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 FEKO and SuzANA simulations of time-harmonic and transient phenomena on transmission lines above perfectly conductive ground plane and real ground plane, respectively. The influence of transmission line length, height above ground and ground electrical parameters to transmission line transient response have been analyzed throughout these simulations. Time harmonic and transient currents on transmission lines have been computed for the case of unit plane wave and electromagnetic pulse (EMP) excitations.

Simulations of electromagnetic field coupling to transmission lines using FEKO and SuzANA codes

The paper reviews the frequency domain modeling of buried dipole antenna using both the Pocklington integro-differential equation and Hallen integral equation formulation. The details pertaining to the numerical solution procedures are outlined as, well. Some strengths and weaknesses of both approaches are presented. A typical computational example for the current distribution induced along the dipole embedded in a lossy ground illustrating both methods is given, as well.

Frequency Domain Modeling of a Dipole Antenna Buried in Lossy Half-Space Pocklington equation versus Hallén equation revisited: 80th Anniversary of the Hallén Integral Equation

The paper deals with a novel approach to carry out uncertainty quantification in modeling of bioheat transfer equation using neural networks and deep learning. The output uncertainty is achieved via Monte Carlo (MC) dropout procedure using Bayesian inference, while the input uncertainty propagation is achieved using MC simulation of the ensemble of physics-informed neural networks (PINNs). The proposed approach uses a neural network with integrated physical knowledge without need of any prior assumptions and mesh generation, respectively. Deterministic modeling is related to both analytical and numerical (finite element method) solution of bioheat transfer equation. The computational example considered in this work pertains to the solution of rather simple one-dimensional problem of bioheat transfer, as a kind of opener to the subject.

Numerical Solution and Uncertainty Quantification of Bioheat Transfer Equation Using Neural Network Approach

Transient Response of Multiple Thin Wires Located at Different Heights Above a Dielectric Half-Space Antenna theory and transmission line approach

This paper, being 3rd part of the study, deals with an application of variational principle to the solution of problems in electro magnetics. Some applications to canonical problems are given and some general aspects of numerical modeling stemming from variational approach are addressed. Finally, Ritz method of solution is presented with related simple example.

Dragan Poljak

Papers

Simulations of electromagnetic field coupling to transmission lines using FEKO and SuzANA codes

Frequency Domain Modeling of a Dipole Antenna Buried in Lossy Half-Space Pocklington equation versus Hallén equation revisited: 80th Anniversary of the Hallén Integral Equation

Numerical Solution and Uncertainty Quantification of Bioheat Transfer Equation Using Neural Network Approach

Transient Response of Multiple Thin Wires Located at Different Heights Above a Dielectric Half-Space Antenna theory and transmission line approach

Review of Least Action Principle in Electromagnetics: Part III: Applications