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

Shipboard HF electromagnetic field distribution is simulated using five wiregrid ship models of different complexity, with a shipboard HF communication transmitter as the source of radiation. The Numerical Electromagnetics Code (NEC 2) is used for computer simulation. Electric field is calculated and then measured in each point. The measurement results are compared with simulation results for each model. The comparison shows that the model of moderate complexity, which albeit includes the main objects in electromagnetic environment, shows the best results. More complex models give similar validation results, but are much more difficult to build and computer-time consuming.

Measurement validation of ship wiregrid models of different complexity

Skripta Numericke metode u elektrotehnici temelje se na visegodisnjem istraživackom, strucnom i nastavnom radu autora na podrucju primjene numerickih metoda u inženjerskom modeliranju.

Numerical Methods in Electrical Engineering

We present an analysis of the response of a grounding electrode located on the top of a mountain. Specifically, we derive an analytical solution for the low-frequency response of a hemispheric grounding electrode buried on the top of a cone-shaped mountain characterized by its apex angle. The derived equation is validated using numerical simulations based on the finite element method obtained using COMSOL. Simulation results show that, for the same ground electrical parameters, the grounding resistance of such an electrode for steep mountains can be significantly higher than that obtained if the electrode is on flat ground. Such situations can occur in particular for the case of telecommunication towers or wind turbines located on mountaintops. The study emphasizes the importance of considering the terrain profile in the evaluation of the grounding resistance of structures located in elevated locations.

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Calculation of the Grounding Resistance of Structures Located on Elevated Terrain

The results of the absorbed electromagnetic (EM) energy in brain models of adults and children due to incident plane wave of 900 MHz and 1800 MHz are presented in this paper. The specific absorption rate (SAR) in the human brain is determined using the EM model based on the surface integral equation formulation. The thermal dosimetry model is based on the form of Pennes’ equation of heat transfer in biological tissue featuring the homogeneous Neumann boundary conditions. The thermal model is handled via the finite elements method. The models of a 10-year and a 5-year-old child brain, respectively, are obtained by linearly reducing the adult one. Although the anatomical accuracy of these models is low compared to MRI-based child models, they may be found useful for rapid dosimetric assessment. The models take into account age-dependent parameters of the brain tissue via total body water concept. The numerical results of the surface electric field obtained by the three brain models are compared, as well as ...

Electromagnetic-thermal dosimetry comparison of the homogeneous adult and child brain models based on the SIE approach

A simple finite element 2D model of the human eye is developed to calculate the steady-state temperature distribution. The mathematical model of the eye is based on the Pennes bio-heat transfer equation. Problem is solved using the weak formulation and the Galerkin-Bubnov procedure. The study was performed to determine the effects of various values of thermal conductivity of lens on temperature distribution inside human eye and also the effects due to changes in ambient temperature and blood temperature.

Dragan Poljak

Papers

Measurement validation of ship wiregrid models of different complexity

Numerical Methods in Electrical Engineering

Calculation of the Grounding Resistance of Structures Located on Elevated Terrain

Electromagnetic-thermal dosimetry comparison of the homogeneous adult and child brain models based on the SIE approach

A Simple Finite Element Model of Heat Transfer in the Human Eye