Resampling to accelerate cross-correlation searches for continuous gravitational waves from binary systems

Continuous-wave (CW) gravitational waves (GWs) call for computationally-intensive methods. Low signal-to-noise ratio signals need templated searches with long coherent integration times and thus fine parameter-space resolution. Longer integration increases sensitivity. Low-mass x-ray binaries (LMXBs) such as Scorpius X-1 (Sco X-1) may emit accretion-driven CWs at strains reachable by current ground-based observatories. Binary orbital parameters induce phase modulation. This paper describes how resampling corrects binary and detector motion, yielding source-frame time series used for cross-correlation. Compared to the previous, detector-frame, templated cross-correlation method, used for Sco X-1 on data from the first Advanced LIGO observing run (O1), resampling is about 20x faster in the costliest, most-sensitive frequency bands. Speed-up factors depend on integration time and search setup. The speed could be reinvested into longer integration with a forecast sensitivity gain, 20 to 125 Hz median, of approximately 51%, or from 20 to 250 Hz, 11%, given the same per-band cost and setup. This paper's timing model enables future setup optimization. Resampling scales well with longer integration, and at 10x unoptimized cost could reach respectively 2.83x and 2.75x median sensitivities, limited by spin-wandering. Then an O1 search could yield a marginalized-polarization upper limit reaching torque-balance at 100 Hz. Frequencies from 40 to 140 Hz might be probed in equal observing time with 2x improved detectors.Comment: 28 pages, 7 figures, 3 table

Novel Discretization Schemes for the Numerical Simulation of Membrane Dynamics

Motivated by the demands of simulating flapping wings of Micro Air Vehicles, novel numerical methods were developed and evaluated for the dynamic simulation of membranes. For linear membranes, a mixed-form time-continuous Galerkin method was employed using trilinear space-time elements, and the entire space-time domain was discretized and solved simultaneously. For geometrically nonlinear membranes, the model incorporated two new schemes that were independently developed and evaluated. Time marching was performed using quintic Hermite polynomials uniquely determined by end-point jerk constraints. The single-step, implicit scheme was significantly more accurate than the most common Newmark schemes. For a simple harmonic oscillator, the scheme was found to be symplectic, frequency-preserving, and conditionally stable. Time step size was limited by accuracy requirements rather than stability. The spatial discretization scheme employed a staggered grid, grouping of nonlinear terms, and polygon shape functions in a strong-form point collocation formulation. Validation against existing experimental data showed the method to be accurate until hyperelastic effects dominate

Applied Signal Processing

Being an inter-disciplinary subject, Signal Processing has application in almost all scientific fields. Applied Signal Processing tries to link between the analog and digital signal processing domains. Since the digital signal processing techniques have evolved from its analog counterpart, this book begins by explaining the fundamental concepts in analog signal processing and then progresses towards the digital signal processing. This will help the reader to gain a general overview of the whole subject and establish links between the various fundamental concepts. While the focus of this book is on the fundamentals of signal processing, the understanding of these topics greatly enhances the confident use as well as further development of the design and analysis of digital systems for various engineering and medical applications. Applied Signal Processing also prepares readers to further their knowledge in advanced topics within the field of signal processing

Local Radial Basis Function Methods for Solving Partial Differential Equations

Meshless methods are relatively new numerical methods which have gained popularity in computational and engineering sciences during the last two decades. This dissertation develops two new localized meshless methods for solving a variety partial differential equations. Recently, some localized meshless methods have been introduced in order to handle large-scale problems, or to avoid ill-conditioned problems involving global radial basis function approximations. This dissertation explains two new localized meshelss methods, each derived from the global Method of Approximate Particular Solutions (MAPS). One method, the Localized Method of Approximate Particular Solutions (LMAPS), is used for elliptic and parabolic partial differential equations (PDEs) using a global sparse linear system of equations. The second method, the Explicit Localized Method of Approximate Particular Solutions (ELMAPS), is constructed for solving parabolic types of partial differential equations by inverting a finite number of small linear systems. For both methods, the only information that is needed in constructing the approximating solution to PDEs, consists of the local nodes that fall within the domain of influence of the data. Since the methods are completely mesh free, they can be used for irregularly shaped domains. Both methods are tested and compared with existing global and local meshless methods. The results illustrate the accuracy and efficiency of our proposed methods

NBS monograph

From Introduction Statement of Objectives: "The purpose of this publication is to provide assistance to the practicing engineer who is faced with the problem of making dynamic measurements of rapidly changing pressures.

