This thesis presents results on the description of plasma waves in terms of wavepackets. The wave field is decomposed into a distribution of wavepackets in a space of position, wavevector, time, and frequency. A complex structure joining each pair of Fourier conjugate variables into a single complex coordinate allows the efficient derivation of equations of motion for the phase space distribution by exploiting its analytic properties. The Wick symbol calculus, a mathematical tool generalizing many convenient properties of the Fourier transform to a local setting, is used to derive new exact phase space equations which maintain full information on the phase of the waves and include effects nonlocal in phase space such as harmonic generation. A general purpose asymptotic expansion of the Wick symbol product formula is used to treat dispersion, refraction, photon acceleration, and ponderomotive forces. Examples studied include the nonlinear Schrödinger equation, mode conversion, and the Vlasov equation. The structure of partially coherent wave fields is understood in terms of zeros in the phase space distribution caused by dislocations in its complex phase which are shown to be correlated with the field entropy. Simulations of plasma heating by crossing electron beams are understood by representing the resulting plasma waves in phase space. The local coherence properties of the beam driven Langmuir waves are studied numerically.

The behaviour of very low frequency (V.L.F.) radio waves propagating in an ionlzed medium, such as the ionosphere and exosphere, may exhibit markedly different characteristics from those of frequencies such as are used for communication in the short-wave bands. The anisotropy introduced into the medium by the presence of the earth's magnetic field has a significant effect, while at frequencies below about 5KHz the presence of heavy positive ions may further affect propagation. In particular it is found that, under suitable conditions, V.L.F. signals may propagate along paths closely following the lines of force of the earth's magnetic field. The study of such signals has a practical interest in that, from consideration of their propagation times and dispersion properties, they can provide an inexpensive method of determining electron densities at well beyond the range of satellite investigation. For this reason, if for no other, theoretical investigation of the paths traced in a model exosphere may indicate how closely the model exosphere approximates the true one. A powerful method of tracing out these paths is by the use of "ray-tracing", provided the properties of the medium vary slowly in space, a condition not always fulfilled in practice. It has been the subject of this thesis to carry out ray-tracing studies, in particular noting the effects of the positive ions in the exosphere; effects which have not received much notice before as they were thought to be unimportant. Intro., p. 1-2.

Neste trabalho, estudamos a evolução temporal de pacotes de ondas gaussiano, propagando-se ao longo de hetero-estruturas clássicas. Estas hetero-estruturas apresentam características e propriedades semelhantes a diversas hetero-estruturas quânticas, as quais são exaustivamente estudadas. Estes sistemas têm recebido muito interesse nestes últimos anos, possibilitando uma melhor compreensão dos próprios sistemas quânticos, bem como o aparecimento de novos transdutores e sonares. Os pacotes de ondas propagam-se em meios que apenas permitem ondas longitudinais. Dentre a gama de sistemas unidimensionais abordados neste trabalho, destacamos o estudo de um emissor de pulsos acústicos, do problema do isolamento acústico de ambientes, enfatizando o problema da transmissão de um pacote de ondas incidindo normalmente em um sistema de dupla parede idêntica, com um meio absorvedor situado entre as paredes, e dos cristais acústicos unidimensionais lineares e não-lineares. Nos sistemas bidimensionais, existe o aparecimento de muitos efeitos que acontecem simultaneamente, como espalhamentos, difração, refração, reflexão e transmissão de ondas acústicas planas e esféricas. Destacamos o estudo de três problemas: 1) Espalhamento de uma onda por um disco não-rigido, com impedância acústica característica menor do que a do meio externo; 2) Propagação de um pulso em um sistema periódico de cilindros perfeitamente rígidos, formando um cristal clássico; 3) Propagação do pacote onda por uma guia perfeitamente rígida, de secção reta constante, a qual é cortada por uma outra guia retangular, de características semelhantes à primeira. A evolução temporal do pacote de ondas foi obtido através do desenvolvimento um novo algoritmo numérico. Este algoritimo é baseado na técnica do Split-Operator (SO), que é uma técnica de separação de operadores diferentes, situados no argumento de uma exponencial. Através deste novo algoritmo, foi ) possível estudar as propriedades dinâmicas de ondas de pressão em sistemas acústicos uni e bidimencionais, calculando a estrutura de bandas onde o método do PWE (do inglês plane-wave-expansion) apresenta fraca convergência ou falha. Comparando o nosso novo algoritimo com o método FDTD (fine difference time-domain method), usualmente utilizado em problemas de acústica, o método possui uma série de vantagens: 1) conserva o espaço de fase; 2) o SO é temporalmente inversível enquanto o FDTD não tem esta propriedade; 3) tem uma estabilidade numérica maior. Um método alternativo de evolução foi desenvolvido a partir do SO, quando consideramos aplicações consecutivas. Este método foi denominado de método Split-Operator Modificado (MSO). Este método tem as mesmas propriedades, porém dispende cerca de 20% menos de tempo computacional. Posteriormente, o método foi generalizado para incluir termos de dissipação e termos não-lineares / In this work, we studied the time evolution of a Gaussian wave packet, moving in classical heterostructures. These heterostructures have similar properties and behavior as quantum artificial structures, which are extensively studied in the literature. These classical heterostructures have been explored in these last years, to understand the quantum systems with more accuracy, as well as, to develop new kind of transducers and sonars. All the considered systems just support longitudinal acoustic waves. Here we studied several unidimensional systems, and the most relevant ones are the periodic pulse emitter, the problem of two identical walls containing an dissipative media placed between them, and the linear and non-linear unidimensional acoustic crystals. For two dimensional systems, we have several phenomena occurring at the same time: scattering, diffraction, refraction, reflection and transmission of plane and circular waves. We analyzed three distinct systems: i) Scattering of a wave due to a non-rigid disc; ii) Pulse propagation through a periodic array of perfectly rigid cylinders; iii) pulse propagation in a rectangular wave guide, crossed by another rectangular wave guide. We present here, a new computational algorithm, based on the Split-Operator (SO) technique, which allow us to study the dynamic properties of pressure waves in one and two-dimensional acoustical systems. With this new algorithm, we studied classical artificial structures, with high mismatch differences, where the PWE (plane-wave-expansion) method converges very slowly or fails. Our new algorithm also allow us to study the dynamitic properties of the system, while the PWE just give us the band structure of the system. Comparing this new time evolution algorithm for acoustic waves in classical systems with the FDTD method (finite difference time-domain method), usually used in problems of acoustics, the method has a series of advantages: i) the phase space is conserved; ii) the SO has time reversal symmetry, while FDTD doesn\'t have this property; iii) the SO has a larger numeric stability. An alternative method for time evolution was developed starting from the SO, when we considered consecutive applications. This method was denominated modified Split-Operator method (MSO). This method has the same properties, however MSO needs about 20% less computational time. Alternatively, the method was extended to systems that present dissipative and non-linear terms

