abstract: Monte Carlo simulations are traditionally carried out for the determination of the amplification of forced vibration response of turbomachine/jet engine blades to mistuning. However, this effort can be computationally time consuming even when using the various reduced order modeling techniques. Accordingly, some investigations in the past have focused on obtaining simple approximate estimates for this amplification. In particular, two of these have proposed the use of harmonic patterns of the blade properties around the disk as an approximate alternative to the many random patterns of Monte Carlo analyses. These investigations, while quite encouraging, have relied solely on single degree of freedom per sector models of the rotor. In this light, the overall focus of the present effort is a revisit of harmonic mistuning of rotors focusing first the confirmation of the previously obtained findings with a more detailed model of the blisk in both conditions of an isolated blade-dominated resonance and of a veering between blade and disk dominated modes. The latter condition cannot be simulated by a single degree of freedom per sector model. Further, the analysis will consider the distinct cases of mistuning due to variations of material properties (Young's modulus) and geometric properties (geometric mistuning). In the single degree of freedom model, both mistuning types are equivalent but they are not, as demonstrated here, in more realistic models. The difference arises because changes in geometry induce not only changes in natural frequencies of the blades alone but of their modes and the importance of these two sources of variability is discussed with both Monte Carlo simulation and harmonic mistuning results. The present investigation focuses also on the possible extension of the harmonic mistuning concept and of its quantitative information that can be derived from such analyses. From it, a novel measure of blade-disk coupling is introduced and assessed in comparison with the coupling index introduced in the past. In conclusions, the low cost of harmonic mistuning computations in comparison with full Monte Carlo simulations is demonstrated to be worthwhile to elucidate the basic behavior of the mistuned rotor in a random setting. / Dissertation/Thesis / Masters Thesis Mechanical Engineering 2014

Recent studies suggest that many protoplanetary disks around pre-main sequence stars with inferred ages of 1-5 Myr (known as Class II protostars) may contain insufficient mass to form giant planets. This may be because by this stage much of the material in the disk has already grown into larger bodies, hiding the material from sight. If this is the case, then these older disks may not be an accurate representation of the initial mass budget in disks for forming planets. To test this hypothesis, I have observed a sample of protostars in the Taurus star forming regions identified as Class I in multiple independent surveys, whose young (<1 Myr old) disks are more likely to represent the initial mass budget of protoplanetary disks. For my dissertation I have used detailed radiative transfer modeling of a multi-wavelength dataset to determine the geometry of the circumstellar material and measure the mass of the disks around these protostars. I discuss how the inferred disk mass distribution for this sample compares with results for the existing 1-5 Myr old disk samples, and what these results imply for giant planet formation. Next, I discuss the cases of three separate, individual Class I protostars discovered through my ongoing survey of Class I protostars whose disks are all of particular interest, each for its own reasons. Each of these disks may provide clues that even at the young ages of Class I protostars, planet formation may already be well underway in their disks. Finally, large disk mass surveys of large star forming regions like the Orion Nebula Cluster may be contaminated by free-free emission from disks that are being photoevaporated by nearby massive stars. I discuss my work with the VLA to constrain the free-free emission spectra for these sources so that current and future millimeter surveys can accurately measure disk masses in the ONC.

Recent high angular resolution observations of protoplanetary disks at different wavelengths have revealed several kinds of structures, including multiple bright and dark rings. Embedded planets are the most used explanation for such structures, but there are alternative models capable of shaping the dust in rings as it has been observed. We assume a disk around a Herbig star and investigate the effect that ice lines have on the dust evolution, following the growth, fragmentation, and dynamics of multiple dust size particles, covering from 1 mu m to 2 m sized objects. We use simplified prescriptions of the fragmentation velocity threshold, which is assumed to change radially at the location of one, two, or three ice lines. We assume changes at the radial location of main volatiles, specifically H2O, CO2, and NH3. Radiative transfer calculations are done using the resulting dust density distributions in order to compare with current multiwavelength observations. We find that the structures in the dust density profiles and radial intensities at different wavelengths strongly depend on the disk viscosity. A clear gap of emission can be formed between ice lines and be surrounded by ring-like structures, in particular between the H2O and CO2 (or CO). The gaps are expected to be shallower and narrower at millimeter emission than at near-infrared, opposite to model predictions of particle trapping. In our models, the total gas surface density is not expected to show strong variations, in contrast to other gap-forming scenarios such as embedded giant planets or radial variations of the disk viscosity.

