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2012 Summer Symposium
30 Aug 2012, Manitoba Hall Board Room, University of Winnipeg
Abstracts
Tim Taves
Review of Gauss-Bonnet Gravitational Collapse
Nils Deppe
Critical Phenomena in Einstein-Gauss-Bonnet Gravity in
Painleve-Gullstrand Coordinates
Einstein-Gauss-Bonnet gravity (EGB) provides a natural higher
dimensional and higher order curvature generalization of Einstein
gravity. It contains a new, presumably microscopic, length scale that
should affect short distance properties of the dynamics, such as
Choptuik scaling. We present the results of a numerical analysis of
self-gravitating massless scalar spherical collapse in five and six
dimenisonal EGB gravity near the threshold of black hole formation.
Although the non-scale invariant nature of Einstein-Gauss-Bonnet
gravity destroys the discrete self similarity, we nonetheless find
evidence for a new type of scaling with interesting properties,
including universality.
William Grafton
Intermediate Value Theorem for Power Series on a non-Archimedean
Field Extension of the Real Numbers
In this talk we will
review the algebraic and topological structures of a non-Archimedean
field extension of the real numbers. Then we will show with examples
how the disconnectedness of the field in the order topology makes
analysis on this field more difficult than in the real case; for
example, there are continuous functions that do not have the
intermediate value property and there are non-constant infinitely
differentiable functions with all derivatives equal to zero
everywhere. We will then review some convergence properties of power
series and show that they satisfy the intermediate value theorem
within their domain of convergence. The proof of the latter theorem is
very different from that of the corresponding result in real analysis;
and it makes use of a non-Archimedean version of the Banach fixed
point theorem.
Jarrett Beck
Antiferromagnetic Ising Model on the Sorrel Net
In this talk I will introduce the concept of geometric frustration in
the context of a newly proposed two dimensional lattice (or net) based
on equilateral triangles. Antiferromagnetic interactions (J1) between
classical Ising spins on triangle based nets result in large residual
entropies (S) per spin (N), for example the triangular net with S/N =
0.323 [1]. Corner-shared triangular nets often have higher residual
entropies due to reduced constraints on each spin, for example the
Kagome net with S/N = 0.50183 [2]. By Monte Carlo simulations and
analytics (for small system sizes) we show that the Ising model on the
sorrel net is highly frustrated, having a residual entropy of S/N =
0.482 [3] . We have considered the effect of adding further nearest
neighbour bond interactions (J2) as might arise in a physical
realization of this model while mentioning recent experimental
research on a lattice with similar symmetry to the Sorrel net [4]. We
also present the phase diagram, magnetic susceptibility, static
structure factor and entropy as a function of J2. Finally we will
present early work on the treatment of the Sorrel net with the dimer
model.
References
1. O.Nagai, T.Horiguchi and S.Myashita in Frustrated Spin Systems,
edited my H.T. Diep, World Scientific, Singapore (2004).
2. K.Kano and S.Naya, Prog. Theo. Phys. 10, 158 (1953).
3. J. M. Hopkinson and J. J. Beck, http://arxiv.org/abs/1207.5836 .
4. T. D. Keene, M. E. Light, M. B. Hursthouse and D. J. Price, Dalton
Trans. 40, 2983, (2011)
Nick Reid
Cosmological Constraints on New Dark Matter Models
Dark matter is a theoretical particle outside the standard model of
physics used to explain the extra gravitational forces felt by visible
matter in the universe. This dark matter is expected to gather at the
center of galaxies in halo formation. Some models of dark matter are
able to explain the large amount of positrons/electrons being produced
in galactic centers.
We are investigating the interactions of dark matter in these models
and the energy these interactions would add to the early universe.
We can then
impose constraints on different properties of dark matter, using
observational data from WMAP7 along with future predictions for the
Planck data.
Josh Jung
Angular Dependence of FMR Measurements in Exchange Coupled NiFe/NiO
Bilayers: Experiment and Theory
Ferromagnetic(FM)/antiferromagnetic(AF) bilayers exhibit the
phenomenon of exchange bias [1] which is characterized by a shift of
the hysteresis loop away from zero field. Recent mea- surements
[2,3,4] performed on NiFe/NiO bilayers using both magnetometry and
ferromagnetic resonance(FMR) techniques have revealed interesting
hysteresis behaviour. Magnetometry mea- surements indicate a shifted
hysteresis loop whereas FMR measurements indicate different hys-
teresis behaviour as a function of the direction of the in-plane
static field. We have used both single domain [5] and micromagnetic
calculations to model the static and dynamic behaviour. Our results
indicate that interfacial anisotropies play an important role.
[1] W.H. Meiklejohn and C.P. Bean, Phys. Rev. 102, 1413 (1956).
[2] K.-W. Lin, M. Mirza, C. Shueh, H.-R. Huang, H.-F. Hsu and J. van Lierop,
Appl. Phys. Lett. 100, 122409 (2012).
[3] N. Grenda, Diplom Thesis,Universität Hamburg (2012).
[4] P. Hyde, Honours Thesis, University of Manitoba (2012).
[5] J. Smit and H.G. Belgers, Philips Res. Rep. 10, 113 (1955).
Dallas Clement
TBA
Ian Russell
Feynman Integral Equations Using Mathematica
In this talk, I will briefly discuss Feynman diagrams and how they can
be used to represent quantum particle interactions and calculate
physical quantities like decay rates. The purpose of our project is to
use Mathematica to manipulate infinite sets of diagrams represented by
integral equations. I'll demonstrate some of Mathematica's basic
tricks and functionality, and then describe some programs we have
written to perform specific tasks.
Travis Redpath
Experimentally spin ice properties arise from a combination of local
anisotropy and long range dipole-dipole interactions. This dipolar
spin ice model has been studied on the Py- rochlore lattice [1]. The
Hyper-kagome lattice is the pure limit of a diluted pyrochlore lattice
[2], with one non-magnetic atom per corner-shared tetrahedron.
This
work probes the properties of the Hyper-kagome lattice with local
Ising spins, an antiferromagnetic nearest-neighbour exchange, and a
long range dipole-dipole interaction using Monte Carlo
simulations. The dipole-dipole interaction energies are calculated
using Ewald summation [3]. Our Monte Carlo uses a hybrid single spin
flip, double loop algorithm which agrees with the analytical result
(see Fig. 1) in the tractable (L=1, 12 spin) limit.
The research was
supported by NSERC (J.M. Hopkinson), a UofM entrance scholarship
(T.E. Redpath), a UMGF (T.E. Redpath), and Research Corporation
(M. Enjalran and P. Carter).
[1] B.C. den Hertog and M.J.P. Gingras,
Phys. Rev. Lett. 84, 3430-3433 (2000).
[2] X Ke, R.S. Freitas,
B.G. Ueland, G.C. Lau, M.L. Dahlberg, R.J. Cava, R. Moessner, and
P. Schiffer, Phys. Rev. Lett. 99, 137203 (2007).
[3] M. Enjalran and
M.J.P. Gingras, arXiv:cond-mat/0307151v1 unpublished.