Wave Number and Input Impedance of a VLF Insulated Linear Antenna in an Anisotropic Ionosphere

We report a method to obtain the wave number and input impedance of a very low frequency (VLF) insulated linear antenna in an anisotropic ionosphere. Due to the anisotropy, electromagnetic fields in the ionosphere are decomposed into the ordinary wave and extraordinary wave. Wave equations for the layered structure are applied to access the wave number of the insulated antenna in the ionosphere via the derivation of the eigenvalue equation by using boundary conditions. The expression for the wave number is given based on some approximation formulas. Then, King’s antenna theory is further employed to solve the input impedance and current distribution of the antenna in the anisotropic medium. After the validation of the method is performed, near-field characteristics for an insulated antenna with different medium parameters in the anisotropic ionosphere are discussed. Effects of the electric density and geomagnetic field of the time-and space-varying anisotropic ionosphere on the distribution of normalized current are analyzed. This finding provides a promising avenue for getting electromagnetic characteristics of space-borne antennas.

Implicit Co-Simulation and Solver-Coupling: Efficient Calculation of Interface-Jacobian and Coupling Sensitivities/Gradients

We consider implicit co-simulation and solver-coupling methods, where different subsystems are coupled in time domain in a weak sense. Within such weak coupling approaches, a macro-time grid is introduced. Between the macro-time points, the subsystems are integrated independently. The subsystems only exchange information at the macro-time points. To describe the connection between the subsystems, coupling variables have to be defined. For many implicit co-simulation and solver-coupling approaches an Interface-Jacobian is required. The Interface-Jacobian describes, how certain subsystem state variables at the interface depend on the coupling variables. Concretely, the Interface-Jacobian contains partial derivatives of the state variables of the coupling bodies with respect to the coupling variables. Usually, these partial derivatives are calculated numerically by means of a finite difference approach. A calculation of the coupling gradients based on finite differences may entail problems with respect to the proper choice of the perturbation parameters and may therefore cause problems due to ill-conditioning. A second drawback is that additional subsystem integrations with perturbed coupling variables have to be carried out. In this manuscript, analytical approximation formulas for the Interface-Jacobian are derived, which may be used alternatively to numerically calculated gradients based on finite differences. Applying these approximation formulas, numerical problems with ill-conditioning can be circumvented. Moreover, efficiency of the implementation may be increased, since parallel simulations with perturbed coupling variables can be omitted. The derived approximation formulas converge to the exact gradients for small macro-step sizes.

Consider the nonuniformity of the electromagnetic field when calibrating thin dipole and loop antennas in electromagnetic field source based on a four-wire transmission line

The influence of nonuniformity of electric and magnetic fields on the calibration accuracy of dipole and loop antennas in field sources based on four-wire transmission lines is theoretically investigated. The paper proposes to take into account the influence of the nonuniformity of the electromagnetic field of a four-wire source when calibrating thin dipole and loop antennas using the equivalence coefficients. The use of these coefficients, taking into account the distributions of the field in the source and the current on the antenna conductors, can significantly weaken the requirement for field uniformity when calibrating antennas. For some common types of antennas, formulas are derived for the equivalence coefficients in the approximation of a four-wire source by an infinite line. Approximation formulas, simplified for engineering calculations, are obtained.

Approximation of elastic-plastic local strains in surface-hardened notched components

Elastic-plastic strains at points relevant for structural failures are usually approximated using formulas based on the stresses determined by elasticity theory. For this purpose, the Neuber approximation is a common method to estimate the local elastic-plastic strains in the notch root, although this is currently only approved for homogeneous components. For surfacehardened notched components, these approximation formulas need to be modified to cover two potential failure points: The notch root as well as the interface between the stronger surface layer and the weaker core material. In the following, a multi-step algorithm is shown that allows the estimation of elastic-plastic local strains at these two points, based on a single elasticitytheoretical solution. A comparison of the approximated values with those from finite element analyses (FEA) reveals that this results in only minor inaccuracies, while the usability is remarkable.

Approximations of Genocchi polynomials of complex order

Approximation formulas for the Genocchi polynomials of complex order are obtained using contour integration with the contour avoiding branch cuts. An alternative expansion is also obtained by expanding a function involving the generating function in a two-point Taylor expansion.