential of a 4-segment Halbach design could be more sinusoidal, the 3-segment design provides less torque ripple for a 24-slot 20-pole fractional slot concentrated winding machine due to mutual harmonics exclusion. The FEM optimization improved the flux distribution and torque performance of a 3-segment Halbach array by adjusting the magnet arc angle and finding an optimum magnetization direction.

In this article, a novel edge-domain decomposition (EDD) method is proposed to solve 3-D nonlinear finite element (FE) problems of electromagnetic devices and transient field circuit co-simulation. The method applies reduced magnetic vector potential formulation to discretize the physical problem based on 3-D edge elements, and the solution region is divided into many sub-domains that only contain one edge unknown. The solution of lightweight nonlinear sub-domain systems can be massively parallelized, and the neighbor-to-neighbor communication scheme eliminates the need to assemble the global FE matrix. This article also introduces an indirect coupling scheme to handle large eddy currents to interface the EDD FE system with external circuits. The abovementioned algorithms are then implemented on a many-core GPU for transient field circuit co-simulation. The result shows an auto-gauging property, and the comparison with a commercial FE software indicates a speedup of over 43 times with relative error less than 2%.

We use boundary triples to find a parametrization of all self-adjoint extensions of the magnetic Schr\"odinger operator, in a quasi-convex domain~$\Omega$ with compact boundary, and magnetic potentials with components in $\textrm{W}^{1}_{\infty}(\overline{\Omega})$. This gives also a new characterization of all self-adjoint extensions of the Laplacian in nonregular domains. Then we discuss gauge transformations for such self-adjoint extensions and generalize a characterization of the gauge equivalence of the Dirichlet magnetic operator for the Dirichlet Laplacian; the relation to the Aharonov-Bohm effect, including irregular solenoids, is also discussed. In particular, in case of (bounded) quasi-convex domains it is shown that if some extension is unitarily equivalent (through the multiplication by a smooth unit function) to a realization with zero magnetic potential, then the same occurs for all self-adjoint realizations., Comment: 34 pages. To appear in Annali della Scuola Normale Superiore di Pisa, Classe di Scienze

The problem of modeling the three-dimensional magnetic field of the overhang parts in a micromotor is considered. The location of the Hall sensor for the monitoring system of the rotor angular position is selected. It is noted that the magnetic field of the winding overhang parts distorts the excitation field, the magnitude of which determines the rotor angular position. To study the distortion of the excitation field, the finite element method is chosen. It is proposed to use formulations in terms of a scalar magnetic potential. To enable such a formulation of the problem, an approach is applied consisting of replacing the lumped winding coils with an equivalent magnetized medium. The parameters of the sinusoidal correction functions for different permanent magnet using in the rotor are determined.

Numerical simulation of the electromagnetic waves propagation through media with non–linear parameters is described. The problem is formulated in terms of the magnetic vector potential with regard of magnetic and electric losses. Results of modelling of the electromagnetic wave propagation in ferroelectric media with nonlinear dependency of dielectric permittivity on the level of the electric field strength are presented. At such propagation, front sharpening of the electromagnetic wave impulse occurs. Influence of the degree of dielectric permittivity non–linearity on the considered processes has been investigated with the help of numerical simulations.

Gas-insulated transmission line (GIL) is nowadays becoming popular in high voltage engineering for power delivery. At power frequency, the metal shell enclosing the transmission line will induce eddy-currents. In practice, it is very important to compute the distribution of the associated induced voltage. Due to complicated structure of practical settings, analytical method is limited in use and the voltage distribution for the conductors are not available if using equivalent circuit method. In this paper, the three dimensional (3D) finite element method (FEM) is implemented for solving the eddy-current field. Magnetic vector potential (MVP)-based formulation is used together with the electric scalar potential (ESP), which is easy to use for handling voltage excitations for grounded conductors. An analytical example and a practical engineering problem is solved using the proposed method, good accuracy is observed.

