Abstracts

Tim Taves
Review of Gauss-Bonnet Gravitational Collapse

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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.

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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.

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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)

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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.

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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).

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Dallas Clement
TBA

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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.

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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.