Testing Isotropy of Cosmic Microwave Background Radiation

We introduce new symmetry-based methods to test for isotropy in cosmic microwave background radiation. Each angular multipole is factored into unique products of power eigenvectors, related multipoles and singular values that provide 2 new rotationally invariant measures mode by mode. The power entropy and directional entropy are new tests of randomness that are independent of the usual CMB power. Simulated galactic plane contamination is readily identified, and the new procedures mesh perfectly with linear transformations employed for windowed-sky analysis. The ILC -WMAP data maps show 7 axes well aligned with one another and the direction Virgo. Parameter free statistics find 12 independent cases of extraordinary axial alignment, low power entropy, or both having 5% probability or lower in an isotropic distribution. Isotropy of the ILC maps is ruled out to confidence levels of better than 99.9%, whether or not coincidences with other puzzles coming from the Virgo axis are included. Our work shows that anisotropy is not confined to the low l region, but extends over a much larger l range.Comment: 40 pages 15 figure

Harmonic-Balance-Based parameter estimation of nonlinear structures in the presence of Multi-Harmonic response and force

Testing nonlinear structures to characterise their internal nonlinear forces is challenging. Often nonlinear structures are excited by harmonic forces and yield a multi-harmonic response. In many systems, particularly ones with strong nonlinearities, the effect of higher harmonics in the force and responses cannot be ignored. Even if the intended excitation is a single frequency sinusoidal force, the interaction of the shaker and the nonlinear structure can lead to harmonics in the applied force. The effects of these higher harmonics of the input force on nonlinear model identification in structural dynamics are often neglected. The objective of this study is to introduce an identification method, motivated by the alternating frequency/time approach using harmonic balance (AFTHB), which is able to consider both multi-harmonic forces and multi-harmonic responses of the system. The proposed AFTHB method can include all significant harmonics by selecting an appropriate time step and sampling frequency to guarantee the accuracy of the results. An analytical harmonic-balance-based (AHB) approach is also considered for comparison. However, the inclusion of all significant harmonics of the response in the analytical expansion of the nonlinear functions is often cumbersome. Furthermore, the AFTHB method can easily cope with complex nonlinearities such as Coulomb friction and with multi-degree of freedom nonlinear systems. Including the effect of higher harmonics in the identification process reduces the approximation error due to truncation and very accurate approximation of the balanced equations of each harmonic is obtained. The proposed identification method requires prior knowledge or an appropriate estimation of the type of system nonlinearities. However, the method of model selection may be used for a set of candidate models, and avoiding a dictionary of arbitrary candidate basis functions significantly reduces the computational costs. This paper highlights the important features of the AFTHB method to ensure accurate estimation using four simulated and two experimental examples. The effects of the number of harmonics considered, the modelling error, measurement noise and the frequency range on the quality of the estimated model are demonstrated

An empirical mean-field model of symmetry-breaking in a turbulent wake

Improved turbulence modeling remains a major open problem in mathematical physics. Turbulence is notoriously challenging, in part due to its multiscale nature and the fact that large-scale coherent structures cannot be disentangled from small-scale fluctuations. This closure problem is emblematic of a greater challenge in complex systems, where coarse-graining and statistical mechanics descriptions break down. This work demonstrates an alternative data-driven modeling approach to learn nonlinear models of the coherent structures, approximating turbulent fluctuations as state-dependent stochastic forcing. We demonstrate this approach on a high-Reynolds number turbulent wake experiment, showing that our model reproduces empirical power spectra and probability distributions. The model is interpretable, providing insights into the physical mechanisms underlying the symmetry-breaking behavior in the wake. This work suggests a path toward low-dimensional models of globally unstable turbulent flows from experimental measurements, with broad implications for other multiscale systems

K2: Background Survey - The search for undiscovered transients in Kepler/K2 data

The K2 mission of the Kepler Space Telescope offers a unique possibility to examine sources of both Galactic and extragalactic origin with high-cadence photometry. Alongside the multitude of supernovae and quasars detected within targeted galaxies, it is likely that Kepler has serendipitously observed many transients throughout K2. Such events will likely have occurred in background pixels, coincidentally surrounding science targets. Analysing the background pixels presents the possibility to conduct a high-cadence survey with areas of a few square degrees per campaign. We demonstrate the capacity to independently recover key K2 transients such as KSN 2015K and SN 2018oh. With this survey, we expect to detect numerous transients and determine the first comprehensive rates for transients with lifetimes of <1 d.This research was supported by an Australian Government Research Training Program (RTP) Scholarship and utilizes data collected by the K2 missio

Robotic processes to accelerate large optic fabrication

The manufacture of metre-scale optics for the next generation of extremely large telescopes (and many other applications) poses a number of unique challenges. For the primary mirror of the European Extremely Large Telescope, each of its 1.45 m segments will need to be completed with nanometre scale accuracy. This demands an unprecedented combination of hybrid fabricating technology to process nearly 1000 segments before the year 2024. One important aspect in improving the current state-of-the-art manufacturing developments is adding an efficient smoothing process that can achieve a faster, and less expensive, manufacturing process-chain. The current process to finish a prototype segment using CNC grinding and CNC polishing takes approximately 1-2 months, and a significant contributing factor in this is the excessive processing times needed to correct the local grinding marks. In this study, therefore, grolishing, an intermediate process between grinding and polishing, is adopted to smooth the part and reduce the overall manufacturing time. This PhD work serves to advance the development of effective robotic grolishing processes (RGP) by the following achievements: (1) to propose the specification and achieve the requirements; (2) to design tools and establish a mechanism for grolishing; (3) to investigate and propose experimental methods to reduce process times while still achieving high performance, reliability and quality surfaces; (4) to establish the RGP and demonstrate that this process can smooth the errors from grinding and provide superior surfaces for polishing to speed up the current process; (5) to develop prototype metrology systems and algorithms to measure grolished surfaces; and, (6) to investigate an innovative proposed method to control mid-spatial frequencies on complex surfaces by using rotating rigid tools. These novel achievements describe the newest fabrication technology, and anticipate the evolution of the process-chain for future high-quality imaging systems for use in astronomy, space-research and laser physics