Customization of the design of antenna using genetic algorithm and finite-difference time-domain technique

Antenna design is an iterative process in which structures are analyzed and changed to comply with certain performance parameters required. The classic approach starts with analyzing a "known" structure, obtaining the value of its performance parameter and changing this structure until the "target" value is achieved. This process relies on having an initial structure, which follows some known or "intuitive" patterns already familiar to the designer. The purpose of this research was to develop a method of designing UWB antennas. What is new in this proposal is that the design process is reversed: the designer will start with the target performance parameter and obtain a structure as the result of the design process. This method provided a new way to replicate and optimize existing performance parameters. The base of the method was the use of a Genetic Algorithm (GA) adapted to the format of the chromosome that will be evaluated by the Electromagnetic (EM) solver. For the electromagnetic study we used XFDTD™ program, based in the Finite-Difference Time-Domain technique. The programming portion of the method was created under the MatLab environment, which serves as the interface for converting chromosomes, file formats and transferring of data between the XFDTD™ and GA. A high level of customization had to be written into the code to work with the specific files generated by the XFDTD™ program. Two types of cost functions were evaluated; the first one seeking broadband performance within the UWB band, and the second one searching for curve replication of a reference geometry. The performance of the method was evaluated considering the speed provided by the computer resources used. Balance between accuracy, data file size and speed of execution was achieved by defining parameters in the GA code as well as changing the internal parameters of the XFDTD™ projects. The results showed that the GA produced geometries that were analyzed by the XFDTD™ program and changed following the search criteria until reaching the target value of the cost function. Results also showed how the parameters can change the search criteria and influence the running of the code to provide a variety of geometries.

Characterization and modeling of multi-conductor transmission line using Finite-difference Time-Domain method

A two-dimensional, 2D, finite-difference time-domain (FDTD) method is used to analyze two different models of multi-conductor transmission lines (MTL). The first model is a two-conductor MTL and the second is a threeconductor MTL. Apart from the MTL's, a three-dimensional, 3D, FDTD method is used to analyze a three-patch microstrip parasitic array. While the MTL analysis is entirely in time-domain, the microstrip parasitic array is a study of scattering parameter Sn in the frequency-domain. The results clearly indicate that FDTD is an efficient and accurate tool to model and analyze multiconductor transmission line as well as microstrip antennas and arrays.

Time-domain simulation of wave-induced ship motions by a Rankine panel method

In this thesis, a numerical program has been developed to simulate the wave-induced ship motions in the time domain. Wave-body interactions have been studied for various ships and floating bodies through forced motion and free motion simulations in a wide range of wave frequencies. A three-dimensional Rankine panel method is applied to solve the boundary value problem for the wave-body interactions. The velocity potentials and normal velocities on the boundaries are obtained in the time domain by solving the mixed boundary integral equations in relation to the source and dipole distributions. The hydrodynamic forces are calculated by the integration of the instantaneous hydrodynamic pressures over the body surface. The equations of ship motion are solved simultaneously with the boundary value problem for each time step. The wave elevation is computed by applying the linear free surface conditions. A numerical damping zone is adopted to absorb the outgoing waves in order to satisfy the radiation condition for the truncated free surface. A numerical filter is applied on the free surface for the smoothing of the wave elevation. Good convergence has been reached for both forced motion simulations and free motion simulations. The computed added-mass and damping coefficients, wave exciting forces, and motion responses for ships and floating bodies are in good agreement with the numerical results from other programs and experimental data.

Principal Component Analysis of Results Obtained from Finite-Difference Time-Domain Algorithms

Finite-Differences Time-Domain (FDTD) algorithms are well established tools of computational electromagnetism. Because of their practical implementation as computer codes, they are affected by many numerical artefact and noise. In order to obtain better results we propose using Principal Component Analysis (PCA) based on multivariate statistical techniques. The PCA has been successfully used for the analysis of noise and spatial temporal structure in a sequence of images. It allows a straightforward discrimination between the numerical noise and the actual electromagnetic variables, and the quantitative estimation of their respective contributions. Besides, The GDTD results can be filtered to clean the effect of the noise. In this contribution we will show how the method can be applied to several FDTD simulations: the propagation of a pulse in vacuum, the analysis of two-dimensional photonic crystals. In this last case, PCA has revealed hidden electromagnetic structures related to actual modes of the photonic crystal.