Computations of quasi-dynamic electromagnetic field of induction machines using the complex magnetic vector potential require the use of the so-called effective magnetization curves, i.e., such in which the magnetic permeability is proportional to the amplitudes of magnetic flux density B or magnetic field strength H, not their instantaneous values. There are several definitions of that parameter mentioned in the literature provided for the case when B or H are monoharmonic. In this paper, seven different methods of determining the effective magnetization curves are compared in relation to the use of a field-circuit multi-harmonic model of an induction machine. The accuracy of each method was assessed by computing the performance characteristics of a solid-rotor induction machine. One new definition of the effective permeability was also introduced, being a function of multiple variables dependent on amplitudes of all the harmonics considered. The analyses demonstrated that the best practical approach, even for the multi-harmonic case, is to express the effective magnetic permeability as the ratio of the amplitudes of the fundamental harmonics of the magnetic flux density and the magnetic field strength, and assuming the sinusoidal variation of the latter.

We present the results of computations of the trajectories (the asymptotic latitude and asymptotic longitude) and the magnetic cut-off rigidity of cosmic ray particles for the airport Deblin, Poland (geographical latitude 51°33′32″N, geographical longitude 21°50′53″E) based on the numerical integration of equations of motion of charged particles of cosmic rays in the Earth's magnetic field. The set of allowed trajectories at a given site on the surface of the Earth is called the asymptotic cone of acceptance. The initial distance from the center of the Earth was taken to be 20 km above the Earth's surface. At about this altitude, most cosmic rays undergo nuclear collisions. Calculations were made for different of models of the International Geomagnetic Reference Field (IGRF) from 1965-2015. The IGRF is an internationally agreed and widely used mathematical model of the Earth’s magnetic field of internal origin. Each constituent model of the IGRF is a set of spherical harmonics of degree n and order m, representing a solution to Laplace’s equation for the magnetic potential arising from sources inside the Earth at a given epoch. In all asymptotic direction calculations, we used sixth-degree expansion of geomagnetic field model. Schmidt normalized spherical harmonic coefficients were taken for the epochs from 1965 to 2015. Knowledge of asymptotic directions and the magnetic rigidity cut-off it is important from the point of view of study different classes of cosmic rays variations intensity and anisotropy.

This paper presented the cost-efficient method to reflect the AC copper loss when conducting the characteristics analysis of EV traction motor using post-process of 2-D magneto-static analysis. From the magnetic vector potential as a result of magneto-static finite element analysis, the distribution of electric field intensity and current density by eddy current in conductors were calculated. Then, considering the current input, the actual distribution of current density was obtained, and the AC copper loss and AC resistance were calculated sequentially. With calculated AC resistances along the overall load conditions, the characteristics analysis of synchronous motor was conducted. Finally, the characteristic analysis results were compared with the results by transient analysis and the results of considering only DC resistance. To investigate distinctly, the motor with hairpin was analyzed due to its large AC copper loss. By applying the proposed method, the efficiency of EV traction motor can be estimated precisely.

In this paper, a computationally effective iron loss calculation method for synchronous machines is presented. The method is based on a single static 2D finite element field solution in the machine cross-section, which makes it much faster than the one based on the time-stepping solution. The developed method is applied to a salient pole synchronous machine, and the computational accuracy is validated against the time-stepping method. The proposed iron losses computation method showed a fair accuracy and a considerable speed-up of the computations. It can be an excellent alternative for the iron losses estimation in the optimization procedure of synchronous machines, where a considerable amount of finite element solutions needs to be carried out. Besides the losses comparison, local reconstruction of the time dependency of other quantities such as the magnetic vector potential and the magnetic flux density is reported for a better understanding of the method.

In magnetically targeted drug delivery system, an external magnetic field on superparamagnetic nanoparticles is combined with molecules of drugs. In this study, a magnetic field was generated using one permanent magnet. The viscous incompressible Navier-Stokes equations were considered for blood flow. The magnetic vector potentials were simulated by Taguchi method and COMSOL Multiphysics. Modeling of the magnetic vector potential was implemented by stepwise regression analysis. Optimization problem of the magnetic vector potential was solved by the genetic algorithm.

Recent experiments with the Aharonov-Bohm geometry have shown that in addition to an electron-interference fringe shift, there is also a lateral displacement of the electron diffraction envelope. In this paper, we derive an electron displacement force based on a second-order expansion of the magnetic vector potential. The analysis illustrates the conservation of canonical angular momentum, where the mechanical angular momentum and field angular momentum sum to a constant of the motion; the azimuthal force required to change the mechanical momentum is thus supplied by changes in field momentum associated with the second-order vector potential term. Our results are consistent with all known Aharonov-Bohm experiments, including interference fringe shifts, lateral displacements, and the absence of longitudinal time delays.

