Coupling between equatorial and auroral ionospheres during polar substorms

The intense substorm activity following the geomagnetic sudden commencement on 8 August 1972 at 2354 UT and on 9 August 1972 at 0037 UT had reversed the eastward electric field at the equatorial station Jicamarca between 0700 and 1200 UT, and this was preceded by similar changes in the westward electric field in the auroral region. This abnormal change at the equatorial latitudes in the American zone (in the night-time) was closely associated with the westward electric field in the Indian zone (in the day-time) causing the counter-electrojet and the sudden disappearance of theq type of equatorialEs. The reversal of the electric field at Jicamarca had caused the generation of theF region irregularities associated with range spreadF. It is suggested that on some occasions the counter equatorial electrojet currents are caused due to the reversal of the equatorial electric fields by the spreading of the auroral electrojet currents to the low latitudes following geomagnetic storms. This suggests a possible link between the equatorial ionosphere and the magnetosphere through the auroral latitudes.     

The well‐posedness of the electric field integral equation for transient scattering from a perfectly conducting body

We consider the scattering of a transient electromagnetic field incident on a body with a smooth, perfectly conducting surface. A standard numerical method for calculating the scattered field is to use a time dependent, surface integral equation (called the electric field integral equation) to calculate the surface currents and charges induced by the incident field—these currents and charges then yield the scattered fields by means of standard integral representations (vector and scalar potentials). In this paper we show that the time‐dependent electric field integral equation is well‐posed in a suitable function space setting. We also investigate the behaviour of the solutions at large time. Copyright © 1999 John Wiley & Sons, Ltd.     

Virtual process design on combined quasi-static and high-speed forming

Sheet metal forming processes play a key role in a vast number of manufacturing cycles. The pursuit of novel approaches and enhancements of process chains is limited by the tremendous cost of experimental investigations. Hence, virtual process design is a suitable tool to overcome this limitation and to investigate new aspects of the processes via computer aided design. This work focuses on the optimization of a class of triggering pulses utilized in combined quasi-static and electromagnetic high-speed forming that avoid reverse currents. As typical example double exponential pulses are treated. Non-linear, constrained optimization exploiting a LSDYNA simulation of the forming process is used to determine parameters defining a triggering current pulse, yielding an enhanced forming result, in terms of sharper drawing radii. A more detailed discussion of the method is presented in [1]. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Child–Langmuir asymptotics applied to a bipolar diode

We apply the Child–Langmuir asymptotics of the Vlasov–Poisson system to the case of a bipolar diode, i.e. a vacuum diode where two species of particles of opposite electric charge are flowing. This leads to a simplified model which, if at least one of the two injected currents is not too large, has a unique solution. Moreover, in that case, the currents flowing inside the diode are limited by the so-called bipolar Child–Langmuir currents. In the case of large currents, other solutions may appear, and the formation of virtual electrodes may occur inside the diode. © 1998 B. G. Teubner Stuttgart—John Wiley & Sons, Ltd.     

Electric leakage current density in phase field simulations for nanogenerator concepts

For the purpose of energy harvesting on the nanoscale with ferroelectric barium titanate (BaTiO₃), our nanogenerator concept transforms parasitic mechanical oscillations into usable electric energy. Experimental difficulties occur in sample preparation, e.g., surface roughness, bonding contact, and leakage currents. Latter can be considered in our finite element phase field model, such that the nanogenerator concept can be optimized. Leakage current density is implemented from different phenomenological approaches. First, Ohm's law represents a linear relation between leakage and electric field. Second, the Space-Charge-Limited Current (SCLC) relation assumes a quadratic dependency on the electric field. So far, SCLC is suitable for one-dimensional problems, however, in two or three dimensions it is not found in literature. Therefore, we discuss a reformulation to bring into account that the electrical field E is a vector out of ℝ³ in our model. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An all-frequency weakly-singular surface integral equation for electromagnetism in dielectric media: Reformulation and well-posedness analysis

We develop and analyze a surface integral equation (SIE) whose solution pertains to numerical simulations of propagating time-harmonic electromagnetic waves in three-dimensional dielectric media. The formulae to evaluate the far-field pattern and propagation of the electric and magnetic fields in the interior and exterior of a dielectric body, through surface integrals, require the solution of a 2×2$2\times 2$ system of weakly-singular SIEs for the two unknown electric and magnetic fields at the interface surface of the dielectric body. The SIE is governed by an operator that is of the classical identity plus compact form. The tangential surface currents and normal surface charges of the dielectric model can be easily computed from the surface electric and magnetic fields.     

