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 clanku je dan prikaz proracuna zastite stapnog gromobrana kao najcesce rabljene gromobranske zastite. Proracun influenciranog naboja nacinjen je pomocu dvije metode: metodom potencijalnih koeficijenata i metodom rubnih elemenata. Na osnovi rezultata proracuna moguce je preciznije definiranje zastitne zone gromobranske stapne havtaljke.

Correction of the protection zone of the metallic post

The paper reviews certain integral equation formulations and related numerical solution methods used in studies of biomedical applications of electromagnetic fields related to transcranial magnetic stimulation (TMS) and nerve fiber stimulation. TMS is modeled via the set of coupled surface integral equations (SIEs), while the numerical solution of governing equations is undertaken via an efficient Method of Moments (MoM) scheme. A myelinated nerve fiber, stimulated by a current generator, is represented by a straight thin wire antenna. The model is based on the corresponding homogeneous Pocklington integro-diferential equation numerically solved via the Galerkin Bubnov Indirect Boundary Element Method (GB-IBEM). Some illustrative numerical results for the TMS induced fields and intracellular current distribution along the myelinated nerve fiber (active and passive), respectively, is obtained.

Integral equation models in some biomedical applications of electromagnetic fields: Transcranial magnetic stimulation (TMS), nerve fiber stimulation

The paper deals with a simple model for an assessment of the current density induced in the human body located in the vicinity of a lightning rod struck by lightning due to an electric field irradiated by the rod. The lightning rod is represented by a straight thin wire antenna excited by an equivalent current source. The current induced along a lightning rod due to a direct lightning strike is determined by solving the homogeneous integro-differential equation of the Pocklington type. The knowledge of the current distribution along the rod provides the calculation of the related irradiated electric field. The corresponding Pocklington equation and field integral relationships are handled via the Galerkin Bubnov scheme of the indirect boundary element method (GB-IBEM). The human body is represented by the symplified cylindrical body model governed by the Pocklington equation for thick wires which is handled numerically via GB-IBEM.

Towards the model for the assessment of the current density induced in the human body due to the electric field irradiated from the rod struck by lightning

Designing antennas for implanted medical devices is a very complex task where one needs to tackle inherently large EM absorption in the human tissue and very limited available space for the antenna. In addition, designers need to carefully limit the power output of the devices due to health safety regulations and small battery volume. Furthermore, the initial designs assume that permittivity and conductivity of different types of human tissues are known. Unfortunately, these values have a significant variation depending on the age, sex and health conditions of the actual patient. Such variations need to be taken into account in initial designs and in this paper we analyze the influence which the uncertainty of the tissues dielectric parameters have on the predictable power density in implanted antenna scenarios.

Uncertainty Estimation of Achievable Radiation Efficiency of Implantable Antennas

The paper deals with stochastic-deterministic modelling of radiated electric field by base station antennas (BSAs) operating in GSM frequency range. Within the framework of deterministic analysis, the total electric field above a two-layered lossy ground is obtained by considering the incident and reflected ray in the far field zone. The influence of nonhomogeneous lower medium is taken into account via two approaches: Fresnel plane wave reflection coefficient (FRM) and simplified reflection coefficient stemming from Modified Image Theory (MIT). Antenna height, relative conductivity, and permittivity of each ground layer, as well as the thickness of the upper ground layer, are considered as input parameters with inherent uncertainty. To quantify the uncertainty of output electric field, deterministic models are treated as black boxes by two stochastic methods, Monte Carlo (MC) and Stochastic Collocation (SC), respectively. Stochastic mean and standard deviation of the output are computed, and sensitivity analysis is carried out in order to analyze the impact of input parameters’ variations on the resulting electric field variance. The presented results expose weakness and strength of the two stochastic methods, particularly identifying the cases when the preferred SC method fails to converge. Furthermore, sensitivity analysis reveals that despite the smallest variation around its respective average value, the antenna height has the highest impact on the output variance at observation points in the vicinity of the antenna. However, as the distance from the antenna increases, the 1st layer depth and its relative electric permittivity become the most significant parameters.

/pdf/stochastic-deterministic-assessment-of-electric-field-2kei6bzj.pdf

Dragan Poljak

Papers

Correction of the protection zone of the metallic post

Integral equation models in some biomedical applications of electromagnetic fields: Transcranial magnetic stimulation (TMS), nerve fiber stimulation

Towards the model for the assessment of the current density induced in the human body due to the electric field irradiated from the rod struck by lightning

Uncertainty Estimation of Achievable Radiation Efficiency of Implantable Antennas

Stochastic-Deterministic Assessment of Electric Field Radiated by Base Station Antenna above a Two-Layered Ground