International audience; A new Boundary Element Method (BEM) formulation has been developed for the computation of 3D eddy currents in both magnetic and conductive regions. The modified magnetic vector potential A * in the active regions and the reduced magnetic scalar potential ϕ in the air are used as unknown variables. The formulation is limited to low-frequency magneto-harmonic problems associated to linear, homogeneous, isotropic and simply-connected regions. In such a configuration , it leads to accurate results with a reduced number of degrees of freedom located on a surface mesh delimiting the air/material interface.

We present analytical results of the equation of state (EOS) described by a model of thermal quark mass and magnetic potential term introduced in Polyakov–Nambu–Jona–Lasinio (PNJL) model for two-flavour quarks. Under the influence of thermal quark mass and magnetic field term in the potential, the calculated results of EOS using the model are enhanced in a good pattern up to the temperature $$T=2.2T_{c} $$ MeV and can follow result similar to the unmagnetised field when the temperature is increased beyond $$T=2.2T_{c}$$ MeV. The result shows that the thermodynamic behaviour agrees well with the standard properties of quantum chromodynamics (QCD) thermodynamics and enhance the result up to $$2.2T_{c}$$ from the earlier predicted results and show the same behaviour beyond $$2.2T_{c}~$$ MeV.

Novel features of turbulent flows have been analyzed recently, for example: (1) the possibility of an ideal invariant, such as the energy, to be transferred both to the small scales and to the large scales, in each case with a constant flux; (2) the existence of non-Gaussian wings in Probability Distribution Functions of kinetic, magnetic, and temperature fluctuations, together with their gradients, thus displaying large-scale as well as small-scale intermittency; and (3) the linear dependence on the control parameter of the effective dissipation in turbulence when non-linear eddies and waves interact. We shall briefly review these results with examples stemming from Solar Wind data, the atmosphere and the ocean with either magnetic fields, stratification, and/or rotation. In a second part, we shall examine numerically the inverse cascades of magnetic and of generalized helicity for Hall-MHD in the presence of forcing. These helical invariants in the ideal non-dissipative case involve various cross-correlations between the velocity and vorticity, the magnetic field, and the magnetic potential. For an ion inertial length larger than the forcing scale, the effect of the waves is significant. It leads to an exponential attenuation of the inverse cascade to large scales, since, through the velocity and vorticity, small scales play an increasing dynamical role for a strong Hall current.

We investigate mixed type boundary-transmission problems of the generalized thermo-electro-magneto elasticity (GTEME) theory for complex elastic anisotropic layered structures containing interfacial cracks. This type of problems are described mathematically by systems of partial differential equations with appropriate transmission and boundary conditions for six dimensional unknown physical field (three components of the displacement vector, electric potential function, magnetic potential function, and temperature distribution function). We apply the potential method and the theory of pseudodifferential equations and prove uniqueness and existence theorems of solutions to different type mixed boundary-transmission problems in appropriate Sobolev spaces. We analyze smoothness properties of solutions near the edges of interfacial cracks and near the curves where different type boundary conditions collide.

We present a full-wave electromagnetics solver to analyze multiscale scattering problems. The developed solver employs potential integral equations, which include both the electric current and the normal component of the magnetic vector potential as unknowns. These formulations are able to circumvent the low-frequency breakdown and related inaccuracy issues encountered when using electric- and magnetic-field integral equations. To analyze multiscale electromagnetic problems involving highly nonuniform discretizations, we solve the obtained matrix equations iteratively by employing a broadband multilevel fast multipole algorithm with incomplete-leaf tree structures. Accuracy and efficiency of the implementation are demonstrated on conical electromagnetic scattering problems.