Time domain decomposition for European options in financial modelling

Finance is one of the fastest growing areas in modern applied mathematics with real world applications. The interest of this branch of applied mathematics is best described by an example involving shares. Shareholders of a company receive dividends which come from the profit made by the company. The proceeds of the company, once it is taken over or wound up, will also be distributed to shareholders. Therefore shares have a value that reflects the views of investors about the likely dividend payments and capital growth of the company. Obviously such value will be quantified by the share price on stock exchanges. Therefore financial modelling serves to understand the correlations between asset and movements of buy/sell in order to reduce risk. Such activities depend on financial analysis tools being available to the trader with which he can make rapid and systematic evaluation of buy/sell contracts. There are other financial activities and it is not an intention of this paper to discuss all of these activities. The main concern of this paper is to propose a parallel algorithm for the numerical solution of an European option. This paper is organised as follows. First, a brief introduction is given of a simple mathematical model for European options and possible numerical schemes of solving such mathematical model. Second, Laplace transform is applied to the mathematical model which leads to a set of parametric equations where solutions of different parametric equations may be found concurrently. Numerical inverse Laplace transform is done by means of an inversion algorithm developed by Stehfast. The scalability of the algorithm in a distributed environment is demonstrated. Third, a performance analysis of the present algorithm is compared with a spatial domain decomposition developed particularly for time-dependent heat equation. Finally, a number of issues are discussed and future work suggested.

Rational Function Interpolation of Electromagnetic Transfer Functions of High-Speed Interconnect Systems from Discrete Time-Domain and Frequency-Domain Data

We present new methodologies to generate rational function approximations of broadband electromagnetic responses of linear and passive networks of high-speed interconnects, and to construct SPICE-compatible, equivalent circuit representations of the generated rational functions. These new methodologies are driven by the desire to improve the computational efficiency of the rational function fitting process, and to ensure enhanced accuracy of the generated rational function interpolation and its equivalent circuit representation. Toward this goal, we propose two new methodologies for rational function approximation of high-speed interconnect network responses. The first one relies on the use of both time-domain and frequency-domain data, obtained either through measurement or numerical simulation, to generate a rational function representation that extrapolates the input, early-time transient response data to late-time response while at the same time providing a means to both interpolate and extrapolate the used frequency-domain data. The aforementioned hybrid methodology can be considered as a generalization of the frequency-domain rational function fitting utilizing frequency-domain response data only, and the time-domain rational function fitting utilizing transient response data only. In this context, a guideline is proposed for estimating the order of the rational function approximation from transient data. The availability of such an estimate expedites the time-domain rational function fitting process. The second approach relies on the extraction of the delay associated with causal electromagnetic responses of interconnect systems to provide for a more stable rational function process utilizing a lower-order rational function interpolation. A distinctive feature of the proposed methodology is its utilization of scattering parameters. For both methodologies, the approach of fitting the electromagnetic network matrix one element at a time is applied. It is shown that, with regard to the computational cost of the rational function fitting process, such an element-by-element rational function fitting is more advantageous than full matrix fitting for systems with a large number of ports. Despite the disadvantage that different sets of poles are used in the rational function of different elements in the network matrix, such an approach provides for improved accuracy in the fitting of network matrices of systems characterized by both strongly coupled and weakly coupled ports. Finally, in order to provide a means for enforcing passivity in the adopted element-by-element rational function fitting approach, the methodology for passivity enforcement via quadratic programming is modified appropriately for this purpose and demonstrated in the context of element-by-element rational function fitting of the admittance matrix of an electromagnetic multiport.

Design, construction, and applications of a high-resolution terahertz time-domain spectrometer

This thesis reports on the design, construction, and initial applications of a high-resolution terahertz time-domain ASOPS spectrometer. The instrument employs asynchronous optical sampling (ASOPS) between two Ti:sapphire ultrafast lasers operating at a repetition rate of approximately 80 MHz, and we thus demonstrate a THz frequency resolution approaching the limit of that repetition rate. This is an order of magnitude improvement in resolution over typical THz time-domain spectrometers. The improved resolution is important for our primary effort of collecting THz spectra for far-infrared astronomy. We report on various spectroscopic applications including the THz rotational spectrum of water, where we achieve a mean frequency error, relative to established line centers, of 27.0 MHz. We also demonstrate application of the THz system to the long-duration observation of a coherent magnon mode in a anti-ferromagnetic yttrium iron oxide (YFeO3) crystal. Furthermore, we apply the all-optical virtual delay line of ASOPS to a transient thermoreflectance experiment for quickly measuring the thermal conductivity of semiconductors.