Orientador: Jose Maria Campos dos Santos / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica / Made available in DSpace on 2018-08-12T16:32:14Z (GMT). No. of bitstreams: 1 Pereira_FlavioNunes_M.pdf: 35059535 bytes, checksum: bdcc933434fe0ba550e4d1291079e6c5 (MD5) Previous issue date: 2009 / Resumo: Este trabalho investiga o problema de propagação de ondas em estruturas do tipo barra com modelos de alta ordem. O enforque principal do trabalho concentra-se na implementação de modelos numéricos que representem o fenômeno da propagação de ondas em barras saudáveis e danificadas por uma trinca. Para a investigação do problema utilizou-se o Método do Elemento Espectral, o qual consiste em uma solução analítica das equações diferenciais da onda no domínio da freqüência utilizando-se técnicas matriciais similares ao Método dos Elementos Finitos. Quatro modelos de barra, com diferentes modos de propagação foram implementados computacionalmente em linguagem Matlab®: o modelo elementar; modelo de Love ou do primeiro modo; o modelo de Mindlin-Herrmann ou de dois modos; e o modelo de Mindlin-McNiven ou dos três modos. Para cada modelo de barra foram implementados os elementos espectrais: saudável finito, saudável semi-finito e trincado. Para avaliar o comportamento da onda durante sua propagação nas estruturas analisadas, diferentes exemplos numéricos foram feitos e validados através de comparações com resultados similares encontrados na literatura. As estruturas são excitadas por forças impulsivas construídas por uma onda senoidal modulada com uma janela triangular. Os resultados confirmam que os modelos de elemento espectral representam muito bem o fenômeno da propagação de onda em uma estrutura e também podem ser usados como uma ferramenta eficiente para a localização de trincas. / Abstract: This work investigates the wave propagation problem in high order rod type structures. The main approach is the implementation of numerical models that represent the phenomenon of wave propagation in healthy and cracked rods. The investigation uses the Spectral Element Method, which consists of an analytical solution of wave deferential equations in the frequency domain using matrix techniques similar to the Finite Element Method. Four rod models with diferent propaga- tion modes were implemented computationally in Matlab® language: the elementary model; Love's model or the first model, Mindlin-Herrmann's model or the two model, and Mindlin- McNiven's model or the three-model. For each type of rod spectral elements were implemented: finite he-althy, throw-o® healthy and cracked. To evaluate the wave propagation behavior in the analyzed structures, diferent numerical examples were made and validated through comparisons with si-milar results from the literature. The structures are excited by impulsive forces built by a sine wave modulated with a triangular window. The results confirm that the Spectral Element Method represent the phenomenon of the wave propagation very well in a structure and they can also be used as an efficient tool for the location of crack. / Mestrado / Mecanica dos Sólidos e Projeto Mecanico / Mestre em Engenharia Mecânica