International audience; In Magnetic Resonance Imaging there are several situations where, for simulation purposes, one wants to compute the magnetic field induced by a cluster of small metallic particles. Given the difficulty of the problem from a numerical point of view, the simplifying assumption that the field due to each particle interacts only with the main magnetic field but does not interact with the fields due to the other particles is usually made. In this paper we investigate from a mathematical point of view the relevancy of this assumption and provide error estimates for the scalar magnetic potential in terms of the key parameter that is the minimal distance between the particles. A special attention was paid to obtain explicit and relevant constants in the estimates. When the "non-interacting assumption" is deficient, we propose to compute a better approximation of the magnetic potential by taking into account pairwise magnetic field interactions between particles that enters in a general framework for computing the scalar magnetic potential as a series expansion.

We determine both the magnetic potential and the electric potential from the exterior partial measurements of the Dirichlet-to-Neumann map in the fractional linear magnetic Calder\'on problem by using an integral identity. We also determine both the magnetic potential and the nonlinearity in the fractional semilinear magnetic Calder\'on problem by using a first order linearization., Comment: 10 pages

Five-phase induction motor contains abundant magnetomotive force harmonics due to the similar number of poles and slots, which will affect the torque performance of the motor. So in this paper, the magnetic potential of squirrel-cage five-phase induction motor is taken as the main research object, and the electromagnetic field theory is adopted, the resultant magnetic potential and stability of five-phase induction motor operating without one phase are analyzed by calculating the electromotive force of each phase, and then the analysis is tested to verify the correctness of the conclusion.

In this article, a variational numerical method is utilized to investigate the nonlinear free vibrations of magneto-electro-elastic (MEE) plates under thermal environment. To this end, first, the basic equations are written based on the first-order shear deformation theory and von Karman's geometric nonlinearity. Next, the constitutive equations are represented in matrix form. In the context of Hamilton's principle, the quadratic and matricized form of energy functional is derived which is then directly discretized on space domain by a method called Variational Differential Quadrature (VDQ). Periodic time differential operators are also constructed for discretizing on time domain. The final solution is obtained by the pseudo arc-length continuation algorithm. The effects of applied electric voltage, applied magnetic potential, temperature change and geometrical parameters on the response curves of MEE plates with different types of boundary conditions are studied.

We consider the influence of the Aharonov–Bohm magnetic potential on the onset of superconductivity within the Ginzburg–Landau model. As the flux of the magnetic potential varies, we obtain a relation with the Little–Parks effect.

MEMS ve NEMS cihazlarının, gittikçe küçülen yapılarıyla beraber kararlı ve verimli çalışabilmesi için tasarımları önem kazanmaktadır. Sınır elemanları yöntemi bu tür cihazların tasarımı için son zamanlarda yaygın olarak kullanılan bir yöntemdir. Bu çalışmada, klasik yöntemler olarak ifade edilen sonlu farklar yöntemi ve sonlu elemanlar yöntemine göre daha yeni bir metot olan sınır elemanları metodu araştırılmıştır. Sınır elemanları yönteminin MEMS tasarımındaki performansını incelemek için MEMS plakası dışında oluşan skaler manyetik potansiyel analiz edilmiştir. İlk olarak problem bölgesi sınırları, sabit sınır elemanı ile bölümlenmiş ve Dirichlet sınır şartları tanımlanarak problem modellenmiştir. Problemi çözmek için Matlab ortamında yeni bir program geliştirilmiştir. Tasarlanan program, limitleri ve eleman sayıları belirlenen iki boyutlu problem bölgesinde, otomatik olarak sonlu elemanlar yöntemi ve sınır elamanları yöntemi için çözüm yapmaktadır. Sonuçların doğruluk derecesini kontrol etmek için problem analitik olarak çözülerek tüm sonuçlar karşılaştırılmıştır. Uygulamada elde edilen sonuçlara göre sınır elemanları yönteminin sonlu elemanlar yöntemine göre problem çözmek için gerekli veriler, uygulama kolaylığı ve sonuçların doğruluğu açısından birçok pozitif yöne sahip olduğu ifade edilebilir. Bu çalışmada elde edilen sonuçlara göre MEMS ve NEMS cihazların elektrostatik ve manyetostatik algılama mesafeleri tespitinde sınır elamanları metodunun kullanılması önerilebilir. Geliştirilen yeni program, bu tür cihazların daha iyi bir tasarıma sahip olmalarına katkı sunabilir Designs of MEMS and NEMS devices are gaining importance for their stable and efficient operation with their shrinking structures. Boundary element method is a widely used method for design of such devices, recently. In this study, finite difference method, which is expressed as classical methods, and boundary element method, which is a newer method compared to finite element method, was investigated. To examine the performance of boundary element method in MEMS design, the scalar magnetic potential formed outside the MEMS plate was analyzed. Firstly, the boundaries of problem region are divided with a fixed boundary element and the problem is modeled by defining Dirichlet boundary conditions. A new program has been developed in Matlab environment to solve the problem. The designed program automatically solves the finite element method and the boundary element method in two-dimensional problem region whose limits and number of elements are determined. To check the accuracy of the results, the problem was solved analytically and all results were compared. According to the results obtained in the application, it can be stated that boundary element method has many positive aspects in terms of the data required for problem solving, the ease of application and the accuracy of the results according to the finite element method. According to the results obtained in this study, it may be suggested to use the boundary element method in detection of electrostatic and magnetostatic sensing distances of MEMS and NEMS devices. The developed program can contribute to better design of such devices.

