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 study of the thermal eﬀect caused by exposure to electromagnetic (cid:12)elds is a focus of this research. To quantify the induced current and temperature distribution in the human body an assessment tool for the frequency range of 50 Hz to 110 MHz has been developed. The major contribution consists of providing a quantitatively accurate and relatively simple model. The formulation of the problem is based on a simpli(cid:12)ed cylindrical representation de(cid:12)ned by the anatomical parameters of the human body. The bio-thermal modeling is carried out in two stages. Firstly, the electromagnetic analysis is based on the transmission lines (TL) theory. Secondly, a thermal modeling based on the thermal networks model (nodal method) is approached. This allows us to quantify the corresponding thermal gradients in the human body.

Transient thermal analysis of human exposure to electromagnetic fields

The analysis of the resistively loaded dipole antenna radiating in homogeneous dielectric medium is performed directly in the time domain. The problem is formulated by means of the time domain Hallen integral equation. The integral equation is solved by the time domain boundary element procedure which enables space and time discretization to be handled separately. Numerical results for the transient antenna current are presented.

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Time Domain Boundary Element Analysis OfResistively Loaded Wire

The benefits of circular polarization range from the reduction of the Faraday rotation effect in satellite systems, to the multipath rejection and independence of antenna orientation in the growing applications of unmanned aerial vehicles. Here, the focus is on the septum feed design which can be implemented in the ground dish or horn antennas, or used standalone as an antenna. It provides left and right hand circular polarization and better circular polarization characteristics within the wide frequency band, in relation to the given literature. The analysis and optimisation of the septum feed is done using the analytical approach, numerical simulations and measurements, and the results show that satisfying impedance and radiation parameters are achieved in the wide frequency band from 5.1 – 6.0 GHz.

Septum Feed Design for Right and Left Circular Polarisation

The paper deals with the calculation of the electric field radiated by a GPR antenna and transmitted into a lossy medium by using different approaches. Realistic bow-tie GPR antenna is modeled using gprMax software (featuring FDTD method) as well as equivalent dipole antenna with corresponding current distribution governed by Hallen integral equation. The magnitudes of the electric field transmitted into a lossy medium at different depths obtained via different approaches are compared.

Electric Field Transmitted into a Lossy Medium Radiated by a GPR Antenna - Comparison of Different Approaches

In this paper, the analysis of exposure reference levels is performed for the case of a half-wavelength dipole antenna positioned in the immediate vicinity of non-planar body parts. The incident power density (IPD) spatially averaged over the spherical and cylindrical surface is computed at the 6-90 GHz range, and subsequently placed in the context of the current international guidelines and standards for limiting exposure to electromagnetic (EM) fields which are defined considering planar computational tissue models. As numerical errors are ubiquitous at such high frequencies, the spatial resolution of EM models needs to be increased which in turn results in increased computational complexity and memory requirements. To alleviate this issue, we hybridise machine learning and traditional scientific computing approaches through differentiable programming paradigm. Findings demonstrate a strong positive effect the curvature of non-planar models has on the spatially averaged IPD with up to 15% larger values compared to the corresponding planar model in considered exposure scenarios.

Dragan Poljak

Papers

Transient thermal analysis of human exposure to electromagnetic fields

Time Domain Boundary Element Analysis OfResistively Loaded Wire

Septum Feed Design for Right and Left Circular Polarisation

Electric Field Transmitted into a Lossy Medium Radiated by a GPR Antenna - Comparison of Different Approaches

Machine learning-assisted antenna modelling for realistic assessment of incident power density on non-planar surfaces above 6 GHz.