Fast numerical methods for mixed, singular Helmholtz boundary value problems and Laplace eigenvalue problems - with applications to antenna design, sloshing, electromagnetic scattering and spectral geometry

This thesis presents a novel class of algorithms for the solution of scattering and eigenvalue problems on general two-dimensional domains under a variety of boundary conditions, including non-smooth domains and certain "Zaremba" boundary conditions - for which Dirichlet and Neumann conditions are specified on various portions of the domain boundary. The theoretical basis of the methods for the Zaremba problems on smooth domains concern detailed information, which is put forth for the first time in this thesis, about the singularity structure of solutions of the Laplace operator under boundary conditions of Zaremba type. The new methods, which are based on use of Green functions and integral equations, incorporate a number of algorithmic innovations, including a fast and robust eigenvalue-search algorithm, use of the Fourier Continuation method for regularization of all smooth-domain Zaremba singularities, and newly derived quadrature rules which give rise to high-order convergence even around singular points for the Zaremba problem. The resulting algorithms enjoy high-order convergence, and they can tackle a variety of elliptic problems under general boundary conditions, including, for example, eigenvalue problems, scattering problems, and, in particular, eigenfunction expansion for time-domain problems in non-separable physical domains with mixed boundary conditions.

A Multiwavelength Study of the Intracluster Medium and the Characterization of the Multiwavelength Sub/millimeter Inductance Camera

The first part of this thesis combines Bolocam observations of the thermal Sunyaev-Zel’dovich (SZ) effect at 140 GHz with X-ray observations from Chandra, strong lensing data from the Hubble Space Telescope (HST), and weak lensing data from HST and Subaru to constrain parametric models for the distribution of dark and baryonic matter in a sample of six massive, dynamically relaxed galaxy clusters. For five of the six clusters, the full multiwavelength dataset is well described by a relatively simple model that assumes spherical symmetry, hydrostatic equilibrium, and entirely thermal pressure support. The multiwavelength analysis yields considerably better constraints on the total mass and concentration compared to analysis of any one dataset individually. The subsample of five galaxy clusters is used to place an upper limit on the fraction of pressure support in the intracluster medium (ICM) due to nonthermal processes, such as turbulent and bulk flow of the gas. We constrain the nonthermal pressure fraction at r500c to be less than 0.11 at 95% confidence, where r500c refers to radius at which the average enclosed density is 500 times the critical density of the Universe. This is in tension with state-of-the-art hydrodynamical simulations, which predict a nonthermal pressure fraction of approximately 0.25 at r500c for the clusters in this sample.

The second part of this thesis focuses on the characterization of the Multiwavelength Sub/millimeter Inductance Camera (MUSIC), a photometric imaging camera that was commissioned at the Caltech Submillimeter Observatory (CSO) in 2012. MUSIC is designed to have a 14 arcminute, diffraction-limited field of view populated with 576 spatial pixels that are simultaneously sensitive to four bands at 150, 220, 290, and 350 GHz. It is well-suited for studies of dusty star forming galaxies, galaxy clusters via the SZ Effect, and galactic star formation. MUSIC employs a number of novel detector technologies: broadband phased-arrays of slot dipole antennas for beam formation, on-chip lumped element filters for band definition, and Microwave Kinetic Inductance Detectors (MKIDs) for transduction of incoming light to electric signal. MKIDs are superconducting micro-resonators coupled to a feedline. Incoming light breaks apart Cooper pairs in the superconductor, causing a change in the quality factor and frequency of the resonator. This is read out as amplitude and phase modulation of a microwave probe signal centered on the resonant frequency. By tuning each resonator to a slightly different frequency and sending out a superposition of probe signals, hundreds of detectors can be read out on a single feedline. This natural capability for large scale, frequency domain multiplexing combined with relatively simple fabrication makes MKIDs a promising low temperature detector for future kilopixel sub/millimeter instruments. There is also considerable interest in using MKIDs for optical through near-infrared spectrophotometry due to their fast microsecond response time and modest energy resolution. In order to optimize the MKID design to obtain suitable performance for any particular application, it is critical to have a well-understood physical model for the detectors and the sources of noise to which they are susceptible. MUSIC has collected many hours of on-sky data with over 1000 MKIDs. This work studies the performance of the detectors in the context of one such physical model. Chapter 2 describes the theoretical model for the responsivity and noise of MKIDs. Chapter 3 outlines the set of measurements used to calibrate this model for the MUSIC detectors. Chapter 4 presents the resulting estimates of the spectral response, optical efficiency, and on-sky loading. The measured detector response to Uranus is compared to the calibrated model prediction in order to determine how well the model describes the propagation of signal through the full instrument. Chapter 5 examines the noise present in the detector timestreams during recent science observations. Noise due to fluctuations in atmospheric emission dominate at long timescales (less than 0.5 Hz). Fluctuations in the amplitude and phase of the microwave probe signal due to the readout electronics contribute significant 1/f and drift-type noise at shorter timescales. The atmospheric noise is removed by creating a template for the fluctuations in atmospheric emission from weighted averages of the detector timestreams. The electronics noise is removed by using probe signals centered off-resonance to construct templates for the amplitude and phase fluctuations. The algorithms that perform the atmospheric and electronic noise removal are described. After removal, we find good agreement between the observed residual noise and our expectation for intrinsic detector noise over a significant fraction of the signal bandwidth.

