Yevhen Ivanenko

On the physical limitations for radio frequency absorption in gold nanoparticle suspensions

This paper presents a study on the physical limitations for radio frequency absorption in gold nanoparticle suspensions. A canonical spherical geometry is considered consisting of a spherical suspension of colloidal gold nanoparticles characterized as an arbitrary passive dielectric material which is immersed in an arbitrary lossy medium. A relative heating coefficient and a corresponding optimal near field excitation are defined taking the skin effect of the surrounding medium into account. For small particle suspensions the optimal excitation is an electric dipole field for which explicit asymptotic expressions are readily obtained. It is then proven that the optimal permittivity function yielding a maximal absorption inside the spherical suspension is a conjugate match with respect to the surrounding lossy material. For a surrounding medium consisting of a weak electrolyte solution the optimal conjugate match can then readily be realized at a single frequency, e.g., by tuning the parameters of a Drude model corresponding to the electrophoretic particle acceleration mechanism. As such, the conjugate match can also be regarded to yield an optimal plasmonic resonance. Finally, a convex optimization approach is used to investigate the realizability of a passive material to approximate the desired conjugate match over a finite bandwidth. The relation of the proposed approach to general Mie theory as well as to the approximation of metamaterials are discussed. Numerical examples are included to illustrate the ultimate potential of heating in a realistic scenario in the microwave regime.

Approximation of dielectric spectroscopy data with Herglotz functions on the real line and convex optimization

This paper describes the ongoing research on approximation of frequency dielectric spectroscopy measurement data. The algorithm based on passive approximation, Hilbert transform and Tikhonov regularization for non-uniformly sampled data is derived. The interpolation and extrapolation problems with application to the dielectric spectroscopy measurement data are solved using convex optimization.

Parameter studies on optimal absorption and electrophoretic resonances in lossy media

This paper summarizes and elaborates on some new results on the optimal absorption in small spherical suspensions based on electrophoretic (plasmonic) resonances and lossy surrounding media. The main application here is to study the physical limitations for radio frequency absorption in gold nanoparticle (GNP) suspensions and its potential to achieve GNP targeted hyperthermia in cancer therapy. Numerical parameter studies are included to demonstrate the analysis approach.

Estimation of complex valued permeability of cable armour steel

This paper presents a model based technique to estimate the complex valued permeability of cable armour steel. An efficient analytical model is derived for the linearized mutual impedance of a transformer coil built on a core of magnetic armour steel. A numerical residue calculation is used to solve the related inverse problem based on impedance data. The analytical model is validated using commercial finite element (FEM) software to establish that edge effects can be neglected. The numerical residue calculation is investigated by studying its convergence based on a simple rectangular quadrature rule in comparison to the composite Simpsons rule. When there are no measurement errors, both methods converge with an unexpected high order (superconvergence). However, in practice the estimation performance will be governed by measurement and model errors. Assuming that there are Gaussian measurement errors, the present performance of the estimation technique is quantified and investigated by means of the Cramér-Rao lower bound. In future, the proposed method will be useful as an input to general calculations of power losses in three-phase power cables.

A multi-resolution 4-D FFT approach to parametric boundary Integral Equations for helical structures

This paper gives a report of an ongoing research to develop parametric boundary integral equations for helical structures and their application in the computation of induced currents and losses in three-phase power cables. The proposed technique is formulated in terms of the Electric Field Integral Equation (EFIE) or the Magnetic Field Integral Equation (MFIE) for a penetrable object together with the appropriate periodic Greens functions and a suitable parameterization of the helical structure. A simple and efficient numerical scheme is proposed for the computation of the impedance matrix in the Method of Moments (MoM) which is based on a multi-resolution 4-D FFT computation followed by polynomial extrapolation. Numerical examples are included demonstrating that the singular integrals have almost linear convergence and hence that linear or quadratic extrapolation can be used to yield accurate results.