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

The paper deals with a simple analytical approach to determine the antenna parameters pertaining to near field zone, such as imaginary part of Poynting vector or the reactive power stored in the thin wire near field. The reactive power is obtained from the Poynting theorem in the complex phasor form. Simple closed form expressions for the electric and magnetic fields in the near field zone are used. An approximate sinusoidal form of the current distribution along the dipole is assumed.

Simplified Analysis of the Thin Wire Near Field Parallel flow along a dipole antenna

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Hybrid fem/bem for human heads exposed to high frequency electromagnetic radiation

The numerical solution of the frequency domain integral equation based formulations require the solution of various double surface integrals. The evaluation of such integrals depends on the distance between the source and observation points, respectively. Many typical integrals can be solved using a numerical integration or a combination of numerical and analytical approach. The paper is on the unit cube test developed for testing various combinations of double surface integrals. Several combinations of source and observation triangles are considered including the far term and near terms, respectively. The numerical solution of integral is facilitated by Gaussian quadrature utilizing the Dunavant's rules for triangles. The extensive tests are carried out to investigate the solution convergence with respect to the increasing frequency and the various utilized discretization schemes.

Unit Cube Test for Double Surface Integrals in Frequency Domain Integral Equation Formulations

Transient electromagnetic field coupling to multiple parallel wires located at different heights above a dielectric half-space is analyzed using the wire antenna theory, and transmission line (TL) method. The wire antenna theory formulation in the time domain is based on the set of the space-time Hallen integral equations. Transmission line approximation is based on the time domain telegrapher's equations. The space time integral equations arising from the wire antenna theory are treated by the time domain Galerkin-Bubnov scheme of the indirect boundary element method (TD GB-IBEM). The corresponding telegrapher's equations are solved using the finite difference time domain (FDTD) Method. Time domain numerical results obtained with both approaches are compared to the results computed via NEC 2 code combined with Inverse Fourier transform (IFT).

Transient response of multiple thin wires located at different heights above a dielectric half-space

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Dragan Poljak

Papers

Simplified Analysis of the Thin Wire Near Field Parallel flow along a dipole antenna

Hybrid fem/bem for human heads exposed to high frequency electromagnetic radiation

Unit Cube Test for Double Surface Integrals in Frequency Domain Integral Equation Formulations

Transient response of multiple thin wires located at different heights above a dielectric half-space

Electromagnetic dosimetry based on EFIE formulation and RWG basis function