Coarse Proximity Spaces

This work is meant to present the current general landscape of the theory of coarse proximity spaces. It is largely comprised of two parts that are heavily interrelated, the study of boundaries of coarse proximity spaces, and the dimension theory of coarse proximity spaces. Along the way a study of the relationships between coarse proximity spaces and other structures in coarse geometry are explored. We begin in chapter 2 by going over the necessary preliminary definitions and concepts from the study of small scale proximity spaces as well as coarse geometry. We then quickly proceed to the introduction of coarse proximity spaces as inspired by the all important metric case. Intuitions from metric spaces serve as an excellent guiding light for the field. Included in chapter 2 is an alternative description of coarse proximities via a coarse neighborhood operator, which mirrors the description of small scale proximities using a proximity neighborhood operator. Chapter 3 discussed the first major branch of coarse proximity theory, the study of boundaries. To each coarse proximity space one can associate a compact Hausdorff space that captures ``closeness at infinity . This is made more concrete when we show that the boundaries of several well known (and indeed all) compactifications arise as the boundaries of coarse proximity spaces. The cases of the Higson corona and the Gromov boundary are explored in detail, among others. This functorial relationship between coarse proximity spaces and compact Hausdorff spaces provides an internal intuitive way of studying the boundaries of compactifications. Chapter 4 is concerned with the relationship between coarse proximity spaces and other structures within coarse geometry. In particular, the relationship between coarse proximities, coarse structures, and asymptotic resemblance spaces is investigated. In contrast with the case of uniform spaces (the small scale analog of coarse spaces) and small scale proximities where every uniform structure induces a proximity structure, we describe exactly when a coarse structure induces a coarse proximity structure and provide an example of a coarse proximity space whose structure is not induced by any coarse structure. As asymptotic resemblances have similarities to coarse proximity structures we also provide an example of a coarse proximity structure that is not induced by, and does not induce, any asymptotic resemblance. The dimension theory of coarse proximity spaces is the topic of chapter 5. In particular, large scale analogs of the large inductive dimension and covering dimension of topological spaces are explored. we related these large scale notions to their small scale counterparts by way of the boundary functor from chapter 3. We finish with two appendices. The first outlines the development of a coarse invariant modeled on the Vietoris topology on the Higson corona. The second discusses possible future directions for research

A revised inventory of Antarctic subglacial lakes

The locations and details of 145 Antarctic subglacial lakes are presented. The inventory is based on a former catalogue of lake-type features, which has been subsequently reanalysed, and on the results from three additional datasets. The first is from Italian radio-echo sounding (RES) of the Dome C region of East Antarctica, from which 14 new lakes are identified. These data also show that, in a number of occasions, multiple take-type reflectors thought previously to be individual lakes are in fact reflections from the same relatively large take. This reduces the former total of lake-type reflectors by six, but also adds a significant level of information to these particular lakes. The second dataset is from a Russian survey of the Dome A and Dome F regions of East Antarctica, which provides evidence of 18 new lakes and extends the coverage of the inventory considerably. The third dataset comprises three airborne RES surveys under-taken by the US in East Antarctica over the last five years, from which forty three new lakes have been identified. Reference to information on Lake Vostok, from Italian and US surveys taken in the last few years, is now included

Sensitivity of the magnetic state of a spin lattice on itinerant electron orbital phase

Spatially extended localized spins can interact via indirect exchange interaction through Friedel oscillations in the Fermi sea. In arrays of localized spins such interaction can lead to a magnetically ordered phase. Without external magnetic field such a phase is well understood via a "two-impurity" Kondo model. Here we employ non-equilibrium transport spectroscopy to investigate the role of the orbital phase of conduction electrons on the magnetic state of a spin lattice. We show experimentally, that even tiniest perpendicular magnetic field can influence the magnitude of the inter-spin magnetic exchange.Comment: To be published in PhysicaE EP2DS proceedin

