1,720,982 research outputs found
Dispersion of Electromagnetic Waves in a Periodic Open Waveguide
No full textWe model guided modes for an infinitely long metallic structure in the lateral direction that is invariant in the transverse direction, and mechanically supported by a dielectric layer This modeling is done without making any assumptions about the width of the slots relative to the spatial period. We do this by representing the electric field by their Floquet series in combination with a plane wave representation for the field between the plates. Applying the appropriate boundary conditions leads us to a determinantal (or dispersion) equation. Complex solutions to this dispersion equation have been found numerically using a sophisticatedly adjusted downhill method in two dimensions. Finally this new method has been used to show the effect of the variation of four important parameters in the modeling of a periodically loaded open waveguide. These parameters are: the number of space harmonics, the permittivity of the dielectric layer, the slot size and the height of the dielectric layer.Telecommunications / Laboratory of Electromagnetic ResearchElectrical EngineeringElectrical Engineering, Mathematics and Computer Scienc
Transient acoustic waves in continuously layered media
No full textElectrical Engineering, Mathematics and Computer Scienc
Modeling of nonlinear medical diagnostic ultrasound
No full textIn this PhD Thesis, a numerical method is described that accurately predicts the pulsed acoustic pressure field generated by a medical diagnostic phased array transducer in a nonlinear acoustic medium. The method is called the Iterative Nonlinear Contrast Source (INCS) method, and it is capable of handling a large-scale, threedimensional domain of interest, in the order of 100 wavelengths in each spatial dimension and 100 periods in the temporal dimension. Unlike many existing methods, the method is based on a full-wave approach and it does not employ an implicit or explicit plane wave approximation. Starting from a set of two nonlinear first-order field equations and a two nonlinear constitutive equations, we show that the nonlinear acoustic field may be approximated with a second-order wave equation which is a lossless form of the Westervelt equation including source terms. The Westervelt equation may be solved efficiently by means of the INCS method. In this method, the nonlinear wave problem is formally solved by a Neumann iterative solution, in which the nonlinear term in the Westervelt equation acts as a nonlinear contrast source and provides iterative corrections to the linear approximation of the nonlinear wave problem. The linear step in the Neumann scheme is solved by a spatiotemporal convolution integral of the (primary or contrast) source with the Green's function of the linear background medium. For the evaluation of the convolution integral as a discrete convolution sum on a spatiotemporal grid, the Green's function and the (primary or contrast) source are filtered and windowed in all spatiotemporal dimensions, allowing for their coarse discretization at the Nyquist limit of two points per wavelength/period for the maximum frequency of interest. This approach is referred to as the Filtered Convolution (FC) method. The resulting discretized convolution sum is efficiently evaluated using a Fast Fourier Transform (FFT) method. Results for various one-dimensional and three-dimensional wave problems show that in all cases the INCS method produces accurate results. A validation experiment with a rectangular transducer also shows that the measured nonlinear acoustic field is reproduced very well with the INCS method. Because of its accuracy, reliability and the general validity of its solution, we conclude that the INCS method can be used as a benchmark model for weak to moderate nonlinear distortion, as it occurs in medical diagnostic ultrasound.Electrical Engineering, Mathematics and Computer Scienc
Finite Element Method Applied to the One-dimensional Westervelt Equation
No full textIn this thesis we researched the applicability, properties and efficiency of the finite element method to solve the one-dimensional Westervelt equation, which describes nonlinear plane wave propagation. The goal was to investigate whether this lesser-known solution method has advantages or disadvantages compared to more commonly used solution techniques. We developed an understanding of nonlinear wave propagation by analyzing the Burgers equation, which we used to benchmark solutions. We used the commercial finite element software package COMSOL to calculate first solutions, where we found that numerical errors occur as the wave propagates through the shock wave formation distance. We examined the effect of several numerical parameters and concluded that reducing the element size decreases the overall error of the solution, both near the shock wave front and elsewhere. This also helps reduce numerical oscillations if present. Increasing the element order also improved the solution. The time stepping algorithm was found to have a strong connection to the element size. The maximum time step depends strongly on the minimum element size. Reducing physical parameters such as the amplitude of the source, or adding damping, were also researched but were shown to have little effect on reducing the numerical error around the shock wave front. The finite element method can solve inhomogeneous domains with relative ease compared to homogeneous domains, which may be an advantage over other methods. We then developed our own Matlab implementation of Galerkin's finite element method for the Westervelt equation to get more insight into the algorithms behind this method and get a better understanding of the effect of numerical parameters. We implemented two different time solvers and we concluded that our specific choice of backward differential formulas was producing more accurate results than more general build-in time solvers that come with COMSOL or Matlab. Furthermore we saw that the accuracy of the solution does not only depend on spatial numerical parameters, but also on the time solving parameters. Different time solving techniques can yield different degrees of accuracy and efficiency, and must therefore be chosen with care. We finally turned to adaptive finite element method techniques in order to improve overall accuracy and efficiency. We have shown that a simple form of adaptiveness can help improve the accuracy of the solution, but its efficiency depends on the implementation and the number of spatial dimensions in which the equation is solved. The finite element method provides different types of adaptiveness, such as local refinement/coarsening, node movement and local change of the order of the basis functions, which may be combined together. We showed the advantages and disadvantages of a node movement implementation based on the MMPDE-6 algorithm. We concluded that more research can be put in incorporating (combined types of) adaptiveness to solve the Westervelt equation.Bachelor Applied Physics and Applied MathematicsNumerical AnalysisElectrical Engineering, Mathematics and Computer Scienc