The propagation of waves through nonlinear media is of interest here, namely as it pertains to two specific examples, a nonlinear dielectric and a hyperelastic solid. In both cases, we examine the propagation of two-dimensional, weakly nonlinear, quasi-planar waves. It is found that such systems will have a nonlinearity that is intrinsically cubic, and therefore, a classical Zabolotskaya-Khokhlov equation cannot give an accurate description of the wave evolution. To determine the general evolution equation in such systems, a multi-timing technique developed by Kluwick and Cox (1998) and Cramer and Webb (1998) will be employed. The resultant evolution equations are seen to involve only one new nonlinearity coefficient rather than the three coefficients found in other studies of cubically nonlinear systems. After determining the general evolution equation, inclusion of relaxation, dispersion and dissipation effects can be easily incorporated. / Master of Science

<p>Failure along rock discontinuities can result in economic losses as well as loss of life. It is essential to develop methods that monitor the response of these discontinuities to shear loading to enable prediction of failure. Laboratory experiments are performed to investigate geophysical techniques to monitor shear failure of a pre-existing discontinuity to detect signatures of impending failure. Previous studies have detected precursors to shear failure in the form of maxima of transmitted waves across a discontinuity under shear. However, those experiments focused on well-matched discontinuities. However, in nature, rock discontinuities are not always perfectly matched because the asperities may be weathered by chemical, physical or mechanical processes. Further, the specific shear mechanism of mismatched discontinuities is still poorly understood. In this thesis, the ability to detect seismic precursors to shear failure for various discontinuity conditions—well-matched (rough and saw-tooth), mismatched (rough), and nonplanar (discontinuity profile with a half-cycle sine wave (HCS))—was assessed. The investigation was carried out through a coupled geophysical and mechanical experimental program that integrated detailed laboratory observations at the micro- and meso-scales. Shear experiments on gypsum discontinuities were conducted to observe changes in compressional (P) and shear (S) waves transmitted across the discontinuity. Digital Image Correlation (DIC) was used to quantify the vertical and horizontal displacements along the discontinuity during shearing to relate the location and magnitude of slip with the measured wave amplitudes. </p> <p>Results from the experiments conducted on planar, well-matched rough discontinuities (grit 36 sandpaper roughness) showed that seismic precursors to failure took the form of peaks in the normalized transmitted amplitude prior to the peak shear stress. Seismic wave transmission detected non-uniform dilation and closure of the discontinuity at a normal stress of 1 MPa. The results showed that large-scale roughness (presence of a HCS) could mask the generation of precursors, as it can cause non-uniform closure/dilation along the fracture plane at low normal stress. </p> <p>The experiments on idealized saw-toothed gypsum discontinuities showed that seismic precursors to failure appeared as maxima in the transmitted wave amplitude and conversely as minima in the reflected amplitudes. Converted waves (S to P & P to S) were also detected, and their amplitudes reached a maximum prior to shear failure. DIC results showed that slip occurred first at the top of the specimen, where the load was applied, and then progressed along the joint as the shear stress increased. This process was consistent with the order of emergence of precursors, i.e., precursors were first recorded near the top and later at the center, and finally at the bottom of the specimen. </p> <p>Direct shear experiments conducted on specimens with a mismatched discontinuity did not show any precursors (in the transmitted amplitude) to failure at low normal stresses (2 MPa), while those precursors appeared at higher normal stresses (5 MPa). The interplay between wave transmission, the degree of mismatch, and the discontinuity’s micro-physical, -chemical and -mechanical properties was assessed through: (1) 3D CT in-situ Xray scans to quantify the degree of mismatch at various normal stresses; (2) micro-indentation testing, to measure the micro-strength of the asperities; and (3) Scanning Electron Microscopy (SEM) and Electron Xray Diffraction (EDX), to study the micro-structure and chemical composition of the discontinuity. The X-ray results showed that contact between asperities increased with normal stress, even when the discontinuity was mismatched. The results indicated that: (1) at 2 MPa, the void aperture was large, so significant shear displacement was needed to interlock and damage the asperities; and (2) the micro-hardness of the asperities of the mismatched discontinuity was larger than that of the well-matched discontinuity, which points to inducing less damage for the same shear displacement. Both mechanisms contribute to the need for larger shear displacements to the mismatched discontinuity asperities to cause damage, which is consistent with the inability to detect seismic precursors to failure. The experimental results suggest that monitoring changes in transmitted wave amplitude across a discontinuity is a promising method for predicting impending failure for well-matched rock discontinuities. Precursor monitoring for mismatched rock discontinuities seems only possible when there is sufficient contact between the two rock surfaces, which occurs at large normal stresses. </p>

Two numerical techniques, the boundary-element method (BEM) and the finite-difference method (FDM), are used for simulating the radiation from horn-loaded compression drivers and from an infinitely-baffled, finite-length pipe. While computations of the horn-loaded compression driver are in steady state, transient analysis of the finite-length pipe is studied as a precursor to transient analysis within the horn-loaded compression driver. BEM numerical simulations show promise for the development of new designs. Numerical simulations serve as a good tool for time and cost-effective prototyping as poor designs are detected before they are built.