Les systèmes planétaires sont nés du gaz et de la poussière des disques circumstellaires autour des étoiles jeunes. Pour comprendre comment les systèmes planétaires se forment, une connaissance détaillée de la structure et de l'évolution de ces disques est requise. Bien que, cela soit presque bien compris pour les régions des disques observés à des échelles spatiales de plusieurs unités astronomiques, la structure de ces disques explorés à l'échelle de quelques unités astronomiques et surtout à moins d'une unité astronomique reste une énigme. Au cours de ces dernières années, il est devenu possible de directement résoudre spatialement la région interne des disques protoplanétaires avec les techniques d'interférométrie optiques. L'objectif de cette thèse est une étude multi-longueur d'onde de l'évolution des disques protoplanétaires en déterminant leur distribution de densité et de température, leur taille, la composition de la poussière et aussi la cinématique du gaz. J’ai construit ma thèse en étudiant trois domaines de longueurs d'onde complémentaires: étude de la photosphère de l'étoile et de son disque gazeux à proximité par le biais de l'interférométrie visible, étude de la structure radiale et verticale du bord interne d'un disque de pré-transition à des fractions d'unité astronomique en interférométrie proche infra-rouge, et la caractérisation des régions des disques situées à quelques unités astronomiques de l'étoile centrale, au travers de la spectroscopie et de l'interférométrie infra-rouge moyen / Planetary systems are born in circumstellar gas and dust disks surrounding Young Stellar Objects (YSOs). To understand how planetary systems form, a detailed knowledge of the structure and evolution of these disks is required. Although, this is almost well understood for the regions of the disks observed with a spatial resolution of several AUs, the structure of these disks probed at a few AU scale and especially inward of 1 AU remains a puzzle. In recent years, it has become possible to directly spatially resolve the inner region of protoplanetary disks with optical interferometry technique. The context of this thesis is a multi-wavelength investigation of the protoplanetary disks evolution by determining their density distribution, their temperature distribution, the size and com- position of the dust components and finally the kinematics of the gas. I have developed my thesis following three complementary wavelength domains: study of the photosphere of the star and its nearby gaseous disk through visible interferometry, study of the radial and vertical structure of the inner rim of a pre-transitional disk at fractions of an AU through near-IR interferometry, and, the characterization of the disk regions at a few AUs from the central star through spectroscopic and mid-IR interferometry. To analyse the visible-, near- and mid-IR interferometric observations, I have focused my attention on three well known sources, 51 OPh, HD 100546 and MWC 480 respectively that they have not been observed in these wavelengths.

No description available.

<p> Planetary migration has become one of the most important processes in planet formation since the first discovery of an exoplanet around 51Peg. A decade after the discovery, the total number of exoplanets has increased to about three hundred. Theoretical work has shown that the disk configuration in which planets are formed strongly affects the subsequent migration of planets within them. Disks evolve and their shape transits from flared to fiat. This is thought to arise because of dust settling. We take this effect into account in our models of planet migration in protoplanetary disks that are heated by the radiation of their central stars. In particular we solve the radiative transfer equation for disks by means of the Monte Carlo method, and then consider planetary migration. We focus on planets around very low mass stars (VLMSs). </p> <p> Our calculations reproduce the disk configurations of Chiang & Goldreich (1997). As dust settles, the superheated and inner layer declines toward the mid-plane. At the same time, dust settling causes the temperature of the upper layer to increase and that of the inner layer to decrease. In order to calculate the migration time accurately, we include the gravity of planets, which causes the density around them to be compressed. This results in shadowing (in front of the planet) and illumination (behind the planet) regions. We included disk evolution by taking into account the effect of dust settling. We found that dust settling itself (without planetary gravity) can reduce the migration time by a factor of 8. When we included the gravity of planets, the effect of dust settling is somewhat washed out. This is because the effect of dust settling on migration acts in a similar way to that of planetary gravity. Thus, when the migration time without dust settling is compared to the case of dust settling (including planetary gravity), dust settling can reduce the migration time by a factor of 2. </p> <p> We also found that the migration time of massive planets(> 5MEB) in such low mass disks, for both cases, is comparable to the disk life time ( rv 107 years). This suggests that planets around VLMS do not plunge into the star within a disk lifetime. This finding is consistent with the discovery of the super-Earth (rv 5.5MEB) at 2.6 AU around M dwarf (Beaulieu et al., 2006). For lower mass planets, the migration time is about two orders of magnitude longer than the disk life time. Thus, the long planetary migration around VLMS does not cause any serious time mismatch problem as in the case of classical T Tauri star system. </p> / Thesis / Master of Science (MSc)

