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

Introduction to Computational Electromagnetics and Electromagnetic Compatibility

A review of computational models coupling some multiple physical phenomena is presented in this paper. Thus, electromagnetic-thermal study of the human head exposed to microwave radiation, magnetohydrodynamics (MHD) approach to plasma physics and numerical simulation of transport equations for fusion phenomena are outlined. Several examples on multiphysics simulation carried out by the authors are given in the paper.

On Some Multiphysics Models for ElectromagneticThermal-Hydrodynamics (ETHD) Analysis

The paper deals with a simplified assessment of distribution of Specific Absorption Rate averaged over a whole body (SAR WB ) for the human exposure to near RFiD reader antennas. SAR WB is computed for various distances between the antenna and the user featuring parallelepiped model of the human body. The frequencies of interest are $f = 100$ kHz, $f = 13.56$ MHz, $f = 915$ MHz and $f = 2.4$ GHz, and the reader is assumed to radiate EIRP of 4 W e.i.r.p. . The obtained results show that for distances between 1 cm and 2 m from the reader antenna SAR WB values are below the allowed limit of 0.4 W/kg for workers.

Assessment of SAR using Simplified Body Representation due to RFiD Field Exposure

The electromagnetic–thermal dosimetry model for the human brain exposed to EM radiation is developed. The electromagnetic (EM) model based on the surface integral equation (SIE) formulation is derived using the equivalence theorem for the case of a lossy homogeneous dielectric body. The thermal dosimetry model of the brain is based on the form of Pennes’ equation of heat transfer in biological tissue. The numerical solution of the EM model is carried using the Method of Moments (MoM) while the bioheat equation is solved using the finite element method. Developed electromagnetic thermal model has been applied in internal dosimetry of the human brain to assess the absorbed electromagnetic energy and consequent temperature rise due to exposure of 900 MHz plane wave.

The Electromagnetic–Thermal Dosimetry Model of the Human Brain

The assessment of human exposure to 5G mobile systems requires the use of numerical methods such as method of moments (MoM). MoM solution of the integral equation based formulation results in the fully populated system matrix whose filling time represents the most time-consuming operation for many problems. As the matrix size is directly related to the frequency of the problem, the numerical solutions in the 5G frequency range will thus put a tremendous computational cost both in terms of matrix fill time but also in the memory allocation. The paper is on the investigation of suitability of numerical integration at 5G frequencies using a unit cube test. The example of double surface integral in case of a combination of coplanar triangles is numerically solved using the Dunavant’s symmetrical quadrature rules for triangles. The results show that depending on the discretization scheme, lower integration orders could be utilized, resulting in the reduced matrix fill time without actually sacrificing the accuracy.

Dragan Poljak

Papers

Introduction to Computational Electromagnetics and Electromagnetic Compatibility

On Some Multiphysics Models for ElectromagneticThermal-Hydrodynamics (ETHD) Analysis

Assessment of SAR using Simplified Body Representation due to RFiD Field Exposure

The Electromagnetic–Thermal Dosimetry Model of the Human Brain

Study on the Suitability of Numerical Integration at 5G Frequencies Using Unit Cube Test