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

Human interaction with the electromagnetic field radiated from a cellular base station antennas

Isolated vs. Interconnected Wind Turbine Grounding Systems: Effect on the Harmonic Grounding Impedance, Ground Potential Rise and Step Voltage

This paper presents a simple analytical model to estimate the radiated fleld for broadband Power line communication (PLC) or metallic wire structures. In our approach, we avoid to discretize the line and compute the current for each segment (dipole). We consider only near and far end currents and their derivatives (voltages) to express analytically the radiated electromagnetic fleld. The case of multiple conductor power line is considered with simplifled hypothesis: cables are not insulated and the surrounding media is homogenous. The basic electromagnetic equations are formulated and applied to the line to provide analytical expressions able to compute flelds in near and far zones which is not usually treated. The main purpose of this paper is to provide an analytical model applied to bare wires corresponding to classical outdoor transmission lines. The advantage of this method is that we do not need to know the current along the line to calculate the radiated flelds; therefore, in our study we use only the currents and voltages at the terminations. The calculation time is strongly reduced compared to dipoles conventional method. Results obtained from the proposed closed-form formulation agree with Feko simulation. For indoor conflgurations, cables are usually insulated and the surrounding media is no more homogeneous; this case is treated with a generalized approach and will be proposed in future paper.

/pdf/analytical-model-for-electromagnetic-radiation-by-bare-wire-3rjdkhfmxr.pdf

Analytical Model for Electromagnetic Radiation by Bare-Wire Structures

Grounding electrode is modelled as an end-driven monopole antenna horizontally buried in a lossy medium. The current distribution along the wire in frequency domain is governed by the half-space Pocklington integral equation. The influence of the air-earth interface is taken into account via the reflection coefficient appearing within the integral equation kernel. The corresponding equation is solved using the variational boundary element procedure. Frequency response of the grounding system is obtained multiplying frequency spectrum of the input impedance with Fourier transform of the input current impulse. The transient impedance is readily calculated applying inverse Fast Fourier Transform to the frequency response of the grounding electrode.

Transient analysis of the grounding electrode based on the wire antenna theory

The paper presents the numerical results for the induced electric field in the various models of the human eye and the head. The comparison between the extracted or the single organ models and the compound organ models placed inside realistic head models obtained from the magnetic resonance imaging scans is presented. The numerical results for several frequencies and polarizations of the incident electromagnetic (EM) plane wave are obtained using the hybrid finite element method/boundary element method (FEM/BEM) formulation and the surface integral equation (SIE) based formulation featuring the use of method of moments, respectively. Although some previous analysis showed the similar distribution of the induced electric field along the pupillary axis obtained in both eye models, this study showed this not to be the case in general. The analysis showed that the compound eye model is much more suitable when taking into account the polarization of the incident EM wave. The numerical results for the brain models showed much better agreement in the maximum values and distributions of the induced surface field between detailed models, while homogeneous brain model showed better agreement with the compound model in the distribution along selected sagittal axis points. The analysis could provide some helpful insights when carrying out the dosimetric analysis of the human eye and the head/brain exposed to high frequency EM radiation.

/pdf/a-study-on-the-use-of-compound-and-extracted-models-in-the-4a4oc491q0.pdf

Dragan Poljak

Papers

Human interaction with the electromagnetic field radiated from a cellular base station antennas

Isolated vs. Interconnected Wind Turbine Grounding Systems: Effect on the Harmonic Grounding Impedance, Ground Potential Rise and Step Voltage

Analytical Model for Electromagnetic Radiation by Bare-Wire Structures

Transient analysis of the grounding electrode based on the wire antenna theory

A Study on the Use of Compound and Extracted Models in the High Frequency Electromagnetic Exposure Assessment