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 the effects of electromagnetic (EM) wave polarization on the induced specific absorption rate (SAR) and the related temperature rise in the homogeneous human brain model. The EM dosimetry model is based on the surface integral equation (SIE) formulation, while the thermal model of the brain is based on related Pennes' heat equation for biological tissue. Higher values of peak SAR for the vertical polarization have been obtained, while SAR averaged over whole brain is similar for both polarizations.

Effects of electromagnetic polarization in homogeneous electromagnetic-thermal dosimetry model of human brain

The antenna theory model of a grounding electrode is presented in this paper. The frequency domain electric field integral equation for a thin wire in a homogeneous lossy medium is solved by means of the boundary element procedure and the equivalent current distribution along the wire is obtained. The frequency spectrum of the input impedance of the grounding system is calculated from the computed current distributions. Multiplying this spectrum with the Fourier transform of the input current impulse results in the frequency response of the grounding system. The transient impedance is then obtained using the inverse fast Fourier transform (IFFT).

Transient response of the earthing electrode in a homogeneous lossy medium

Frequency domain deterministic-stochastic analysis of the transient current induced along a ground penetrating radar dipole antenna over a lossy half-space

The paper deals with the assessment of the electric field above a multilayered ground radiated by a base station antenna. A case of two two-layered ground is considered. The influence of the air-layered ground interface is taken into account via the corresponding total reflection coefficient. Several variables of upper ground layer configuration are varied. The calculations are carried out for the far field area only.

A Simplified Method for the Assessment of the Electric Field above a Multilayer Radiated by a Base Station Antenna

The paper deals with analytical calculation of spectra integrals of HF signals which can be regarded as measures for quantifying the human exposure to signals with continuous spectra. Signals generated by Digital Audio Broadcasting (DAB) are of interest. An approach based on the well-established expressions stemming from the signal theory, where integrals of radiated field spectra are calculated from the measured field amplitudes, is used. A computational example dealing with measured DAB spectra is presented.

Dragan Poljak

Papers

Effects of electromagnetic polarization in homogeneous electromagnetic-thermal dosimetry model of human brain

Transient response of the earthing electrode in a homogeneous lossy medium

Frequency domain deterministic-stochastic analysis of the transient current induced along a ground penetrating radar dipole antenna over a lossy half-space

A Simplified Method for the Assessment of the Electric Field above a Multilayer Radiated by a Base Station Antenna

Analytical Calculation of Integral Measures for Quantifying Human Exposure to HF Signals with Continuous Spectra