Q(sqrt(-3))-Integral Points on a Mordell Curve

We use an extension of quadratic Chabauty to number fields,recently developed by the author with Balakrishnan, Besser and M ̈uller,combined with a sieving technique, to determine the integral points overQ(√−3) on the Mordell curve y2 = x3 − 4

Adomian decomposition method, nonlinear equations and spectral solutions of burgers equation

Tese de doutoramento. Ciências da Engenharia. 2006. Faculdade de Engenharia. Universidade do Porto, Instituto Superior Técnico. Universidade Técnica de Lisbo

Numerical Modelling of Extreme Waves: The Role of Nonlinear Wave-Wave Interactions

The real monsters of the ocean, extreme waves, haunted mariners since the early days of human activities in the sea. Despite having caused numerous accidents and casualties, their systematic study began only in 2000s. Many mechanisms have been proposed to simulate these rare but catastrophic events, with the most prominent being wave focusing. This is connected to the NewWave theory, which has been used extensively in experimental and numerical modelling. However, the majority of the studies fail to capture the distinguishing characteristics of extreme waves, due to the inherent high nonlinearity of the problem and shortcomings of the modelling practice, but also due to inadequate knowledge of the underlying physics. Overcoming these issues is unquestionably necessary for understanding extreme waves and including them in the engineering design practice. The nonlinearity of the problem lies upon the nonlinear wave-wave interactions, which violate the fundamental linear assumptions of NewWave and pose challenges to numerical models. The present work aims at contributing in both understanding the nature of nonlinear wave-wave interactions during the formation of extreme wave events, and examining the applicability and performance of numerical solvers via their systematic validation with state-of-the-art techniques that give new insights into the problem. A range of phase-resolving and phase-averaged models are employed to cover different scales and examine the undergoing physical processes. Through the study of limiting breaking unidirectional dispersive wave groups in finite water depth, it is demonstrated that the free-wave spectrum undergoes considerable transformation and a large portion of energy is transferred to higher and lower harmonics. These effects can be attributed to the action of near-resonant and bound nonlinearities, which have however robust mathematical description. As such, a large part of the thesis is devoted to analytical methods towards establishing an efficient integrated framework for estimating extreme wave profiles, going beyond the classic NewWave. Overall, the present work is a balance of physics and numerics to tackle parts of the challenging problem of extreme waves and improve safety at sea

Dynamic brain networks explored by structure-revealing methods

The human brain is a complex system able to continuously adapt. How and where brain activity is modulated by behavior can be studied with functional magnetic resonance imaging (fMRI), a non-invasive neuroimaging technique with excellent spatial resolution and whole-brain coverage. FMRI scans of healthy adults completing a variety of behavioral tasks have greatly contributed to our understanding of the functional role of individual brain regions. However, by statistically analyzing each region independently, these studies ignore that brain regions act in concert rather than in unison. Thus, many studies since have instead examined how brain regions interact. Surprisingly, structured interactions between distinct brain regions not only occur during behavioral tasks but also while a subject rests quietly in the MRI scanner. Multiple groups of regions interact very strongly with each other and not only do these groups bear a striking resemblance to the sets of regions co-activated in tasks, but many of these interactions are also progressively disrupted in neurological diseases. This suggests that spontaneous fluctuations in activity can provide novel insights into fundamental organizing principles of the human brain in health and disease. Many techniques to date have segregated regions into spatially distinct networks, which ignores that any brain region can take part in multiple networks across time. A more natural view is to estimate dynamic brain networks that allow flexible functional interactions (or connectivity) over time. The estimation and analysis of such dynamic functional interactions is the subject of this dissertation. We take the perspective that dynamic brain networks evolve in a low-dimensional space and can be described by a small number of characteristic spatiotemporal patterns. Our proposed approaches are based on well-established statistical methods, such as principal component analysis (PCA), sparse matrix decompositions, temporal clustering, as well as a multiscale analysis by novel graph wavelet designs. We adapt and extend these methods to the analysis of dynamic brain networks. We show that PCA and its higher-order equivalent can identify co-varying functional interactions, which reveal disturbed dynamic properties in multiple sclerosis and which are related to the timing of stimuli for task studies, respectively. Further we show that sparse matrix decompositions provide a valid alternative approach to PCA and improve interpretability of the identified patterns. Finally, assuming an even simpler low-dimensional space and the exclusive temporal expression of individual patterns, we show that specific transient interactions of the medial prefrontal cortex are disturbed in aging and relate to impaired memory