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

In the real life, antenna is not placed in the free space. It is backed by a pole, wall or other structure, and often surrounded by other conductive objects in the immediate vicinity. Modern GSM base stations even employ configurations of multiple antennas per sector, where two antennas are placed so close that they can scatter each other's radiation. This work shows how conductive objects in the close proximity of the antenna can significantly distort the radiation pattern of the antenna. GSM operators should take this effect into account, since antenna gain can vary a few dB in the boresight direction, and even more in the other directions of the main lobe. The manufacturer-provided radiation pattern for antenna in free space should then be considered with added uncertainty. Results suggest that pattern distortion effect could be employed deliberately if needed, adding a simple rod or reflector in the vicinity of the antenna, to add a few dB in wanted direction.

http://ieeexplore.ieee.org/iel5/9062/28750/01290996.pdf

Analysis of a GSM base station antenna near conductive object: far field pattern distortion

Time domain power measure associated with the currents and charges induced on straight horizontal wires above perfect ground is proposed. The formulation is based on a set of coupled space-time Hallen integral equations. The time domain power flow measure is given by the negative time derivative of the spatial integral of the squared current and charge along the wires.

Time Domain Measure for Power Flow of Thin Wire Electromagnetic Field

Some thermal dosimetry methods for the analysis of human exposure to high frequency (HF) electromagnetic radiation are reviewed in this work The formulation is based on the bio-heat transfer equation Calculating the distribution of specific absorption rate (SAR) inside the biological body provides an assessment of a related thermal response to HF electromagnetic fields The temperature increase is obtained by solving the bio-heat transfer equation for different exposure scenarios via Boundary Element Method (BEM) and Finite Element Method (FEM), respectively Some illustrative computational examples are presented in the paper

/pdf/some-numerical-methods-of-thermal-dosimetryfor-applications-3u85du0as4.pdf

Some Numerical Methods Of Thermal DosimetryFor Applications In Bioelectromagnetics

Time domain energy measures assiciated with the currents and charges induced on the finite length wires embedded in a dielectric half-space are calculated. The formulation is based on the corresponding space-time Hallen integral equation. The effects of two media configuration are taken into account via the Fresnel reflaction and transmission coefficient, respectively. Currents and charges along the wires are obtained by solving the Hallen integral equation via time-domain Galerkin-Bubnov scheme of indirect Boundary Element Method (GB-IBEM). The assesment of time domain energy measures involves spitial integration of the squared current and charge along the wires.

Time domain analysis of the energy stored in the near field of finite length wires embedded in a dielectric half-space

In this paper, a direct time domain approach based on the corresponding transmission lines equations and Finite Difference Time Domain (FDTD) method is proposed to analyze a direct lightning strike to a cascade of transmission line towers. The proposed model deals with a real case of towers being connected by ground wires and equipped with grounding systems with different topologies, as well(vertical or horizontal conductor buried in the ground, crow's feet in the ground...). In particular, this work realistically represents the tower geometry and accounts for the propagation phenomena along the tower and between the towers. The proposed direct time domain approach deals with rather complex electrical devices (towers, ground wires and grounding systems), but at the same time requires very low computational cost and also provides relatively simple implementation. Some illustrative computational examples related to some engineering applications are given in the paper.

Dragan Poljak

Papers

Analysis of a GSM base station antenna near conductive object: far field pattern distortion

Time Domain Measure for Power Flow of Thin Wire Electromagnetic Field

Some Numerical Methods Of Thermal DosimetryFor Applications In Bioelectromagnetics

Time domain analysis of the energy stored in the near field of finite length wires embedded in a dielectric half-space

Modeling of the Direct Lightning Strike on a Towers Cascade Equipped with its Protections