523 research outputs found
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 -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
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