Development of Novel Time-Domain Electromagnetic Methods for Offshore Groundwater Studies: A Data Application from Bat Yam, Israel

Recent marine long-offset transient electromagnetic (LOTEM) measurements yielded the offshore delineation of a fresh groundwater body beneath the seafloor in the region of Bat Yam, Israel. The LOTEM application was effective in detecting this freshwater body underneath the Mediterranean Sea and allowed an estimation of its seaward extent. However, the measured data set was insufficient to understand the hydrogeological configuration and mechanism controlling the occurrence of this fresh groundwater discovery. Especially the lateral geometry of the freshwater boundary, important for the hydrogeological modelling, could not be resolved. Without such an understanding, a rational management of this unexploited groundwater reservoir is not possible. Two new high-resolution marine time-domain electromagnetic methods are theoretically developed to derive the hydrogeological structure of the western aquifer boundary. The first is called Circular Electric Dipole (CED). It is the land-based analogous of the Vertical Electric Dipole (VED), which is commonly applied to detect resistive structures in the subsurface. Although the CED shows exceptional detectability characteristics in the step-off signal towards the sub-seafloor freshwater body, an actual application was not carried out in the extent of this study. It was found that the method suffers from an insufficient signal strength to adequately delineate the resistive aquifer under realistic noise conditions. Moreover, modelling studies demonstrated that severe signal distortions are caused by the slightest geometrical inaccuracies. As a result, a successful application of CED in Israel proved to be rather doubtful. A second method called Differential Electric Dipole (DED) is developed as an alternative to the intended CED method. Compared to the conventional marine time-domain electromagnetic system that commonly applies a horizontal electric dipole transmitter, the DED is composed of two horizontal electric dipoles in an in-line configuration that share a common central electrode. Theoretically, DED has similar detectability/resolution characteristics compared to the conventional LOTEM system. However, the superior lateral resolution towards multi-dimensional resistivity structures make an application desirable. Furthermore, the method is less susceptible towards geometrical errors making an application in Israel feasible. In the extent of this thesis, the novel marine DED method is substantiated using several one-dimensional (1D) and multi-dimensional (2D/3D) modelling studies. The main emphasis lies on the application in Israel. Preliminary resistivity models are derived from the previous marine LOTEM measurement and tested for a DED application. The DED method is effective in locating the two-dimensional resistivity structure at the western aquifer boundary. Moreover, a prediction regarding the hydrogeological boundary conditions are feasible, provided a brackish water zone exists at the head of the interface. A seafloor-based DED transmitter/receiver system is designed and built at the Institute of Geophysics and Meteorology at the University of Cologne. The first DED measurements were carried out in Israel in April 2016. The acquired data set is the first of its kind. The measured data is processed and subsequently interpreted using 1D inversion. The intended aim of interpreting both step-on and step-off signals failed, due to the insufficient data quality of the latter. Yet, the 1D inversion models of the DED step-on signals clearly detect the freshwater body for receivers located close to the Israeli coast. Additionally, a lateral resistivity contrast is observable in the 1D inversion models that allow to constrain the seaward extent of this freshwater body. A large-scale 2D modelling study followed the 1D interpretation. In total, 425 600 forward calculations are conducted to find a sub-seafloor resistivity distribution that adequately explains the measured data. The results indicate that the western aquifer boundary is located at 3600 m - 3700 m before the coast. Moreover, a brackish water zone of 3 Omega*m to 5 Omega*m with a lateral extent of less than 300 m is likely located at the head of the freshwater aquifer. Based on these results, it is predicted that the sub-seafloor freshwater body is indeed open to the sea and may be vulnerable to seawater intrusion.

Calibração da Reflectometria no Domínio do Tempo (TDR) para a estimativa da concentração da solução no solo

Time Domain Reflectometry (TDR) is a reliable method for in-situ measurements of the humidity and the solution concentration at the same soil volume. Accurate interpretation of electrical conductivity (and soil humidity) measurements may require a specific calibration curve. The primary goal of this work was to establish a calibration procedure for using TDR to estimate potassium nitrate concentrations (KNO3) in soil solution. An equation relating the electrical conductivity measured by TDR and KNO3 concentration was established enabling the use of TDR technique to estimate soil water content and nitrate concentration for efficient fertigation management.

Estimativas do teor de umidade empregando o método GPR: uma avaliação comparativa em experimentos de laboratório e campo

Este trabalho faz uma análise das estimativas de teores de umidade obtidas com o método Ground Penetrating Radar (GPR) comparativamente às determinadas com os métodos Time Domain Reflectometry (TDR) e gravimétrico. Os dados foram obtidos em dois experimentos diferentes: um experimento controlado em laboratório buscando reproduzir um meio homogêneo onde foram obtidas as medidas de umidade com GPR (antenas de 1 GHz) e TDR, e outro experimento de campo onde foram obtidos dados com GPR (antenas de 200 MHz) e de amostras de solos do local. Para a obtenção das estimativas a partir do método GPR foram analisados os eventos relativos à onda de transmissão direta entre as antenas, onda refratada criticamente e onda refletida em interfaces com diferentes propriedades elétricas.O GPR mostrou-se sensível às variações de umidades presentes nos dois experimentos e apresentou boa correlação com os dados obtidos com TDR (REQM de0,007 m³m-3) e das amostras (REQM de 0,039 m³m-3).

