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

This paper compares a numerical model of a vertical dipole placed in the air, along the z-axis, above a lossy half space with a model with assumed current distribution (triangular and sinusoidal). The electric field is computed for various heights above ground and various ratios of the physical length and wavelength of the antenna. The obtained results show that both approaches give similar results under certain conditions.

Electric Field Radiated By a Vertical Dipole Antenna Above a Lossy Half Space by using Calculated and Assumed Current Distribution

In this work, transient coupling between the bus bars of the Air Insulation Substation (AIS) and the control cable located at its proximity is analyzed. The present study accounts for the real complex geometry of the bus bars and the finite conductivity of the soil. A time domain formulation of the problem is proposed in this work. The direct time domain formulation based on the use of Transmission Line (TL) theory and the Finite Difference Time Domain (FDTD) solution method. The excitations are given in the form of the localized current or voltage generator, respectively, and related electrical field radiated by bus bars. To ensure the electromagnetic compatibility (EMC) requirements the current induced in the transmission cable is analyzed by means of the Pencil Method that will allow one to identify the dominant frequencies in the interference signal. Various illustrative examples are given in the paper.

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Electromagnetic Compatibility in Air Insulation Substation

At millimeter waves (MMW), the current state of research in computational dosimetry is mainly relying on flat-surface tissue-equivalent models to simplify the exposure assessment by disregarding geometrical irregularities characteristic of conformal surfaces on realistic models. However, this can lead to errors in estimation of dosimetric quantities on non-planar body parts with local curvature radii comparable to the wavelength of the incident field. In this study, we address this problem by developing an averaging technique for the assessment of the absorbed power density (<inline-formula><tex-math notation="LaTeX">$S_{\text{ab}}$</tex-math></inline-formula>) on the anatomically-accurate electromagnetic (EM) model of the human ear. The dosimetric analysis is performed for the plane-wave exposure at 26 and 60 GHz, and the accuracy of the proposed method is verified by using two commercial EM software. Furthermore, we compare the two definitions of <inline-formula><tex-math notation="LaTeX">$S_{\text{ab}}$</tex-math></inline-formula> provided in the international guidelines and standards for limiting exposure to EM fields above 6 GHz. Results show marginal relative differences between the obtained values from the two different definitions (within about 6 %) in all considered scenarios. On the other hand, in comparison to flat models, the spatial maximum <inline-formula><tex-math notation="LaTeX">$S_{\text{ab}}$</tex-math></inline-formula> on the ear is up to about 20 % larger regardless of definition. These findings demonstrate a promising potential of the proposed method for the assessment of <inline-formula><tex-math notation="LaTeX">$S_{\text{ab}}$</tex-math></inline-formula> on surfaces of anatomical models at frequencies upcoming for the 5th generation (5G) wireless networks and beyond

Area-Averaged Transmitted and Absorbed Power Density on a Realistic Ear Model

The paper deals with several measurement and calculation procedures applicable in 5G New Radio technology. It brings the comparison of measured and calculated electric field levels for the purpose of simplification of industry field work. The structure of 5G New Radio signal is shortly explained, as well as all applied measurement procedures: Code-Selective Procedure, Frequency-Selective Procedure and Channel Power. The results are presented in 95% confidence interval and compared to the valid limit values. For the purpose of electric field calculation, several approximations procedures are used: Free Space, Perfect Ground Reflection and lossy ground reflection based on reflection coefficients arising from Fresnel and Modified Image Theory approach, respectively. Some illustrative results are given in the paper.

On 5G Radiated Field Measurement/Calculation Procedures and Exposure Compliance Limits

The paper deals with the characterization of electric field radiated by a GPR antenna and transmitted into a lossy medium. Realistic bow-tie GPR antenna is modeled as an equivalent dipole antenna with current distribution governed by Hallen integral equation. Electric field transmitted into a lossy medium is determined using Boundary Element formalism for the solution of field integral formulas. Electric field distribution at a certain depth is calculated using this procedure.

Dragan Poljak

Papers

Electric Field Radiated By a Vertical Dipole Antenna Above a Lossy Half Space by using Calculated and Assumed Current Distribution

Electromagnetic Compatibility in Air Insulation Substation

Area-Averaged Transmitted and Absorbed Power Density on a Realistic Ear Model

On 5G Radiated Field Measurement/Calculation Procedures and Exposure Compliance Limits

Calculation of the Transient Electric Field Transmitted in a Lossy Medium Radiated by an Equivalent GPR Dipole Antenna