Jorge A. Portí

Analysis of the finite difference time domain technique to solve the Schrödinger equation for quantum devices

An extension of the finite difference time domain is applied to solve the Schrodinger equation. A systematic analysis of stability and convergence of this technique is carried out in this article. The numerical scheme used to solve the Schrodinger equation differs from the scheme found in electromagnetics. Also, the unit cell employed to model quantum devices is different from the Yee cell used by the electrical engineering community. A bound for the time step is derived to ensure stability. Several numerical experiments in quantum structures demonstrate the accuracy of a second order, comparable to the analysis of electromagnetic devices with the Yee cell.

Finite difference time domain Simulation of the Earth-ionosphere resonant cavity: Schumann resonances

This paper presents a numerical approach to study the electrical properties of the Earths atmosphere. The finite-difference time-domain (FDTD) technique is applied to model the Earths atmosphere in order to determine Schumann resonant frequencies of the Earth. Three-dimensional spherical coordinates are employed and the conductivity profile of the atmosphere versus height is introduced. Periodic boundary conditions are implemented in order to exploit the symmetry in rotation of the Earth and decrease computational requirements dramatically. For the first time, very accurate FDTD results are obtained, not only for the fundamental mode but also for higher order modes of Schumann resonances. The proposed method constitutes a useful tool to obtain Schumann resonant frequencies, therefore to validate electrical models for the terrestrial atmosphere, or atmospheres of other celestial bodies.

Absorbing boundary conditions for the TLM method

The numerical behavior of different absorbing boundary conditions when applied to the transmission-line modeling (TLM) method is presented. These conditions may be classified into three different groups according to the way they are derived. The first group is obtained by discretizing one-way analytical conditions derived for the analytical wave equation. The second group is a set of discrete conditions directly obtained for the discrete wave equation. The last group is based on appropriate reflection coefficients derived purely from transmission-line theory. Because of their different behaviors, the numerical study is explicitly carried out for both two- and three-dimensional free-space scattering problems. >

A study of the propagation of electromagnetic waves in Titan's atmosphere with the TLM numerical method

Abstract A numerical modeling of the electromagnetic characteristics of Titan’s atmosphere is carried out by means of the TLM numerical method, with the aim of calculating the Schumann resonant frequencies of Saturn’s satellite. The detection and measurement of these resonances by the Huygens probe, which will enter Titan’s atmosphere at the beginning of 2005, is expected to show the existence of electric activity with lightning discharges in the atmosphere of this satellite. As happens with the Schumann frequencies on Earth, losses associated with electric conductivity will make these frequencies lower than theoretically expected, the fundamental frequency being located between 11 and 15 Hz. This numerical study also shows that the strong losses associated to the high conductivity make it impossible for an electromagnetic wave with a frequency of 10 MHz or lower, generated near the surface, to reach the outer part of Titan’s atmosphere.

Subsectional-polynomial E-pulse synthesis and application to radar target discrimination

A new family of extinction-pulses (E-pulses), called subsectional-polynomial E-pulses, is presented. This new type of E-pulse is constructed by choosing polynomials of degree Q as subsectional basis-functions in the E-pulse expansion. The main feature of this family of E-pulses is that the waveforms are continuous and smooth. Several topics concerning the E-pulse technique are investigated, such as: insensitivity to the exact number of natural modes present in the target response; aspect-angle independence; and effects of additive white Gaussian noise. Numerical results, using the response of a thin cylinder and a sphere, show that the subsectional-polynomial E-pulses improve the results obtained using subsectional-rectangular E-pulses. >

Dispersion analysis for a TLM mesh of symmetrical condensed nodes with stubs

In this paper, the dispersion characteristics of a TLM mesh formed by interconnected symmetrical condensed nodes with stubs are calculated using two different formulations. The dispersion relation derived is an implicit function of the wave number, frequency, dielectric permittivity, and magnetic permeability. Group and phase velocities are obtained for the three fundamental directions and different values of the relative permittivity. The study demonstrates that an increase in the modeled-medium permittivity leads to a decrease in the cutoff frequency for TLM numerical results. >

Parallel 3D-TLM algorithm for simulation of the Earth-ionosphere cavity

A parallel 3D algorithm for solving time-domain electromagnetic problems with arbitrary geometries is presented. The technique employed is the Transmission Line Modeling (TLM) method implemented in Shared Memory (SM) environments. The benchmarking performed reveals that the maximum speedup depends on the memory size of the problem as well as multiple hardware factors, like the disposition of CPUs, cache, or memory. A maximum speedup of 15 has been measured for the largest problem. In certain circumstances of low memory requirements, superlinear speedup is achieved using our algorithm. The model is employed to model the Earth-ionosphere cavity, thus enabling a study of the natural electromagnetic phenomena that occur in it. The algorithm allows complete 3D simulations of the cavity with a resolution of 10km, within a reasonable timescale.

Shumann resonances and electromagnetic transparence in the atmosphere of Titan

Abstract Among the multiple questions that the CASSINI/HUYGENS mission tries to answer is the likelihood of electric discharges in Titans atmosphere. The instruments “Huygens Atmospheric Structure Instrument” and “Radio and Plasma Wave Science” will probe the electromagnetic emissions during the Huygens descent and Cassini flybys, respectively. Although no lightning was observed during Voyagers encounters with Titan in 1980 and 1981, this does not exclude the existence of lightning phenomena. Recent investigations show that lightning discharges could occur in the lower atmosphere, such as the detection of methane condensation clouds in the troposphere and the theoretical prediction of an electric field that would be sufficient enough to cause lightning. We present a numerical model of Titans atmosphere with the aim of calculating the resonance frequencies and the atmospheric transparency to electromagnetic waves. The detection and measurement of these resonances, Schumann frequencies, by the Huygens probe, would show the existence of electric activity connected with lightning discharges in the atmosphere. As it happens with the Schumann frequencies of Earth, losses associated with the electric conductivity will make these frequencies to be lower than the theoretically predicted, the fundamental one being located between 11 and 15 Hz. An analytical study shows that the strong losses associated with the high conductivity make it impossible that an electromagnetic wave generated near the surface with a frequency of 10 MHz or lower reaches the outer part of Titans atmosphere. Therefore the detection of electromagnetic waves coming from Titans lower atmosphere by the RPWS instrument is very unlikely.

Time domain simulation of electromagnetic cloaking structures with TLM method

The increasing interest in invisible cloaks has been prompted in part by the availability of powerful computational resources which permit numerical studies of such a phenomenon. These are usually carried out with commercial software. We report here a full time domain simulation of cloaking structures with the Transmission Line Modeling (TLM) method. We first develop a new condensed TLM node to model metamaterials in two dimensional situations; various results are then presented, with special emphasis on what is not easily achievable using commercial software.

A numerical analysis of wire antennas loaded with varistor-composite materials

The behavior of wire antennas loaded at the driving point with varistor-composite materials is analyzed in the time domain via a numerical formulation. Varistor-composite materials are nonlinear transient arresters with a subnanosecond response time. Connecting these nonlinear elements in parallel with the feeding transmission line and adjusting the characteristic curves of varistor materials (i.e., current density and dielectric constant versus electric-field strength), the nonlinear load drains off currents of excessive potential levels. At operating voltages the material presents a higher impedance path and the arrester interference with the normal operation of the antenna under protection is minimal. >