Modeling the impact of discretizing rotor angular position on computation of field-oriented current components in high speed electric drives

Modern drives consist of alternating current electric motors, and the field-oriented control (FOC) of such motors enables fast, precise, and robust regulation of a drive's mechanical variables such as torque, speed, and position. The control algorithm, implemented in a microprocessor, requires feedback from motor currents, and the quality of this feedback is essential to a drive's control properties. Motor phase currents are sampled and processed in order to extract their mean over a digital control interval. Afterwards, the mean phase currents are transformed into a rotating field-oriented reference frame to enable controlling the mechanical variables. The field-oriented frame rotates continuously, but in practice the transformation is carried out using a discrete angular position. This paper investigates how the discretization impacts the computed field-oriented currents in high speed drives, where the rotor displacement during a control interval is substantial. A continuous-time model of field-oriented currents is indicated as a reference to quantify errors. An original approach to normalize variables and to solve the model analytically is proposed in order to investigate how the errors related to rotor position discretization are influenced by drive operating conditions. The analytical solution is validated by computer simulation. The results show that the currently applied methodology of computing field-oriented current components, due to an invalid assumption, introduces errors of a few percent when a drive operates at high speed. These errors can be compensated using the presented solution.     

Eddy-current braking of a translating solid bar by a magnetic dipole

The paper addresses the problem of a conducting rectangular bar of square cross-section which is moving with constant velocity in the field of an arbitrarily oriented magnetic dipole. The braking Lorentz force on the bar is obtained by FEM and compared with the analytical solution for a moving infinite plate in the field of a magnetic dipole [2]. The computation of the induced currents requires solution of a Laplace equation with mixed boundary conditions for the electric potential inside the moving bar. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

ALE-based 3D FE simulation of electromagnetic forming

Electromagnetic forming is a contact-free high-speed forming process. The deformation of the work piece is driven by the Lorentz force which results from the interaction of a pulsed magnetic field with eddy currents induced in the work piece by the field itself. The purpose of this work is to present a fully-coupled three-dimensional simulation of this process. For the mechanical structure, a thermoelastic, viscoplastic, electromagnetic material model is relevant, which is incorporated in a large-deformation dynamic formulation. The electromagnetic fields are governed by Maxwell's equations under quasistatic conditions. To consider their reduced regularity at material interfaces Nédélec elements are applied. Coupling takes the form of the Lorentz force, the electromotive intensity and the current geometry of the work piece. A staggered solution scheme based on a Lagrangian mesh for the work piece and an ALE formulation for the electromagnetic field is employed. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the determination of the parameters that describe a quasistatic electromagnetic field in an electrically conducting shell

We state the initial equations and the boundary conditions for determining the parameters that describe a quasistatic electromagnetic field perturbed by the action of external electric currents in a this nonferromagnetic shell. Translated fromMatematichni Metody i Fiziko-Mekhanichni Polya, Vol. 38, 1995.     

Homogenization of time harmonic Maxwell equations: the effect of interfacial currents

We consider the Maxwell equations for a composite material consisting of two phases and enjoying a periodical structure in the presence of a time‐harmonic current source. We perform the two‐scale homogenization taking into account both the interfacial layer thickness and the complex conductivity of the interfacial layer. We introduce a variational formulation of the differential system equipped with boundary and interfacial conditions. We show the unique solvability of the variational problem. Then, we analyze the low frequency case, high and very high frequency cases, with different strength of the interfacial currents. We find the macroscopic equations and determine the effective constant matrices such as the magnetic permeability, dielectric permittivity, and electric conductivity. The effective matrices depend strongly on the frequency of the current source; the dielectric permittivity and electric conductivity also depend on the strength of the interfacial currents. Copyright © 2016 John Wiley & Sons, Ltd.     

Investigations on clamping effects with Die-Less-Hydroforming-Structures

When using a special forming technology called “Die-Less Hydroforming” to create objects, due to the lack of a conventional forming tool (like a die or a punch) and depending on a particular cutting of the blank geometry, it is possible to generate some special clamping effects when inflating the seal-welded blanks. In our contribution, we present results of a study of these clamping effects in extracts, which have been investigated by means of practical inflating tests as well as numerical forming simulations using LS-DYNA with “Die-Less-Hydroforming”-samples having a special geometry that looks like a “Pac-Man”. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Equilibrium State of Inhomogeneous Plasma

We consider the problem of a self-consistent determination of an essentially inhomogeneous equilibrium state of classical plasma. The solutions of the stationary Vlasov–Poisson equations are constructed in the form of a localized transition layer that separates the domains of homogeneous plasmas with different equilibrium parameters. The layer can also transform into a local perturbation inside a homogeneous plasma. In both cases, the solution contains neither mass currents nor electric currents, and all electrodynamic and hydrodynamic quantities and their derivatives are continuous. The parameters of the adjacent domains uniquely determine the transition layer structure.     

