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 book is divided in three parts. The first part deals with introductory topics in EMC, namely, it is concerned with the fundamentals of electromagnetic theory, basics in numerical modeling and simple computational models in the analysis of static, quasistatic and scattering problems. The second part of the book deals with an analysis of the wire antennas using the frequency domain (FD) and the time domain (TD) integral equation formulation, respectively. Finally, the third part of the book deals with the solution of some specific EMC problems by means of the wire antenna theory presented in Part II.

/pdf/advanced-modeling-in-computational-electromagnetic-1d2uhnwx7i.pdf

Advanced Modeling in Computational Electromagnetic Compatibility

The paper deals with the transient impedance calculation for simple grounding systems. The mathematical modelmodel is based on the thin wire antenna theory. The formulation of the problem is posed in the frequency domain, while the corresponding transient response of the grounding system is obtained by means of the inverse Fourier transform. The current distribution induced along the grounding system due to an injected current is governed by the corresponding frequency domain Pocklington integro-differential equation. The influence of a dissipative half-space is taken into account via the reflection coefficient (RC) appearing within the integral equation kernel. The principal advantage of the RC approach versus rigorous Sommerfeld integral approach is simplicity of the formulation and significantly less computational cost. The Pocklington integral equation is solved by the Galerkin Bubnov indirect boundary element procedure thus providing the current distribution flowing along the grounding system. The outline of the Galerkin Bubnov indirect boundary element method is presented in Part II of this work. Expressing the electric field in terms of the current distribution along the electrodes the feed point voltage is obtained by integrating the normal field component from infinity to the electrode surface. The frequency dependent input impedance is then obtained as a ratio of feed-point voltage and the value of the injected lightning current. The frequency response of the grounding electrode is obtained multiplying the input impedance spectrum with Fourier transform of the injected current waveform. Finally, the transient impedance of the grounding system is calculated by means of the inverse Fourier transform. The vertical and horizontal grounding electrodes, as simple grounding systems, are analyzed in this work. The Part I of this work is related to the vertical

/pdf/wire-antenna-model-for-transient-analysis-of-simple-5ce2tm2fwp.pdf

Wire Antenna Model for Transient Analysis of Simple Grounding Systems, Part II: the Horizontal Grounding Electrode

Human Exposure to Electromagnetic Fields

The paper deals with two models of Tesla's propagation concept of wireless transmission of energy. A transmission line (TL) approximation and antenna model approaches are both implemented to analyze the Tesla's propagation concept. The Tesla's propagation path through the ground has been represented by an equivalent conductor excited at one end by the current source. The current distribution and the voltage have been calculated analytically. In particular, the voltage is calculated from standard TL equation and Generalized Telegrapher's equation formulation. Results for the voltage and generated power are presented in the paper.

Full wave model versus transmission line representation of Tesla's wave propagation: 155 th anniversary of birth of Nikola Tesla

In this paper, we present a transmission line representation of various Teslapsilas oscillating transmitters and of propagation based on ldquotrue conductionrdquo, a Teslapsilas concept of non-Hertzian wireless transmission. We follow bits of Teslapsilas papers, mainly ldquoThe True Wirelessrdquo, from which is obvious that his theory is in essence compatible to the transmission line theory, and compare results obtained by the model and those given by Tesla, as well as predict some theoretical characteristics of his resonating coils. Although his conception of a more efficient radio transmission by ldquonon-Hertzian wavesrdquo has never been recognized exactly what he claimed it to be, his concept of radio apparatus prevailed as they were the first patented true radio systems.

Dragan Poljak

Papers

Advanced Modeling in Computational Electromagnetic Compatibility

Wire Antenna Model for Transient Analysis of Simple Grounding Systems, Part II: the Horizontal Grounding Electrode

Human Exposure to Electromagnetic Fields

Full wave model versus transmission line representation of Tesla's wave propagation: 155 th anniversary of birth of Nikola Tesla

Some notes on transmission line representations of Tesla’s transmitters