<p> Through HI observations, galactic gas discs can be observed to extend past the edge of the star forming disk. Observations of HI in these extended galactic disks consistently show significant velocity dispersion, which suggests a non-thermal origin. This suggests that turbulence in the gas is contributing significantly to the observed velocity dispersion. To address this, a new parallel adaptive mesh three dimensional shearing-box implementation with adaptions for evening numerical diffusion effects, self-gravity in the shearing boundary conditions and appropriate vertical boundary conditions has been built, based on the FLASH code. This code is used to perform local simulations, incorporating differential rotation, self-gravity, stratification, hydrodynamics and cooling. These simulations explore possible mechanisms for driving turbulent motions through thermal and self-gravitational instabilities coupling to differential rotation. In isothermal simulations a marginally stable disk is found to be stable against forming a gravitoturbulent quasi-steady state. In simulations including cooling, where the disk conditions do not trigger the formation of a two-phase medium, it is found that perturbations to the flow damp without leading to a sustained mechanism for driving turbulence. In cases where a two-phase medium develops, gravitational angular momentum transporting stresses are much greater, creating a possible mechanism for transferring energy from galactic rotation to turbulence, though a gravitoturbulent quasi-steady state is not found. The differing angular momentum transport properties of the single phase and two phase regimes of the disk suggests a significant dynamical division can be drawn between the two, which may occur far outside the star formation cutoff in a galactic disk. </p> / Thesis / Master of Science (MSc)

The application of laser Doppler vibrometry to high speed rotating structures has been hampered by technical limitations. Whereas full-field three-dimensional velocity measurements can be made on stationary structures, the capability on rotating structures is limited to low speed, one-dimensional, steady state operation. This work describes the implementation of a self-tracking laser vibrometry system which overcomes many of the limitations of current techniques for vibration measurements on rotating structures. A model of the self-tracker is developed and used to predict the effects of static misalignments on the position and velocity errors. These predictions are supported by experimental results and simplified models of the self-tracker. NOTE: (02/2011) An updated copy of this ETD was added after there were patron reports of problems with the file. / Ph. D.

The Brjuno numbers play a fundamental role in the study of the 1-dimensional Complex Dynamics Theory. In this work we examine the proof of the Brjuno theorem by using elements of Number Theory. We also examine the topological version of the proof given by J. Yoccoz and his renormalization principle. If α ∈ ℝ\ℚ, we also describe how the existence of a Siegel disk at the origin for the polynomial P(𝑧) = exp(2πiα)·(𝑧 − 𝑧²) implies the linearization of any germ of the form 𝑓(𝑧) = exp(2πiα)·𝑧 + 𝑂(𝑧²). / Master of Science

The research presented in this thesis investigates several aspects of the evolutionary processes of T Tauri stars and their accompanying circumstellar disks. The versatile Monte Carlo radiation transfer technique, with several modifications and extensions, is used throughout to study the structure and constitution of both the circumstellar disk at large and the changeable and dynamic inner disk regions. The photopolarimetric variability of AA Tau in the Taurus star forming region is modelled in a fully 3D manner. I find that a magnetospherically induced warp in the accretion disk at roughly the stellar co-rotation radius occults the star and reproduces both the observed period and duration and the required brightness and polarisation variations. The model SEDs allow estimates of the disk mass, radial extent and large- scale density structure. Using a modified SPH code we find the interaction of a 5.2kG stellar magnetic field inclined at 30° to the rotation axis with the disk, is capable of generating a warp of the size and shape needed to reproduce the observed variations. Modified Monte Carlo models capable of incorporating any number of dust particle grain sizes distributed throughout the disk in vertical and radial distributions, in a fully 3D manner are presented. This versatile tool allows the investigation of evolutionary processes such as dust settling and grain growth predicted to occur in T Tauri sources as they age. A Mie Scattering code was also adapted and incorporated into the models allowing us to determine optical properties for dust grains and distributions of any size. I present model SEDs fitting the latest publicly available IR data for a number of T Tauri sources and reproduce the observational effects of dust grain growth and settling with a high degree of success. The fits are by no means unique and the structural parameters required to produce them are quite uncertain but it is possible to determine useful information on the larger scale structure and bulk constituents of these disks. A fully 3D non-LTE radiative transfer code using CO line emissions as a tracer of the disk dynamics and able to simulate any disk structure or geometry, either analytical or imported from a hydrodynamic simulation, is presented. Signatures attributed to the disk dynamics and spiral density structure derived from hydrodynamic simulations of massive disks are investigated and resolved. Line profiles and contour maps of the velocity of the emitting material are generated and compared with observations.