Energy inequalities and error estimates for axisymmetric torsion of thin elastic shells of revolution

The problem motivating this investigation is that of pure axisymmetric torsion of an elastic shell of revolution. The analysis is carried out within the framework of the three-dimensional linear theory of elastic equilibrium for homogeneous, isotropic solids. The objective is the rigorous estimation of errors involved in the use of approximations based on thin shell theory.

The underlying boundary value problem is one of Neumann type for a second order elliptic operator. A systematic procedure for constructing pointwise estimates for the solution and its first derivatives is given for a general class of second-order elliptic boundary-value problems which includes the torsion problem as a special case.

The method used here rests on the construction of “energy inequalities” and on the subsequent deduction of pointwise estimates from the energy inequalities. This method removes certain drawbacks characteristic of pointwise estimates derived in some investigations of related areas.

Special interest is directed towards thin shells of constant thickness. The method enables us to estimate the error involved in a stress analysis in which the exact solution is replaced by an approximate one, and thus provides us with a means of assessing the quality of approximate solutions for axisymmetric torsion of thin shells.

Finally, the results of the present study are applied to the stress analysis of a circular cylindrical shell, and the quality of stress estimates derived here and those from a previous related publication are discussed.

Large plane deformations of thin elastic sheets of neo-hookean material

Large plane deformations of thin elastic sheets of neo-Hookean material are considered and a method of successive substitutions is developed to solve problems within the two-dimensional theory of finite plane stress. The first approximation is determined by linear boundary value problems on two harmonic functions, and it is approached asymptotically at very large extensions in the plane of the sheet. The second and higher approximations are obtained by solving Poisson equations. The method requires modification when the membrane has a traction-free edge.

Several problems are treated involving infinite sheets under uniform biaxial stretching at infinity. First approximations are obtained when a circular or elliptic inclusion is present and when the sheet has a circular or elliptic hole, including the limiting cases of a line inclusion and a straight crack or slit. Good agreement with exact solutions is found for circularly symmetric deformations. Other examples discuss the stretching of a short wide strip, the deformation near a boundary corner which is traction-free, and the application of a concentrated load to a boundary point.

Fast Lattice Green's Function Methods for Viscous Incompressible Flows on Unbounded Domains

In this thesis, a collection of novel numerical techniques culminating in a fast, parallel method for the direct numerical simulation of incompressible viscous flows around surfaces immersed in unbounded fluid domains is presented. At the core of all these techniques is the use of the fundamental solutions, or lattice Green’s functions, of discrete operators to solve inhomogeneous elliptic difference equations arising in the discretization of the three-dimensional incompressible Navier-Stokes equations on unbounded regular grids. In addition to automatically enforcing the natural free-space boundary conditions, these new lattice Green’s function techniques facilitate the implementation of robust staggered-Cartesian-grid flow solvers with efficient nodal distributions and fast multipole methods. The provable conservation and stability properties of the appropriately combined discretization and solution techniques ensure robust numerical solutions. Numerical experiments on thin vortex rings, low-aspect-ratio flat plates, and spheres are used verify the accuracy, physical fidelity, and computational efficiency of the present formulations.

A singular perturbation method of calculating the behavior of supercavitating hydrofoils with rounded noses

A simple, direct and accurate method to predict the pressure distribution on supercavitating hydrofoils with rounded noses is presented. The thickness of body and cavity is assumed to be small. The method adopted in the present work is that of singular perturbation theory. Far from the leading edge linearized free streamline theory is applied. Near the leading edge, however, where singularities of the linearized theory occur, a non-linear local solution is employed. The two unknown parameters which characterize this local solution are determined by a matching procedure. A uniformly valid solution is then constructed with the aid of the singular perturbation approach.

