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

U radu se razmatra izloženost covjeka elektromagnetskim poljima od ekstremno niskih do mikrovalnih frekvencija. Ljudsko tijelo predstavljeno je realisticnim racunalnim modelima u smislu geometrije i elektricnih svojstava organa. Modeli na niskim frekvencijama temelje se na kvazistatickim aproksimacijama, Laplaceovoj jednadžbi i numerickome modeliranju primjenom metode rubnih elemenata. Modeli na visokim frekvencijama zasnovani su na cjelovitom elektromagnetskome modelu i odgovarajucoj Helmholtzovoj jednadžbi. U radu se razmatraju primjeri vezani za izloženost glave covjeka elektrostatskom polju monitora, izloženost trudnice i fetusa poljima niskih frekvencija te izloženost oka mikrovalnim frekvencijama. Dobiveni rezultati upucuju na cinjenicu da su pod nekim ekstremnim okolnostima moguci scenariji u okviru kojih karakteristicni parametri polja prelaze granicne vrijednosti propisane domacom i međunarodnom legislativom. Primjerice, prilikom izloženosti trudne žene elektricnom polju dalekovoda, u fetusu se inducira visestruko veca gustoca struje od vrijednosti koja se inducira u mozgu trudnice. U radu su nadalje opisani mehanizmi interakcije elektromagnetskih polja s ljudskim tijelom. Nakon toga iznesene su dosadasnje spoznaje vezane za bioloske ucinke polja ekstremno niskih frekvencija i radio-frekvencija. Također su raspravljene zastitne mjere vezane za međunarodne i domace sigurnosne smjernice i granice izloženosti.

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Izloženost ljudi neionizirajućim elektromagnetskim poljima od ekstremno niskih do mikrovalnih frekvencija

A comparison between two theoretical methods, recently adopted for evaluating induced currents in a human body, is here presented. In both cases, a vertical ELF electric field is assumed for the coupling to a standard human subject. Specifically, the diakoptic method (DM), applied to a homogeneous multi-sphere model of man with low partitioning degree, and the Boundary Element Method (BEM), applied to a non-homogeneous model with high partitioning degree, have been selected. The analytical and numerical formulations, respectively distinctive of the above methods, are carefully described and a number of data are reported and commented upon.

/pdf/a-comparative-study-on-the-induced-current-density-in-humans-22kqlsfc55.pdf

A Comparative Study on the Induced Current Density in Humans Exposed to ELF Electric Fields

Lightning Induced Current on a Metallic Post-Frequency Domain Analysis

This paper outlines an analytical model for the assessment of the electric field radiated by a base station antenna system above a two-layered medium. The model used in electric field strength assessment is based on Modified Image Theory method (MIT). The obtained results for the electric field are compared to the results calculated for the single layer configuration. Several variables have been varied to examine the impact of two-layered medium. The calculations have been undertaken for the far field only.

Analytical Technique to Determine the Electric Field Above a Two-Layered Medium

This paper presents the stochastic model of the bioheat transfer equation to assess the temperature distribution in the biological tissue. This is an important issue in planning and modeling of biomedical applications of electromagnetic (EM) fields such as EM HyperThermia (EM HT) procedures used in the treatment of certain cancer types. The presented approach aims to incorporate the uncertainties in the tissue thermal parameters aiming to quantify the uncertainty in the output temperature. The novel stochastic collocation method is implemented to estimate the stochastic mean and variance, as well as, to carry out the sensitivity analysis of model. The obtained results are the first step and a sort of an opener for the full stochastic modeling of EM HT.

Dragan Poljak

Papers

Izloženost ljudi neionizirajućim elektromagnetskim poljima od ekstremno niskih do mikrovalnih frekvencija

A Comparative Study on the Induced Current Density in Humans Exposed to ELF Electric Fields

Lightning Induced Current on a Metallic Post-Frequency Domain Analysis

Analytical Technique to Determine the Electric Field Above a Two-Layered Medium

Stochastic Sensitivity Analysis of Bioheat Transfer Equation