There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

A criterion is given for the convergence of numerical solutions of the Navier-Stokes equations in two dimensions under steady conditions. The criterion applies to all cases, of steady viscous flow in two dimensions and shows that if the local ' mesh Reynolds number ', based on the size of the mesh used in the solution, exceeds a certain fixed value, the numerical solution will not converge.

On the Navier-Stokes equations

The electromagnetic fields within a detailed model of the human eye and its surrounding bony orbit are calculated for two different frequencies of plane-wave irradiation: 750 MHz and 1.5 GHz. The computation is performed with a finite-difference algorithm for the time-dependent Maxwell's equations, carried out to the sinusoidal steady state. The heating potential, derived from the square of the electric field, is used to calculate the temperatures induced within the eyeball of the model. This computation is performed with the implicit alternating-direction (IAD) algorithm for the heat conduction equation. Using an order-of-magnitude estimate of the heat-sinking capacity of the retinal blood supply, it is determined that a hot spot exceeding 40.4/spl deg/C occurs at the center of the model eyeball at an incident power level of 100 mW/cm/sup 2/ at 1.5 GHz.

Computation of the Electromagnetic Fields and Induced Temperatures Within a Model of the Microwave-Irradiated Human Eye

Transcranial magnetic stimulation in basic and clinical neuroscience: A comprehensive review of fundamental principles and novel insights.

We discuss the transmission line (TL) theory and its application to the problem of lightning electromagnetic field coupling to TLs. We start with the derivation of the general field-to-TL coupling equations for the case of a single-wire line above a perfectly conducting ground. The derived equations are solely based on the thin-wire approximation and they do take into account high-frequency radiation effects. Under the TL approximation, the general equations reduce to the Agrawal et al. field-to-TL coupling equations. After a short discussion on the underlying assumptions of the TL theory, three seemingly different but completely equivalent approaches that have been proposed to describe the coupling of electromagnetic fields to TLs are presented. The derived equations are then extended to deal with the presence of losses and multiple conductors and expressions for the line parameters, including the ground impedance and admittance, are presented. The time-domain representation of the field-to-TL coupling equations, which allows for a straightforward treatment of nonlinear phenomena as well as the variation in the line topology, is also described. Solution methods in the frequency domain and in the time domain are given and application examples with reference to lightning-induced voltages are presented and discussed. Specifically, the effects of ground losses and corona are illustrated and discussed. When the traveling voltage and current waves are originated from lumped excitation sources located at a specific location along a TL (direct lightning strike), both the corona phenomenon and ground losses result, in general, in an attenuation and dispersion of propagating surges along TLs. However, when distributed sources representing the action of the electromagnetic field from a nearby lightning illuminating the line are present, ground losses and corona phenomenon could result in important enhancement of the induced voltage magnitude.

A Review of Field-to-Transmission Line Coupling Models With Special Emphasis to Lightning-Induced Voltages on Overhead Lines

The paper deals with a simple analytical approach to determine the transmitted field and transmitted power density (TPD) due to radiation of Hertz dipole in front of planar lossy half-space representing the simplified human tissue model. Human tissue is represented by muscle electrical properties on a given frequency. Dependence on the frequency and distance from the planar interface is analyzed. Some illustrative examples are presented.

On the Concept of the Transmitted Field and Transmitted Power Density for Simplified Case of Hertz Dipole

The paper deals with the concept of magnetic current loop as a source model for finite thin-wire antennas. The formulation is based on the Pocklington integro-differential equation with reduced kernel, which is handled by means of various numerical techniques, mostly using the Galerkin-Bubnov variant of Indirect Boundary Element Method. Extensive numerical experiments were carried out on various dipole and monopole antennas using different sources delta gap, magnetic frill, and magnetic current loop, and results for input admittance are compared with measured data. The magnetic current loop source ensures accurate solution for input admittance. Copyright © 2014 John Wiley & Sons, Ltd.

Magnetic current loop as a source model for finite thin-wire antennas

Electromagnetic-thermal analysis of the human body exposed to base station antenna radiation is presented in this work. The formulation of the problem is based on a simplified cylindrical representation of the human body. Electromagnetic part of the analysis involves incident and internal field dosimetry, while the thermal model deals with the bio-heat transfer processes in the body. The electric field induced in the body is determined from the axial current induced in the body. This current distribution along the body is obtained by solving the Pocklington integral equation for a thick cylinder. The Pocklington integral equation is solved numerically via the Galerkin-Bubnov boundary element method (GB-BEM). Once the internal electric field and related total absorbed power in the human body is obtained, it is possible to calculate a corresponding temperature rise in the body due to the GSM exposure. This temperature rise is determined by solving the bio-heat transfer equation.

The electromagnetic-thermal analysis of human exposure to radio base station antennas

The paper deals with two different approaches for the analysis of electromagnetic field coupling to finite length buried conductors based on the wire antenna theory (AT) and the transmission line (TL) method, respectively. The wire antenna formulation deals with the corresponding set of Pocklington integro-differential equation, while the transmission line model uses the Telegrapher's equations. The set of Pocklington equations is solved via the Galerkin-Bubnov scheme of the Indirect Boundary Element Method (GB-IBEM), while the transmission line equations are treated using the chain matrix method and modal equation to derive per unit length parameters. Some illustrative numerical results for the frequency response of several configurations of buried conductors, obtained via different approaches, are given in this paper.

Electromagnetic field coupling to multiple buried thin wires - Antenna model versus transmission line approach

The goal of this paper is to investigate correlation between electrostatic field of video display units (VDU's) generated around human head located in front of VDU and display-face distance. The mathematical model is based on the Laplace equation for the electrostatic potential. The finite element model for the assessment of the electrostatic field is derived. The electrostatic field is calculated for different distances between display and the human head and for different sizes of display, respectively. Results were compared with results obtained by the finite difference method (FDM). The advantage of the presented numerical method is a high resolution and a higher accuracy, compared to the FDM results.

Dragan Poljak

Papers

On the Concept of the Transmitted Field and Transmitted Power Density for Simplified Case of Hertz Dipole

Magnetic current loop as a source model for finite thin-wire antennas

The electromagnetic-thermal analysis of human exposure to radio base station antennas

Electromagnetic field coupling to multiple buried thin wires - Antenna model versus transmission line approach

Electrostatic field around human head in front of Video display unit: Field as a function of display - face distance