WITP Summer Student Symposium 2015
28 Aug 2015, Room 326 Allen Building, University of Manitoba
Abstracts
Jennifer West
Bilateral symmetry in supernova remnants and the connection to the
Galactic magnetic field
Supernova explosions are some of the most significant and
transformative events in our Universe. Understanding Supernova
Remnants (SNRs), the leftover remains of these explosions, is
fundamental to our understanding of the chemical enrichment and
magnetism in galaxies, including our own Milky Way. We model the
radio synchrotron emission from Galactic SNRs using the ``Hammurabi''
synchrotron modelling code. We incorporate current models of Galactic
magnetic field and electron density to simulate the emission from the
SNRs as a function of their position in the Galaxy. We do this in an
effort to understand the connection between SNRs and their
environment and to investigate the relationship between the angle of
the symmetry axis of the SNR and the Galactic Magnetic field. This
relationship has implications for understanding the magnetic field
geometry and cosmic ray electron distribution in SNRs, and possibly
even a new method for determining or constraining the distances to
SNRs.
Kelvin Au
A Unique X-ray Emitting Compact Object in a Young Supernova Remnant
1E 161348-5055 (hereafter, 1E) is a strange compact object discovered
in X-rays. It is located in the young supernova remnant (SNR) RCW103,
about 3.3 kpc away. Its observed ~6.67-hour periodic modulation is
uncharacteristically slow compared with the traditional neutron star
model which makes 1E a difficult object to classify and unique among
all pulsar-SNR associations. In hopes of shedding further insight
into 1E's mysterious nature, twenty observations of 1E spanning over
a decade made by NASA's Chandra X-ray Observatory were analyzed and
will be presented here along with a very brief introduction on the
field.
Brad Cownden
A Derivation of the Equation of Motion for a Magnetic Monopole
Although not yet observed in nature, magnetic monopoles have long been
hypothesized to complete the electric-magnetic duality symmetry, and
are required to predict the quantization of electric charge. However,
in the action for this theory there does not exist the required
coupling term between the magnetic "charge" and the vector potential,
A; thus, monopoles must be coupled to the electromagnetic field
through a dual potential, A. In this work, we consider a moving
magnetic monopole described only by the vector potential A. Using
techniques derived from considering charged D3-branes in flux
compactifications, we are able to write the field strength in terms
of explicit functions of the monopole's position, plus the regular
vector potential. Using this novel approach, we are able to recover
the Lorentz force law for the monopole without the use of a dual
potential.
Paul Mikula
Yang-Mills Flow in the Abelian Higgs Model
The Yang-Mills flow equations are a parabolic system of partial differential
equations determined by the gradient of the Yang-Mills functional, whose
stationary points are given by solutions to the equations of motion. We
consider the flow equations for a Yang-Mills-Higgs system, where the gauge
field is coupled with a scalar field. In particular we consider the Abelian
case with axial symmetry. In this case we have vortex solutions corresponding
to GinzburgÂLandau model of superconductivity. In this case the flow equations
are reduced to two coupled partial differential equations in two variables,
which we can solve numerically given initial conditions. Looking at the
behaviour of the flow near the classical vortex solutions in this model tells
us about the stability of the solutions. Study of the flow in the
dimensionally reduced Abelian case provides a starting point for studying flows
in more complicated cases, such as non-Abelian Higgs models, or full 3+1
dimensional theories. Using the AdS/CFT correspondence, which provides an
equivalency between the field theory and a gravitational theory in one higher
dimension where YangÂMills flow could be compared with more well known
geometric flow equations such as Ricci flow.
Ryan Sherbo
On the Algebraic and Topological Structures of the Levi-Civita
Field
In this talk I will review the algebraic and topological structure of
the Levi-Civita field which is the smallest non-Archimedean field
extension of the real numbers that is real closed and complete in the
order topology. In fact, the field is small enough for its numbers to
be implemented on a computer and used for computational applications.
Will Grafton
On the Convergence and Analytical Properties of Power Series over the
Levi-Civita Field
In this talk, I will review the convergence and analytical properties
of power series on the Levi-Civita field as well as the properties of
analytic functions on an interval [a,b] of the field. In particular, I
will show that these have the same smoothness properties as real
power series and real analytic functions on a real interval.
Darren Flynn
Measure Theory and Integration over the Levi-Civita Field
The Levi-Civita field has many counter-intuitive properties, e.g. the
existence of bounded sets with no infimum or supremum and the
existence of non-constant functions whose derivative is zero
everywhere. In this talk I will discuss the difficulties that arise
from trying to do integration in the presence of the aforementioned
artifacts as well as the techniques used to overcome said
difficulties.
Gidon Bookatz
On Locally Uniformly Differentiable Functions in the Levi-Civita
Field
In the Levi-Civita field, the notions of continuity and
differentiability induced by the order topology are too weak to
obtain many of the results of real calculus. Specifically, the results
of the intermediate value theorem and the mean value theorem no
longer follow from the usual notions of continuity and
differentiability. In this talk we discuss the concept of locally
uniform differentiability: in particular, how it can be used to
obtain analogous results on the Levi-Civita field, and how it compares
to the concept of continuous differentiability.