Coarsening Dynamics of Crystalline Thin Films

The formation of pyramid-like structures in thin-film growth on substrates with a quadratic symmetry, e.g., {001} surfaces, is shown to exhibit anisotropic scaling as there exist two length scales with different time dependences. Analytical and numerical results indicate that for most realizations coarsening of mounds is described by an exponent n=0.2357. However, depending on material parameters, n may lie between 0 (logarithmic coarsening) and 1/3. In contrast, growth on substrates with triangular symmetries ({111} surfaces) is dominated by a single length scale and an exponent n=1/3.Comment: RevTeX, 4 pages, 3 figure

Mean Field and the Single Homopolymer

We develop a statistical model for a confined chain molecule based on a monomer grand canonical ensemble. The molecule is subject to an external chemical potential, a backbone interaction, and an attractive interaction between all monomers. Using a Gaussian variable formalism and a mean field approximation, we analytically derive a minimum principle from which we can obtain relevant physical quantities, such as the monomer density, and we explore the limit in which the chain is subject to a tight confinement. Through a numerical implementation of the minimization process we show how we can obtain density profiles in three dimensions for arbitraty potentials, and we test the limits of validity of the theory.Comment: 15 pages, 7 figure

Field-tunable magnetic phases in a semiconductor-based two-dimensional Kondo lattice

We show the existence of intrinsic localized spins in mesoscopic high-mobility GaAs/AlGaAs heterostructures. Non-equilibrium transport spectroscopy reveals a quasi-regular distribution of the spins, and indicates that the spins interact indirectly via the conduction electrons. The interaction between spins manifests in characteristic zero-bias anomaly near the Fermi energy, and indicates gate voltage-controllable magnetic phases in high-mobility heterostructures. To address this issue further, we have also designed electrostatically tunable Hall devices, that allow a probing of Hall characteristics at the active region of the mesoscopic devices. We show that the zero field Hall coefficient has an anomalous contribution, which can be attributed to scattering by the localized spins. The anomalous contribution can be destroyed by an increase in temperature, source drain bias, or field range.Comment: To be published in PhysicaE EP2DS proceedin

Automated detection and characterization of Antarctic basal units using radar sounding data: demonstration in Institute Ice Stream, West Antarctica

Basal units – visibly distinct englacial structures near the ice-bed interface – warrant investigation for a number of reasons. Many are of unknown composition and origin, characteristics that could provide substantial insight into subglacial processes and ice-sheet history. Their significance, moreover, is not limited to near-bed depths; these units appear to dramatically influence the flow of surrounding ice. In order to enable improved characterization of these features, we develop and apply an algorithm that allows for the automatic detection of basal units. We use a tunable layer-optimized SAR processor to distinguish these structures from the bed, isochronous englacial layers and the ice-sheet surface, presenting a conceptual framework for the use of radio-echo character in the identification of ice-sheet features. We also outline a method by which our processor could be used to place observational constraints on basal units’ configuration, composition and provenance

Imaging bedrock topography and geological controls on ice streams flowing in the Wilkes Subglacial Basin sector of East Antarctica

The northern Wilkes Subglacial Basin (NWSB) in East Antarctica underlies the catchments of the Matusevich, Cook, Ninnis and Mertz Glaciers, which are largely marine-based and hence particularly sensitive to past and future ocean and climate warming. Here we use airborne radar, aeromagnetic and airborne gravity data to image bedrock topography, subglacial geology and deeper crustal structure and assess its influence on ice sheet dynamics in the NWSB. The previously identified Central Basins extend beneath the fast flowing Cook ice streams, indicating that potential ocean-induced changes could propagate further into the interior of the ice sheet. By analogy with the better exposed Rennick Graben in northern Victoria Land, these deep subglacial basins are interpreted here as grabens that steer fast glacial flow. With the aid of depth to source estimates and forward magnetic and gravity models, we image the 3D variability in geological basal boundary conditions, including Beacon sediments and Jurassic basaltic rocks and uplifted basement blocks within and along the flanks of these grabens. A remarkable contrast in magnetic anomaly signatures is observed over the coastal and inland segments of the Cook ice stream catchment. We model several km thick early Cambrian to late Neoproterozoic sedimentary basins in the basement of the coastal region, in contrast to a prominent Proterozoic basement high at the onset of fast glacial flow further inland. We further hypothesise that this difference affects geothermal heat flux at the base of the ice sheet, which could in turn influence basal melting and subglacial hydrology