Self-adaptive isogeometric spatial discretisations of the first and second-order forms of the neutron transport equation with dual-weighted residual error measures and diffusion acceleration

As implemented in a new modern-Fortran code, NURBS-based isogeometric analysis (IGA) spatial discretisations and self-adaptive mesh refinement (AMR) algorithms are developed in the application to the first-order and second-order forms of the neutron transport equation (NTE). These AMR algorithms are shown to be computationally efficient and numerically accurate when compared to standard approaches. IGA methods are very competitive and offer certain unique advantages over standard finite element methods (FEM), not least of all because the numerical analysis is performed over an exact representation of the underlying geometry, which is generally available in some computer-aided design (CAD) software description. Furthermore, mesh refinement can be performed within the analysis program at run-time, without the need to revisit any ancillary mesh generator. Two error measures are described for the IGA-based AMR algorithms, both of which can be employed in conjunction with energy-dependent meshes. The first heuristically minimises any local contributions to the global discretisation error, as per some appropriate user-prescribed norm. The second employs duality arguments to minimise important local contributions to the error as measured in some quantity of interest; this is commonly known as a dual-weighted residual (DWR) error measure and it demands the solution to both the forward (primal) and the adjoint (dual) NTE. Finally, convergent and stable diffusion acceleration and generalised minimal residual (GMRes) algorithms, compatible with the aforementioned AMR algorithms, are introduced to accelerate the convergence of the within-group self-scattering sources for scattering-dominated problems for the first and second-order forms of the NTE. A variety of verification benchmark problems are analysed to demonstrate the computational performance and efficiency of these acceleration techniques.Open Acces

Digital Filters and Signal Processing

Digital filters, together with signal processing, are being employed in the new technologies and information systems, and are implemented in different areas and applications. Digital filters and signal processing are used with no costs and they can be adapted to different cases with great flexibility and reliability. This book presents advanced developments in digital filters and signal process methods covering different cases studies. They present the main essence of the subject, with the principal approaches to the most recent mathematical models that are being employed worldwide

Digital Filters

The new technology advances provide that a great number of system signals can be easily measured with a low cost. The main problem is that usually only a fraction of the signal is useful for different purposes, for example maintenance, DVD-recorders, computers, electric/electronic circuits, econometric, optimization, etc. Digital filters are the most versatile, practical and effective methods for extracting the information necessary from the signal. They can be dynamic, so they can be automatically or manually adjusted to the external and internal conditions. Presented in this book are the most advanced digital filters including different case studies and the most relevant literature

The Design and Construction of a Green Laser and Fabry-Perot Cavity System for Jefferson Lab\u27s Hall A Compton Polarimeter

A high finesse Fabry-Perot cavity with a frequency doubled green laser (CW, 532 nm) have been built and installed in Hall A of Jefferson Lab for high precision Compton polarimetry project in spring of 2010. It provides a high intensity circularly polarized photon target for measuring the polarization of electron beam with energies from 1.0 GeV to 11.0 GeV in a nondestructive manner. The IR beam (CW, 1064 nm) from a Ytterbium doped fiber laser amplifier seeded by a Nd:YAG narrow linewidth NPRO laser is frequency doubled in by a single-pass Periodically Poled Lithium Niobate (PPMgLN) crystal. The maximum achieved green power at 5 W IR pump power was 1.74 W with a total conversion efficiency of 34.8%. The frequency locking of this green light to the cavity resonance frequency is achieved by giving a feedback to Nd:YAG crystal via laser piezoelectric (PZT) actuator by Pound-Drever-Hall (PDH) technique. The data shows the maximum amplification gain of our cavity is about 4,000 with a corresponding maximum intra-cavity power of 3.7 kW. The polarization transfer function has been measured in order to determine the intra-cavity laser polarization within the measurement uncertainty of 0.7%. The PREx experiment at JLab, used this system for the first time and achieved 1.0% precision in electron beam polarization measurement at 1.0 GeV