The present work is divided into two parts. In Part I isolated supercavitating hydrofoils of arbitrary profile shape with parabolic noses are investigated by the present method and its results are compared with the new computational results made with Wu and Wang's exact "functional iterative" method. The agreement is very good. In Part II this method is applied to a linear cascade of such hydrofoils with elliptic noses. A number of cases are worked out over a range of cascade parameters from which a good idea of the behavior of this type of important flow configuration is obtained.

Some of the computational aspects of Wu and Wang's functional iterative method heretofore not successfully applied to this type of problem are described in an appendix.

New doubly periodic waves of the (2+1)-dimensional double sine-Gordon equation

New exact solutions of the (2 + 1)-dimensional double sine-Gordon equation are studied by introducing the modified mapping relations between the cubic nonlinear Klein-Gordon system and double sine-Gordon equation. Two arbitrary functions are included into the Jacobi elliptic function solutions. New doubly periodic wave solutions are obtained and displayed graphically by proper selections of the arbitrary functions.

Estrelas dantescas nas galáxias de Haroldo de Campos

Uma constante no trabalho plural de Haroldo de Campos é o apreço pela intertextualidade. Em um percurso que toca as mais distantes e distintas galáxias, destacamos uma constelação: quatro textos literários (Finismundo: a última viagem, Signância quase céu, Galáxias e A máquina do mundo repensada) que entram em diálogo com a Commedia, de Dante Alighieri, e uma tradução de Haroldo de seis cantos do paraíso. Desdobrando o interesse de Haroldo de Campos pelo concreto da obra, partimos de algumas soluções formais dos textos em questão para pensar a experiência estética e a diferença entre as visões de mundo das obras comparadas.O estudo da Commedia permite perceber configurações formais que aproximam o leitor da experiência mística da personagem ao apresentá-la como experiência estética. O interesse de Haroldo de Campos está no potencial estético da obra de Dante. Confrontando o texto do poeta italiano com a tradução e com os quatro poemas citados acima, mostramos as semelhanças e diferenças dos processos de tradução e mimesis nas diversas metamorfoses pelas quais a Commedia passa nas criações de Haroldo de Campos

外差干涉仪混频误差分析

共光路外差干涉仪具有很高的分辨率．但因为安装、调试误差会产生非线性误差．影响系统的测量精度。着重分析了在共光路外差干涉仪中由激光光源的椭圆偏振化和沃拉斯顿棱镜的安装方位角误差同时存在的情况下，引起的频率混叠综合误差的大小及变化规律。结果发现其造成的非线性误差可达2．2nm，同时还发现两者造成的误差在某些情况下存在一定程度的相互抵消作用。讨论了提高测量系统精度的有效措施，对正确设计和调试激光外差测试系统、提高测量系统精度具有重要意义。

Simulação do processo de transferência de calor não linear condução-radiação por meio de um esquema linear em diferenças finitas.

Neste trabalho o processo não linear de transmissão de calor condução-radiação é abordado num contexto bidimensional plano e simulado com o uso de um esquema linear em diferenças finitas. O problema original é tratado como o limite de uma sequencia de problemas lineares, do tipo condução-convecção. Este limite, cuja existência é comprovada, é facilmente obtido a partir de procedimentos básicos, accessíveis a qualquer estudante de engenharia, permitindo assim o emprego de hipóteses mais realistas, já que não se tem o limitante matemático para a abordagem numérica de uma equação diferencial parcial elíptica. Neste trabalho foi resolvido o problema de condução de calor em regime permanente em uma placa com condições de contorno convectivas e radioativas utilizando-se o software MatLab, vale ressaltar, que a mesma metodologia é aplicável para geometrias mais complexas.

Bartonella species detection in captive, stranded and free-ranging cetaceans

We present prevalence of Bartonella spp. for multiple cohorts of wild and captive cetaceans. One hundred and six cetaceans including 86 bottlenose dolphins (71 free-ranging, 14 captive in a facility with a dolphin experiencing debility of unknown origin, 1 stranded), 11 striped dolphins, 4 harbor porpoises, 3 Risso's dolphins, 1 dwarf sperm whale and 1 pygmy sperm whale (all stranded) were sampled. Whole blood (n = 95 live animals) and tissues (n = 15 freshly dead animals) were screened by PCR (n = 106 animals), PCR of enrichment cultures (n = 50 animals), and subcultures (n = 50 animals). Bartonella spp. were detected from 17 cetaceans, including 12 by direct extraction PCR of blood or tissues, 6 by PCR of enrichment cultures, and 4 by subculture isolation. Bartonella spp. were more commonly detected from the captive (6/14, 43%) than from free-ranging (2/71, 2.8%) bottlenose dolphins, and were commonly detected from the stranded animals (9/21, 43%; 3/11 striped dolphins, 3/4 harbor porpoises, 2/3 Risso's dolphins, 1/1 pygmy sperm whale, 0/1 dwarf sperm whale, 0/1 bottlenose dolphin). Sequencing identified a Bartonella spp. most similar to B. henselae San Antonio 2 in eight cases (4 bottlenose dolphins, 2 striped dolphins, 2 harbor porpoises), B. henselae Houston 1 in three cases (2 Risso's dolphins, 1 harbor porpoise), and untyped in six cases (4 bottlenose dolphins, 1 striped dolphin, 1 pygmy sperm whale). Although disease causation has not been established, Bartonella species were detected more commonly from cetaceans that were overtly debilitated or were cohabiting in captivity with a debilitated animal than from free-ranging animals. The detection of Bartonella spp. from cetaceans may be of pathophysiological concern.

