Study and analysis of telemetry systems for the Saturn vehicle Final report

Analyses of telemetry systems used on Saturn launch vehicle

On the relationship between topological and geometric defects

The study of topology in solids is undergoing a renaissance following renewed interest in the properties of ferroic domain walls as well as recent discoveries regarding topological insulators and skyrmionic lattices. Each of these systems possess a property that is `protected' in a symmetry sense, and is defined rigorously using a branch of mathematics known as topology. In this article we review the formal definition of topological defects as they are classified in terms of homotopy theory, and discuss the precise symmetry-breaking conditions that lead to their formation. We distinguish topological defects from geometric defects, which arise from the details of the stacking or structure of the material but are not protected by symmetry. We provide simple material examples of both topological and geometric defect types, and discuss the implications of the classification on the resulting material properties

Emergence of topological electronic phases in elemental lithium under pressure

Lithium, a prototypical simple metal under ambient conditions, has a surprisingly rich phase diagram under pressure, taking up several structures with reduced symmetry, low coordination numbers, and even semiconducting character with increasing density. Using first-principles calculations, we demonstrate that some predicted high-pressure phases of elemental Li also host topological electronic structures. Beginning at 80 GPa and coincident with a transition to the Pbca phase, we find Li to be a Dirac nodal line semimetal. We further calculate that Li retains linearly-dispersive energy bands in subsequent predicted higher pressure phases, and that it exhibits a Lifshitz transition between two Cmca phases at 220 GPa. The Fd-3m phase at 500 GPa forms buckled honeycomb layers that give rise to a Dirac crossing 1 eV below the Fermi energy. The well-isolated topological nodes near the Fermi level in these phases result from increasing p-orbital character with density at the Fermi level, itself a consequence of rising 1s core wavefunction overlap, and a preference for nonsymmorphic symmetries in the crystal structures favored at these pressures. Our results provide evidence that under pressure, bulk 3D materials with light elements, or even pure elemental systems, can undergo topological phase transitions hosting nontrivial topological properties near the Fermi level with measurable consequences; and that, through pressure, we can access these novel phases in elemental lithium.Comment: 5 pages, 5 figures, accepted for publicatio

Doolin: History and Memories

This book is about growing up in Doolin, County Clare, Ireland in the 1940s. It is based heavily on the author’s memories and recollections, reinforced and supported by historical and archival research. Contained herein are a variety of stories and memories, tales and yarns, all documenting a way of life that is now only found in the folklore and historic records of ‘old Ireland’. The selection of episodes and experiences is eclectic, based on memory and reminiscences, chats with friends and family and all is blended with detailed historical investigation. Our overall aspiration is that this book will help to recreate the spirit and character of a time, a place and a people from long ago. Perhaps some of the memories are presented in ‘soft-focus’, but we make no apology for this sentimentality. The recollections from those times are happy ones, where life was simpler, and much less complicated. This book is intentionally situated in what Seamus Ennis described as ‘the old world’ of Darby Griffy, and is dedicated to our ancestors, who were uncomplicated, yet strong people, in tune with the land, their ancestors, their language and their culture. While the overall focus of the book is on daily life in Doolin in the 1940s, the documentary and archaeological history of the area is also explored, with sections detailing the main historical features of the landscape, the important landmarks, and historical events. Particular attention is paid to the quarries and mines, and the early education of the area, which were important influences on daily life in the period under exploration

Superfluid density and condensate fraction in the BCS-BEC crossover regime at finite temperatures

The superfluid density is a fundamental quantity describing the response to a rotation as well as in two-fluid collisional hydrodynamics. We present extensive calculations of the superfluid density \rho_s in the BCS-BEC crossover regime of a uniform superfluid Fermi gas at finite temperatures. We include strong-coupling or fluctuation effects on these quantities within a Gaussian approximation. We also incorporate the same fluctuation effects into the BCS single-particle excitations described by the superfluid order parameter \Delta and Fermi chemical potential \mu, using the Nozi\`eres and Schmitt-Rink (NSR) approximation. This treatment is shown to be necessary for consistent treatment of \rho_s over the entire BCS-BEC crossover. We also calculate the condensate fraction N_c as a function of the temperature, a quantity which is quite different from the superfluid density \rho_s. We show that the mean-field expression for the condensate fraction N_c is a good approximation even in the strong-coupling BEC regime. Our numerical results show how \rho_s and N_c depend on temperature, from the weak-coupling BCS region to the BEC region of tightly-bound Cooper pair molecules. In a companion paper by the authors (cond-mat/0609187), we derive an equivalent expression for \rho_s from the thermodynamic potential, which exhibits the role of the pairing fluctuations in a more explicit manner.Comment: 32 pages, 12 figure

Spatial interference from well-separated condensates

We use magnetic levitation and a variable-separation dual optical plug to obtain clear spatial interference between two condensates axially separated by up to 0.25 mm -- the largest separation observed with this kind of interferometer. Clear planar fringes are observed using standard (i.e. non-tomographic) resonant absorption imaging. The effect of a weak inverted parabola potential on fringe separation is observed and agrees well with theory.Comment: 4 pages, 5 figures - modified to take into account referees' improvement