Magnetic Properties of MBE Grown La0.6Sr0.4MnO3 Thin Films

Honorable Mention Winner This project investigates the magnetic properties of a La1-xSrxMnO3 (x = 0.40) sample of high quality. This sample was grown one atomic layer at a time by Prof. Warusawithana using UNF’s Molecular Beam Epitaxy (MBE) machine. These magnetic properties are investigated over a range of temperatures from 5 to 400 K in fields up to 7 T. We make use of the techniques to analyze the sample to determine to a high degree of precision the critical temperature of the sample, we determined it to be 252 K. We further identified the saturated magnetization, remnant magnetization, and coercive field at 5 K to be 0.00733 emu/g, 0.00563 emu/g and 0.0090 T respectivel

Menelaus' theorem, Clifford configurations and inversive geometry of the Schwarzian KP hierarchy

It is shown that the integrable discrete Schwarzian KP (dSKP) equation which constitutes an algebraic superposition formula associated with, for instance, the Schwarzian KP hierarchy, the classical Darboux transformation and quasi-conformal mappings encapsulates nothing but a fundamental theorem of ancient Greek geometry. Thus, it is demonstrated that the connection with Menelaus' theorem and, more generally, Clifford configurations renders the dSKP equation a natural object of inversive geometry on the plane. The geometric and algebraic integrability of dSKP lattices and their reductions to lattices of Menelaus-Darboux, Schwarzian KdV, Schwarzian Boussinesq and Schramm type is discussed. The dSKP and discrete Schwarzian Boussinesq equations are shown to represent discretizations of families of quasi-conformal mappings.Comment: 26 pages, 9 figure

Closed Universes, de Sitter Space and Inflation

We present a new approach to constructing inflationary models in closed universes. Conformal embedding of closed-universe models in a de Sitter background suggests a quantisation condition on the available conformal time. This condition implies that the universe is closed at no greater than the 10% level. When a massive scalar field is introduced to drive an inflationary phase this figure is reduced to closure at nearer the 1% level. In order to enforce the constraint on the available conformal time we need to consider conditions in the universe before the onset of inflation. A formal series around the initial singularity is constructed, which rests on a pair of dimensionless, scale-invariant parameters. For physically-acceptable models we find that both parameters are of order unity, so no fine tuning is required, except in the mass of the scalar field. For typical values of the input parameters we predict the observed values of the cosmological parameters, including the magnitude of the cosmological constant. The model produces a very good fit to the most recent CMBR data. The primordial curvature spectrum predicts the low-l fall-off in the CMB power spectrum observed by WMAP. The spectrum also predicts a fall-off in the matter spectrum at high k, relative to a power law. A further prediction of our model is a large tensor mode component, with r~0.2.Comment: 38 pages, 25 figure

Curvature line parametrized surfaces and orthogonal coordinate systems. Discretization with Dupin cyclides

Cyclidic nets are introduced as discrete analogs of curvature line parametrized surfaces and orthogonal coordinate systems. A 2-dimensional cyclidic net is a piecewise smooth $C^1$-surface built from surface patches of Dupin cyclides, each patch being bounded by curvature lines of the supporting cyclide. An explicit description of cyclidic nets is given and their relation to the established discretizations of curvature line parametrized surfaces as circular, conical and principal contact element nets is explained. We introduce 3-dimensional cyclidic nets as discrete analogs of triply-orthogonal coordinate systems and investigate them in detail. Our considerations are based on the Lie geometric description of Dupin cyclides. Explicit formulas are derived and implemented in a computer program.Comment: 39 pages, 30 figures; Theorem 2.7 has been reformulated, as a normalization factor in formula (2.4) was missing. The corresponding formulations have been adjusted and a few typos have been correcte