Abundance of cetaceans in the oceanic northern Gulf of Mexico from 2003 and 2004 ship surveys

The Gulf of Mexico (GMx) is a subtropical marginal sea of the western North Atlantic Ocean with a diverse cetacean community. Ship-based, line-transect abundance surveys were conducted in oceanic waters (>200 m deep) of the northern GMx within U.S. waters (380,432 square km) during summer 2003 and spring 2004. Data from these surveys were pooled and minimum abundance estimates were based on 10,933 km of effort and 433 sightings of at least 17 species.The most commonly sighted species (number of groups) were pantropical spotted dolphin, Stenella attenuata (115); sperm whale, Physeter macrocephalus (85); dwarf/pygmy sperm whale, Kogia sima/breviceps (27); Risso’s dolphin, Grampus griseus (26); and bottlenose dolphin, Tursiops truncatus (26). The most abundant species (number of individuals; coefficient of variation) were S. attenuata (34,067; 0.18); Clymene dolphin, S. clymene (6,575; 0.36); T. truncatus (3,708; 0.42); and striped dolphin, S. coeruleoalba (3,325; 0.48). The only large whales sighted were P. macrocephalus (1,665; 0.20) and Bryde’s whale, Balaenoptera edeni (15; 1.98). Abundances for other species or genera ranged from 57 to 2,283 animals. Cetaceanswere sighted throughout the oceanic northern GMx, and whereas many species were widely distributed, some had more regional distributions. Compared to abundance estimates for this area based on 1996-2001 surveys, the estimate for S. attenuata was significantly smaller (P <0.05) and that for the spinner dolphin, S. longirostris, appeared much smaller. Also, P. macrocephalus estimates were based on less negatively biased estimates of group-size using 90-minute counts during 2003 and 2004.

The Hudson-Raritan Estuary as a crossroads for distribution of blue (Callinectes sapidus), lady (Ovalipes ocellatus), and Atlantic rock (Cancer irroratus) crabs

Blue (Callinectes sapidus)(Portunidae),lady (Ovalipes ocellatus)(Portunidae), and Atlantic rock (Cancer irroratus) (Cancridae) crabs inhabit estuaries on the northeast United States coast for parts or all of their life cycles. Their distributions overlap or cross during certain seasons. During a 1991–1994 monthly otter trawl survey in the Hudson-Raritan Estuary between New York and New Jersey, blue and lady crabs were collected in warmer months and Atlantic rock crabs in colder months. Sex ratios, male:female, of mature crabs were 1:2.0 for blue crabs, 1:3.1 for lady crabs, and 21.4:1 for Atlantic rock crabs. Crabs, 1286 in total, were subsampled for dietary analysis, and the dominant prey taxa for all crabs, by volume of foregut contents, were mollusks and crustaceans. The proportion of amphipods and shrimp in diets decreased as crab size increased. Trophic niche breadth was widest for blue crabs, narrower for lady crabs, and narrowest for Atlantic rock crabs. Trophic overlap was lowest between lady crabs and Atlantic rock crabs, mainly because of frequent consumption of the dwarf surfclam (Mulinia lateralis) by the former and the blue mussel (Mytilus edulis) by the latter. The result of cluster analysis showed that size class and location of capture of predators in the estuary were more influential on diet than the species or sex of the predators.