Measurement, Decoherence and Master Equations

In the first part of this thesis we concern ourselves with the problem of generating pseudo-random circuits. These are a series of quantum gates chosen at random, with the overall effect of implementing unitary operations with statistical properties close to that of unitaries drawn at random with respect to the Haar measure. Such circuits have a growing number of applications in quantum-information processing, but all known algorithms require an external input of classical randomness. We suggest a scheme to implement random circuits in a weighted graph state. The input state is entangled with the weighted graph state and a random circuit is implemented by performing local measurements in one fixed basis only. A central idea in the analysis of this proposal is the average bipartite entanglement generated by the repeated application of such circuits on a large number of randomly chosen input product states. For a truly random circuit, this should agree with that obtained by applying unitaries at random chosen uniformly with respect to the Haar measure, values which can be calculated using Pages Conjecture. Part II is largely concerned with continuous variables (CV) systems. In particular, we are interested in two descriptions. That of the class of Gaussian states, and that of systems which can be adequately described through the use of Markovian master equations. In the case of the latter, there are a number of approaches one may take in order to derive a suitable equation, all of which require some sort of approximation. These approximations can be made based on a mixture of mathematical and physical grounds. However, unfortunately it is not always clear how justified we are in making a particular choice, especially when the test system we wish to describe includes its own internal interactions. In an attempt to clarify this situation, we derive Markovian master equations for single and interacting harmonic systems under different scenarios, including strong internal coupling. By comparing the dynamics resulting from the corresponding master equations with numerical simulations of the global systems evolution, we assess the robustness of the assumptions usually made in the process of deriving the reduced Markovian dynamics. This serves to clarify the general properties of other open quantum system scenarios subject to treatment within a Markovian approximation. Finally, we extend the notions of the smooth min- and smooth max-entropies to the continuous variable setting. Specifically, we have provided expressions to evaluate these measures on arbitrary Gaussian states. These expressions rely only on the symplectic eigenvalues of the corresponding covariance matrix. As an application, we have considered their use as a suitable measure for detecting thermalisation

Acoustically driven control of mobile robots for source localization in complex ocean environments

Ocean based robotic systems are an opportunity to combine the power of acoustic sensing in the water with sophisticated control schemes. Together these bodies of knowledge could create autonomous systems for mapping acoustic fields and localizing underwater sources. However, existing control schemes have often been designed for land and air robots. This creates challenges for applying these algorithms to complex ocean environments. Acoustic fields are strongly frequency dependent, can rarely be realistically modeled analytically, have complex contours where the feature of interest is not always located at the peak pressure, and include many sources of background noise. This work addresses these challenges for control schemes from three categories: feedback and observer control, gradient ascent control and optimal control. In each case the challenges of applying the control scheme to an acoustic field are enumerated and addressed to create a suite of acoustically driven control schemes. For many of these algorithms, the largest issue is the processing and collection of acoustic data, particularly in the face of noise. Two new methods are developed to solve this issue. The first is the use of Principal Component Analysis as a noise filter for acoustic signals, which is shown to address particularly high levels of noise, while providing the frequency dependent sound pressure levels necessary for subsequent processing. The second method addresses the challenge that an analytical expression of the pressure field is often lacking, due to uncertainties and complexities in the environmental parameters. Basis functions are used to address this. Several candidates are considered, but Legendre polynomials are selected for their low error and reasonable processing time. Additionally, a method of intermediate points is used to approximate high frequency pressure fields with low numbers of collected data points. Following this work, the individual control schemes are explored. A method of observer feedback control is proposed to localize sources by linearizing the acoustic fields. A gradient ascent method for localizing sources in real time is proposed which uses Matched Field Processing and Bayesian filters. These modifications allow the gradient ascent algorithm to be compatible with complex acoustic fields. Finally, an optimal control method is proposed using Pontryagin's Maximum Principle to derive trajectories in real time that balance information gain with control energy. This method is shown to efficiently map an acoustic field, either for optimal sensor placement or to localize sources. The contribution of this work is a new collection of control schemes that use acoustic data to localize acoustically complex sources in a realistic noisy environment, and an understanding of the tradeoffs inherent in applying each of these to the acoustic domain

Mathematical models of cell signalling in heterogeneous populations

Immune cells express thousands of receptors on their membrane surface to sense their environment and communicate with each other. Receptors bind specifically to extra-cellular molecules called ligands. The binding of a ligand to its receptor initiates an intra-cellular signalling cascade which leads to the control of cellular fate, such as division, death, migration or differentiation. As every cell expresses a different number of receptors, each cell responds differently to a given ligand. First motivated by seemingly paradoxical experimental observations on the interleukin-7/interleukin-7 receptor (IL-7/IL-7R) receptor-ligand system, this thesis investigates how receptor copy numbers impact the cell's response, as measured by the amplitude and the half-maximal effective concentration (or EC50). In particular, deterministic mathematical models of various receptor-ligand systems are developed. For each model, making use of algebraic tools, such as Grobner bases, analytic expressions for the amplitude and the EC50 are computed. Such expressions allow one to identify precisely how a cell's response depends on the receptor core structure, namely receptor chain copy numbers and receptor architecture. They also reduce numerical errors and facilitate parameter inference, as demonstrated by the fitting of two IL-7R models to the motivating experimental data set. The results obtained are generalised to a larger family of receptor-ligand systems, for which the amplitude is computed without the use of advanced algebraic tools. Finally, as the immune system relies on the coordination of many cells to fight pathogens, the complex relationship between the cell population dynamics and the receptor copy number distribution in the cellular population is examined. To this end, agent-based models of increasing complexity, which model the competition for interleukin-2 (IL-2) within the T cell population, are constructed, by adding stochastic cellular events one at a time. A mathematical description of each model is provided, which enables us, when possible, to derive the desired receptor copy number distribution (in this case for the IL-2 receptor)