Electromagnetic interaction of moving conductors with magnets: kinematic solutions for infinitely long square and cylindrical geometries

The electromagnetic drag force on a point dipole near a moving conductor caused by the induced electric currents is investigated by numerical and analytical computations. Our focus is on prototypical configurations for Lorentz force velocimetry, i.e. velocity measurement from the electromagnetic drag force on the dipole. We examine the particular cases of conducting infinite bars of square or round cross-section, which are moving with constant velocity in the field of arbitrary oriented magnetic dipole. In addition, we study the laminar liquid-metal flow in a square duct. The motion of the conductor is prescribed. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Sufficient Global Stability Condition for a Model of the Synchronous Electric Motor under Nonlinear Load Moment

We study a model of the synchronous electric motor, which is described by a system of ordinary differential equations, including equations for electric currents in the windings of the rotor. The load moment is assumed to be a nonlinear function of the angular velocity of the rotor, allowing a linear estimate. The system of differential equations under consideration has a countable number of stationary solutions corresponding to the operating mode of uniform rotation of the rotor with the angular velocity equal to the angular velocity of rotation of the magnetic field in the stator. An effective sufficient condition is derived under which any motion of the rotor of the synchronous electric motor tends with time to uniform rotation.     

Lie group analysis of gravity currents

We consider shallow water theory to study the self-similar gravity currents that describe the motion of a heavy fluid flowing into another lighter ambient fluid. Gratton and Vigo investigated the shallow water theory representing the self-similar gravity currents by using dimensional analysis [J. Gratton, C. Vigo, Self-similarity gravity currents with variable inflow revisited: Plane currents, J. Fluid. Mech. 258 (1994) 77–104]. But in this study, the self-similarity solutions of the one-layer shallow-water equations representing gravity currents are investigated by using Lie group analysis and it is shown that Lie group analysis is the generalization of the dimensional analysis for investigating the self-similarity solutions of the one-layer shallow-water equations. Applying Lie group theory, reduced equations of the shallow water equations are found. Therefore, it becomes possible to obtain the similarity forms depending on the Lie group parameters and also the self-similarity solutions for the special values of these group parameters.     

Mathematical model for crack arrest of a transversely cracked piezoelectromagnetic strip – Part I

A magnetic, electric and mechanical yield model is proposed for a cracked piezoelectromagnetic ceramic narrow strip. The strip is subjected to anti-plane mechanical and in-plane electric and magnetic loads, consequently the crack opens in self-similar fashion forming a magnetic, a saturation and a slide zone ahead each tip. These in turn are arrested by prescribing a magnetic, electric and mechanical load, respectively. Employing Fourier integral transform the problem reduces to the solution of three dual integral equations. The solution of dual integral equations is then expressed in terms of Fredholm integral equation of second kind. Expressions are derived for yield induction zone, slide-yield zone and saturation zone lengths, energy release rate. A case study is carried for BaTiO₃–CoFe₂O₄ and results are presented graphically. It is shown that proposed model is capable of crack opening arrest under small-scale-yielding.     

Reaction–diffusion systems for the microscopic cellular model of the cardiac electric field

The paper deals with a mathematical model for the electric activity of the heart at microscopic level. The membrane model used to describe the ionic currents is a generalization of the phase‐I Luo–Rudy, a model widely used in 2‐D and 3‐D simulations of the action potential propagation. From the mathematical viewpoint the model is made up of a parabolic reaction diffusion system coupled with an ODE system. We derive existence and some regularity results. Copyright © 2006 John Wiley & Sons, Ltd.     

Discrete Fredholm properties and convergence estimates for the electric field integral equation

The Galerkin discretization of the Electric Field Integral Equation is reinvestigated. We prove quasi-optimal convergence estimates at nonresonant frequencies, using orthogonal splittings of the Galerkin space. At resonant frequencies we show that the spurious electric currents radiate only weakly in the exterior domain. This is achieved through the study of some finitely degenerated problems in terms of LBB Inf-Sup estimates and the use of discrete Helmholtz decompositions.

     

Method of conformal mappings for calculation of electric currents in magnetospheres of compact stars

In the two-dimensional approximation with the method of conformal mappings, we analyze the magnetic-field structure in the magnetosphere of a compact star. The dependence of the solution on the input parameters of the model is investigated. The direct and reverse electric currents are calculated in the magnetosphere.