小麦春化相关基因元件克隆分析与小麦矮化突变体的研究

一、 春化相关基因全长cDNA序列及其启动子的克隆与分析研究 通过建立小麦（Triticum aestivum. L. cv Jingdong No.1）胚芽春化cDNA文库，以春化相关基因VER2的3’端序列为探针，筛选获得全长1195 bp cDNA序列，它编码300个氨基酸。在VER2中存在植物疾病抗性反应蛋白和茉莉酸诱导凝集素两种蛋白的结构域。另外在VER2蛋白中存在核定位信号和多种磷酸酶的作用位点，VER2可能参与了多种调控途径。 以VER2基因的cDNA为探针，利用改进的池式PCR以及高密度膜杂交筛选的方法，从小麦TAC基因组文库中获得41,788 bp的基因组克隆，该序列含有11个基因，其中VER2基因位于第三个基因。VER2基因组序列含有3个内含子，4个外显子与cDNA序列100%同源。通过对转录起始点和转录终止点的分析，进一步证明从cDNA文库筛选得到的VER2基因为全长序列。 对VER2基因的上游启动子区域进行分析，发现基因上游启动子区存在三个小的重复序列，每个片段有482 bp，另有两个较大的重复序列，每个片段有2,161 bp。对上游2.8 kb启动子区（不含重复序列）的响应元件分析，其包括ABA响应元件（ABRE）、茉莉酸甲酯响应元件（Me-JARE）、胚乳特异性表达元件、参与淀粉酶合成的元件以及存在类似GA响应元件（ATAACAAAC）如ATAACATAC等等。根据VER2基因上游6 kb序列结构特点，将VER2启动子区域进行缺失突变形成10个片段，分别以GUS和GFP为报告基因构建成瞬间表达载体和植物表达载体等四类质粒。通过基因枪方法将最大片段（6 kb）驱动GFP报告基因的瞬间表达载体转入经春化处理或未春化处理的小麦幼叶中，结果发现GFP在春化处理的幼叶中表达，而在未春化处理的幼叶中不表达，说明VER2基因的启动子驱动基因转录受春化处理调控。 二、 小麦矮化突变体的研究 通过对小麦矮化突变体gaid遗传生理分析发现该突变体为半显性阻断GA信号途径，由此发现在赤霉素信号途径中，α-淀粉酶的诱导一定程度上通过某些与株高相关的基因控制。突变体gaid呈现对高浓度的脱落酸更敏感，当ABA浓度达到10-6M时，突变体的生长几乎完全受到了抑制，而野生型的生长需要ABA浓度达到10-5M时才能完全受到抑制。通过突变体gaid对乙烯等抑制型生长调节剂的响应实验研究，首次提出GA调控植物伸长生长存在两条信号途径，即GA基础水平信号途径（GA basal level signaling pathway）和GA正常水平信号途径（GA normal level signaling pathway），而乙烯以及高浓的GA合成抑制剂（如PAC）是通过第一条途径（GA基础水平信号途径）起作用。光形态建成中对植株生长的抑制作用存在独立于GA的信号途径。 突变体gaid的根系在强光照（63.5 Es-1m-2）和培养基内（低氧）的生长条件下，表现出弯曲、变短、加粗等异常性状，而随光照强度的减弱，这种根系异常生长的表型也减弱，在暗培养中则完全消失，但无论在哪种环境条件下，相对野生型对照而言，突变体的种子根短、侧根少。低浓度的ABA（10-8M）可以恢复突变体gaid根系在强光低氧条件下的正常生长发育。然而利用IAA及其极性运输的抑制剂（TIBA）、乙烯生物合成前提物（ACC）及合成抑制剂（AOA）处理突变体gaid，并没有发现突变体根系的生长发育得到恢复。 突变体gaid可能是一个新的属于小麦GA信号途径中的负调控基因（GAID）发生了突变或超表达，导致其负调控作用增强，呈现半显性的矮化突变。在与另一已知小麦GA信号途径中的负调控基因RHT的关系研究上发现，GAID可能对RHT蛋白磷酸化后的降解途径起抑制作用。通过双向电泳发现突变体gaid与野生型对照（京冬1号）在生长过程中存在差异蛋白，这将有助于对GA信号途径分子机理的深入研究。

A comparison of different failure assessment methodologies applied to the NESC-1 test

Predictions for a 75x205mm surface semi-elliptic defect in the NESC-1 spinning cylinder test have been made using BS PD 6493:1991, the R6 procedure, non-linear cracked body finite element analysis techniques and the local approach to fracture. All the techniques agree in predicting ductile tearing near the inner surface of the cylinder followed by cleavage initiation. However they differ in the amount of ductile tearing, and the exact location and time of any cleavage event. The amount of ductile tearing decreases with increasing sophistication in the analysis, due to the drop in peak crack driving force and more explicit consideration of constraint effects. The local approach predicts a high probability of cleavage in both HAZ and base material after 190s, while the other predictions suggest that cleavage is unlikely in the HAZ due to constraint loss, but likely in the underlying base material. The timing of this event varies from ∼150s for R6 predictions to ∼250-300s using non-linear cracked body analysis.