Distribution and storage characterization of soil solution for drip irrigation

The increased use of marginal quality water with drip irrigation requires sound fertigation practices that reconcile environmental concerns with viable crop production objectives. We conducted experiments to characterize dynamics and patterns of soil solution within wet bulb formed by drip irrigation. Time-domain reflectometry probes were used to monitor the distribution of potassium nitrate (KNO(3)) and water distribution from drippers discharging at constant flow rates of 2, 4 and 8 L h(-1) in soil-filled containers. Considering results from different profiles, we observed greater solute storage near the dripper decreasing gradually towards the wetting front. About half of the applied KNO(3) solution (48%) was stored in the first layer (0-0.10 m) for all experiments, 29% was stored in the next layer (0.10-0.20 m). Comparing different dripper flow rates, we observed higher solution storage for 4 L h(-1), with 45, 53 and 47% of applied KNO(3) solution accumulating in the first layer (0-0.10 m) for dripper flow rates of 2, 4 and 8 L h(-1), respectively. The results suggest that based on the volume and frequency used in this experiment, it would be advantageous to apply small amounts of solution at more frequent intervals to reduce deep percolation losses of applied water and solutes.

Sampling and TDR probe insertion in the determination of the volumetric soil water content

Volumetric soil water content (theta) can be evaluated in the field by direct or indirect methods. Among the direct, the gravimetric method is regarded as highly reliable and thus often preferred. Its main disadvantages are that sampling and laboratory procedures are labor intensive, and that the method is destructive, which makes resampling of a same point impossible. Recently, the time domain reflectometry (TDR) technique has become a widely used indirect, non-destructive method to evaluate theta. In this study, evaluations of the apparent dielectric number of soils (epsilon) and samplings for the gravimetrical determination of the volumetric soil water content (thetaGrav) were carried out at four sites of a Xanthic Ferralsol in Manaus - Brazil. With the obtained epsilon values, theta was estimated using empirical equations (thetaTDR), and compared with thetaGrav derived from disturbed and undisturbed samples. The main objective of this study was the comparison of thetaTDR estimates of horizontally as well as vertically inserted probes with the thetaGrav values determined by disturbed and undisturbed samples. Results showed that thetaTDR estimates of vertically inserted probes and the average of horizontally measured layers were only slightly and insignificantly different. However, significant differences were found between the thetaTDR estimates of different equations and between disturbed and undisturbed samples in the thetaGrav determinations. The use of the theoretical Knight et al. model, which permits an evaluation of the soil volume assessed by TDR probes, is also discussed. It was concluded that the TDR technique, when properly calibrated, permits in situ, nondestructive measurements of q in Xanthic Ferralsols of similar accuracy as the gravimetric method.

Availability of soil water under tillage systems, mulch management and citrus rootstocks

The increased availability of soil water is important for the management of non-irrigated orange orchards. The objective of this study was to evaluate the availability of soil water in a Haplorthox (Rhodic Ferralsol) under different tillage systems used for orchard plantation, mulch management and rootstocks in a "Pêra" orange orchard in northwest Paraná, Brazil. An experiment in a split-split-plot design was established in 2002, in an area cultivated with Brachiaria brizantha grass in which three tillage systems (no tillage, conventional tillage and strip-tillage) were used for orchard plantation. This grass was mowed twice a year between the rows, representing two mulch managements in the split plots (no mulching and mulching in the plant rows). The split-split-plots were represented by two rootstocks ("Rangpur" lime and "Cleopatra" mandarin). The soil water content in the plant rows was evaluated in the 0-20 cm layer in 2007 and at 0-20 and 20-40 cm in 2008-2009. The effect of soil tillage systems prior to implantation of orange orchards on soil water availability was less pronounced than mulching and the rootstocks. The soil water availability was lower when "Pêra" orange trees were grafted on "Cleopatra" mandarin than on "Rangpur" lime rootstocks. Mulching had a positive influence on soil water availability in the sandy surface layer (0-20 cm) and sandy clay loam subsurface (20-40 cm) of the soil in the spring. The production of B. brizantha between the rows and residue disposal in the plant rows as mulch increased water availability to the "Pêra" orange trees.