The aim of this thesis is to introduce my work which has generally been focused on optical wavefronts that have the unusual property of resisting commonplace phenomena such as diffraction and dispersion. Interestingly, these special beams are found both in linear and nonlinear situations. For example, in the linear regime, localized spatio-temporal waves which resemble the spherical harmonic symmetries of the hydrogen quantum orbitals can simultaneously negotiate both diffractive and dispersive effects. In the nonlinear regime, dressed optical filaments can be arranged to propagate multi-photon produced plasma channels orders of magnitude longer than expected. The first portion of this dissertation will begin by surveying the history of diffraction-free beams and introducing some of their mathematical treatments. Interjected throughout this discussion will be several relevant concepts which I explored during my first years a CREOL. The discussion will then be steered into a detailed account of diffraction/dispersion free wavefronts which display hydrogen-like symmetries. The second segment of the document will cover the highly nonlinear process of optical filamentation. This chapter will almost entirely investigate the idea of the dressed filament, an entity which allows for substantial prolongation of this light string. I will then conclude by delving into the topic of supercontinuum generation in parabolic multimode fibers which, in the upcoming years, has great potential of becoming important in optics.

By nature discrete solitons represent self-trapped wavepackets in nonlinear periodic structures and result from the interplay between lattice diffraction (or dispersion) and material nonlinearity. In optics, this class of self-localized states has been successfully observed in both one-and two-dimensional nonlinear waveguide arrays. In recent years such lattice structures have been implemented or induced in a variety of material systems including those with cubic (Kerr), quadratic, photorefractive, and liquid-crystal nonlinearities. In all cases the underlying periodicity or discreteness leads to new families of optical solitons that have no counterpart whatsoever in continuous systems. In the first part of this dissertation, a theoretical investigation of linear and nonlinear optical wave propagation in semi-infinite waveguide arrays is presented. In particular, the properties and the stability of surface solitons at the edge of Kerr (AlGaAs) and quadratic (LiNbO3) lattices are examined. Hetero-structures of two dissimilar semi-infinite arrays are also considered. The existence of hybrid solitons in these latter types of structures is demonstrated. Rabi-type optical transitions in z-modulated waveguide arrays are theoretically demonstrated. The corresponding coupled mode equations, that govern the energy oscillations between two different transmission bands, are derived. The results are compared with direct beam propagation simulations and are found to be in excellent agreement with coupled mode theory formulations. In the second part of this thesis, the concept of parity-time-symmetry is introduced in the context of optics. More specifically, periodic potentials associated with PT-symmetric Hamiltonians are numerically explored. These new optical structures are found to exhibit surprising characteristics. These include the possibility of abrupt phase transitions, band merging, non-orthogonality, non-reciprocity, double refraction, secondary emissions, as well as power oscillations. Even though gain/loss is present in this class of periodic potentials, the propagation eigenvalues are entirely real. This is a direct outcome of the PT-symmetry. Finally, discrete solitons in PT-symmetric optical lattices are examined in detail.

In this study, the properties of the reflected paths and scattering phenomena were investigated in the LMDS band (28 GHz). We used the newly developed sampling swept time delay short pulse (SSTDSP) sounder to collect field data in certain locations on the Virginia Tech campus. The sounder collected the channel impulse response analog waveform, sampled, digitized and reconstructed it. The stored data were used to produce the power delay profile and other channel parameters. In particular, we collected scattered and reflected data regarding the channel response with different incident angle and distance set-ups from brick and limestone walls. We used the reflected pulse width and maximum excess delay derived from each power delay profile to analyze the rough surface scattering phenomena. We found that limestone and brick walls exhibited some diffuse scattering. The reflected pulse of a limestone wall had more maximum excess delay spread than did a brick wall at -15dB power threshold. The mean maximum excess delay for the reflected pulse of the limestone wall measurement set-ups was more than two times that of the brick wall. With equal transmitter and receiver distances to the wall, we found that as the incident angle increased, the maximum excess delay decreased but the perpendicular reflection coefficient increased. It is recommended that for future study, a second generation SSTDSP sounder will replicate the measurement with larger distance and angle set-ups as well as in non-line-of-sight areas. / Master of Science