Modelling the Induced Oscillations of Elements on a Silicon Transducer
No full textIn this report, we will try to model a silicon chip with elements, as used in current experiments, with the aim to find a suitable and fast model for the transducer used. The specific question we will try to address is: How well can we model the effects of induced oscillation on other elements on a silicon chip? Induced oscillations can create problems when miniaturizing heart imaging technology for example, as the incoming signal cannot be properly converted to an image. The biharmonic equation dictates the displacement of the elements with respect to a force acting on the chip. Hence, using assumptions and numerical methods, the biharmonic equation can only be split into two coupled equations. We will look at two different boundary conditions for both of these equations; either the glue used to attach the transducer to the substrate is simply supporting the transducer, or clamping the transducer in place. We will model the biharmonic equation using Peisker's method, as well as the simply supported boundary problem. Both of these will require us to reformulate the biharmonic equation in the frequency domain, and linearize the impedance for a range between 1MHz and 9:5MHz. The results from this will then be compared to the Newmark-Beta method solution, by looking at the stability, efficiency, and accuracy. From this we can also answer the second question we will try to address: How well can Peisker's method be used to solve a fourth order differential equation? We expect that the solution to the simply supported boundary conditions look similar to the Newmark-Beta method, as they both have the same boundary conditions. Furthermore, the solution from the Peisker method should not look very different either, as they are all describing the same biharmonic equation. We found that both the Peisker method and the solution to the simply supported boundary problem look very similar, and both look like the Newmark-Beta method solution. Both methods and the non-iterative solution from the simply supported boundary problem show induced oscillations on the transducer. From this we can conclude that the simply supported boundary problem is preferred over the Newmark-Beta method due to its computation time and preferred over the Peisker method due to its computation time and smaller truncation error. The simply supported boundary problem can be more efficiently implemented than the Peisker model, as there is no need for iterations. Hence, it can be relatively quickly simulated. From this report we have seen that we can effectively model the effects of induced oscillation on other elements on a silicon chip, through the Peisker method, the Newmark-Beta method and the simply supported boundary problem. To answer our second question, Peisker's method is an effective and accurate method to model the biharmonic equation, a fourth order differential equation. However, the simply supported boundary problem is preferred.Electrical Engineering, Mathematics and Computer ScienceDelft Institute of Applied Mathematic
Using The Non-Linear Effect of Ultrasound to Perform a Temperature Measurement in Water
No full textFor local hyperthermia treatments it is of importance to know the temperature of the target and of the tissue around the target. The lack of easy accessible methods to measure the temperature non-invasively can make this a cumbersome task. In this thesis an earlier proposed method which uses the non-linearity of ultrasound to determine the temperature non-invasively is studied and a novel adjusted form of this method is proposed. The novel method uses a send wave which will generate a second harmonic. This wave is then compared to a second wave, which contains the same spectrum as the second harmonic generated by the first wave. The applicability of this method is studied by using a KZK simulation to see if the method can work in a pulse echo configuration, where the echo’s come from a small sample placed in water with scatter points closer together than the wavelength of the send wave. From those simulations it is shown that the new method is able to acquire the temperature of the medium.Medical physicsBiomedical EngineeringMechanical, Maritime and Materials Engineerin
Numerical solution of nonlinear acoustic wave problems employing a green's function approach
No full textThe design of phased array transducers for medical diagnostic ultrasound asks for an understanding of the nonlinear propagation of acoustic wavefields. Most existing numerical models are based on the linearized model equations, but in the recent decades several numerical models have been developed that incorporate weak nonlinear propagation as well. In this study, we present an approach that enables the computation of large-scale, three-dimensional, weakly nonlinear wavefields in the time domain. It is based on the Neumann iterative method, which enables the successive use of the solution of a linear wave problem, where the nonlinearity is treated as a contrast source. The linear wave problem is formulated as a convolution integral with a free space Green`s function kernel. If the Green`s function is adequately regularized, this method enables us to discretize the spatiotemporal domain with step sizes up to the limit given by the Nyquist-Shannon sampling theorem for a bandlimited signal. The remaining spatiotemporal derivatives are handled with high-order finite difference schemes. The proposed method is validated with a one-dimensional nonlinear wave problem. We evaluate the wavefield, including harmonic frequencies up to the fifth harmonic. The results are compared with a solution of the lossless Burgers` equation. It is observed that already after a small number of iterations the computed result shows perfect agreement with those of the Burgers` equation. In this paper, we make plausible that the proposed method can be straightforwardly extended to more complex problems. The volume integral equation approach opens the road to solving time domain nonlinear wave problems in three dimensions. Furthermore, the method can be adapted to media with attenuation and inhomogeneity.Applied Science
Apparatus for mooring ships
No full textThe invention relates to an apparatus for mooring ships that have a magnetisable hull, embodied with a series of magnets disposed on or at a quayside, wherein the magnets have magnetic cores that are comb-shaped, with the teeth of the comb forming the magnetic poles and are oriented away from the quayside.Electrical Engineering, Mathematics and Computer Scienc
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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