This paper studies nonlinear dynamic characteristics of a nonlocal two-phase piezo-magnetic beam based on a refined higher-order beam formulation and piezoelectric reinforcement scheme. The piezoelectric reinforcement can cause an enhanced vibration behavior of smart nanobeams under magnetic field. Nonlinear governing equations of a smart nanobeam are derived based on refined beam theory, and a numerical trend is provided to obtained nonlinear vibration frequency. This research shows that changing the volume fraction of piezoelectric phase in the material has a great influence on vibration behavior of smart nanobeam under electric and magnetic fields. Also, it can be seen that nonlinear vibration behavior of smart nanobeam is dependent on the magnitude of exerted electric voltage, magnetic potential, hardening elastic foundation and shear deformation.

Measuring the geomagnetic field accurately in real time is essential for the high-precision geomagnetic navigation for missiles. Infrared seekers contain a permanent magnet, which interferes with geomagnetic measurement terribly. The existing researches on modeling and shielding are generally on basis of mathematic methods for compensation. Here, we explore a physical shielding method to weaken the magnetic field and improve the accuracy of geomagnetic measurement. The Galerkin finite element method for scalar magnetic potential are first introduced, and distribution of interferential magnetic field in infrared seekers is analyzed, with an emphasis on various shielding schemes simulated using finite element software ANSYS. In addition, measured values are obtained via physical experiments accordingly. In comparison with measured values, good shielding effects have been achieved. The results are of guiding significance not only for improving the accuracy of magnetic measurement, but for presenting a magnetic shielding method based on finite element method.

A novel 2-D/1-D approach to simulate the eddy currents in a single thin iron sheet is presented. The introduced method utilizes ideas of the multiscale finite-element method by reducing the 3-D problem to a 2-D one. This is achieved via a decomposition of the solution with respect to its dependence on the coordinate directions. The decomposition is approximated using an expansion into polynomial shape functions. Integration over the respective coordinate gives an explicit 2-D problem. This eliminates the need to iteratively solve two coupled problems, as it is done in conventional 2-D/1-D methods. As another important advantage, the presented method allows for the incorporation of air gaps between the steel sheets. This can be done “for free,” i.e., without the introduction of additional unknowns and without changing the complexity of the resulting problem. The derivation is shown in detail for both the magnetic vector potential and the current vector potential formulation, giving explicit formulas for low polynomial orders of the used shape functions and illustrating how to proceed for shape functions of arbitrary degree. Finally, the developed method is tested in two numerical examples utilizing different geometries for the iron sheet and the computational efficiency is studied via comparison with a suitable standard finite-element model.

Compared to conventional perpendicular magnetic recording, heat-assisted magnetic recording occurs at temperatures more than twice as high in degrees Kelvin. The ability of head field to align the medium magnetization over the short duration in recording a bit is limited by the ratio of magnetic potential energy to the thermal energy. In this letter, we present a systematic micromagnetic modeling study of the transition jitter resulting from thermal agitation during the recording process. As we continue to decrease grain size in order to increase recording areal density, the height of grains in the recording medium needs to increase accordingly to keep the number of magnetization-misaligned grains to a minimum.