2013 Summer Symposium
29 Aug 2013, Allen Building Room 519, University of Manitoba
Abstracts
Brad Cownden
Modern models of extra dimensions in string theory
It is well known that Type IIB string theory necessitates ten-dimensional
spacetime; namely, the four-dimensional Minkowski spacetime that we
experience (locally) as well as a compactified, six-dimensional Euclidean
spacetime whose topological properties contribute to the 4-d physics we
observe. By taking the low energy limit of Type IIB string theory, we
obtain a 10-d supergravity theory that can help us explore the impact
string
physics has in the 4 large dimensions. In particular, modern 6-d
compactifications are based on Calabi-Yau manifolds, which are imbued with
certain desirable topological properties. However, many of the results
obtained in the literature so far do not consider the 6-d space to be
dynamic, i.e., position-dependent deformation of the Calabi-Yau due to
field energy densities or point charges are ignored.
In this talk I will outline a procedure for describing the interactions of
fundamental fields with a dynamic Calabi-Yau manifold, and how to produce
a 4-d theory from this via dimensional reduction. This procedure is widely
applicable to a variety of important string-related problems and so will
be done in the most general way possible. The fields present are generic
extensions of electrodynamic field theory while the semi-classical string
objects called D3-branes are also present on the 6-d manifold. This type
of problem helps to provide a theoretical framework for inflationary
models of the early universe.
Nick Reid
A dark theory for a light problem
TBA
Joe Smith
The 4-vertex in scalar-Ψ4 theory using the 2PI effective
action
The basic goal is to calculate the probability that
a scattering event between subatomic particles will occur. In a many
body system at finite temperature, this involves summing over an
infinite number of amplitudes. Special techniques must be applied in
order to satisfy certain symmetries of the physical theory that
restrict this summation. We use the ``2 Particle Irreducible'' effective
action for the reason that is satisfies these symmetries. In this talk
I will describe a program that solves the equations involved in the
2PI method. It eventually relaxes to final values for the event
amplitudes at all points in momentum space.
Gabriel Chernitsky
Searching for gamma radiation in dwarf galaxies
A 511 keV
line (gamma radiation) has been detected from our galactic core. It's
known that positronium annihilation causes this, but there are many
theories that try to explain the presence of positrons in the centre
of the Milky Way. One theory is that dark matter produces positrons
through annihilation or scattering. There have been previous
calculations regarding the photon ``flux'' from the Milky Way, and the
amounts of positrons being produced. We can now investigate other
galaxies for evidence of dark matter annihilation or
scattering. Nearby dwarf galaxies are known to have a large density of
dark matter. If dark matter produces positrons, we would then expect
to see a comparable amount of "flux" from these dwarf galaxies as we
would see in the Milky Way. We will be using equations that pertain
with models of the Milky Way and apply them to galaxies like Segue 1
to find flux values.
Morgan Mercredi
Cell migration in competing chemotactic environments
Chemotaxis is a biological process that describes the influence of
specific chemical substances on the migration of organisms. The
cell-level processes give rise to collective behaviour of large
populations of cells. This is important for self-organization into
macroscopic structures such as tissue and aggregation patterns in
bacteria. In this talk, I will present a partial differential
equation model for a single cell species in the presence of two
competing chemical fields, and describe conditions under which various
patterns of behaviour, including spatio-temporal pattern formation and
the 'blow-up' phenomenon, may occur, and demonstrate these with
two-dimensional numerical simulations based on a Crank-Nicholson/ADI
method.
Jared Enns
Dark light: Exploring dark radiation models
Dark radiation is a proposed dark matter model in which dark matter or
standard model particles may produce theorized "dark neutrinos",
(ν'). This summer we explored various scatters, decays, and annihilations
involving ν' and other particles in the model.
Nils Deppe
Adaptive mesh refinement for constrained 1D hyperbolic systems
Many problems in physics, such as gravitational collapse, turn
out to be well modeled by systems of partial differential equations
(PDEs) where the (hyperbolic) evolution equations are coupled to
constraint equations. The constraint equations depend on spatial
derivatives only, and must be satisfied at each time step. In 1+1D the
constraint equations simply become either first or second order
ordinary differential equations. Discussed will be how solutions to
such systems can be found numerically in adaptive mesh refinement
framework, which allows for high resolution of small scale phenomena
by placing finer mesh there where the solution exhibits ``interesting''
behaviour. This technique helps keep computational costs to a minimum,
though care must be taken when implementing such an algorithm as
additional computational overhead is produced by the placement and
movement of refined mesh.
Allison Kolly
Gravitational collapse in anti-de Sitter space
TBA
Ben Guest
A new galactic pulsar candidate revealed by the Chandra X-ray Observatory
A core-collapse supernova occurs when a massive star
finally loses the battle with gravity. It is one of the most energetic
events in the universe, releasing in an instant enough energy to
outshine an entire galaxy. This primary flash is by no means the
end. What remains is a supernova remnant (SNR) containing a rapidly
rotating neutron star (pulsar) surrounded by a cloud of highly
energetic particles known as a pulsar wind nebula. NASA's Chandra
X-ray Observatory is the most powerful X-ray telescope known to date
showing with an unprecedented resolution the workings of neutron stars
and the way they interact with, and energize, their surroundings.
This talk will present the results of a Chandra observation of a
supernova remnant revealing a new pulsar candidate in our galaxy
through an X-ray imaging and spectroscopic study of its surrounding
nebula. The focus of the talk will be on the theoretical foundations
which allow the characteristics of the SNR's powering engine
(i.e. pulsar) - such as rotation rate, energetics, magnetic field and
age - to be estimated without being directly measured. Such studies
have impact on our understanding of the aftermath of supernova
explosions and the physics of some of the most magnetic objects in the
universe.
Chelsea Braun
Supernova remnants as astrophysical laboratories for the formation
of the elements
The intersection between nuclear physics
and astrophysics, nuclear astrophysics, allows us to examine the
formation of the elements within an exploding star. The core-collapse
explosion of a star can reach unimaginably high temperatures and
densities within the time-frame of a few seconds. With these
conditions, nuclear physics takes on a large role, where unstable
nuclides rapidly form chains of nuclear reactions and some of the
heaviest elements are formed. Nucleosynthesis models theorize the
expected yields during this core-collapse process. Following the
explosion witnessed as a ``supernova,'' the remnant referred to as a
``supernova remnant (SNR)'' emits in the X-ray band, and the ejected
layers of the exploded star (ejecta) remain visible for thousands of
years. The Chandra X-ray telescope is sensitive to emission in the
0.5-10 keV range allowing us to probe the heavy elements created by
the supernova. By comparing the abundances of the ejecta inferred from
fitting X-ray spectra to the nucleosynthesis yields from core-collapse
models, the progenitor mass can be determined.
Angel Barria
On the algebraic and topological structures of the Levi-Civita
field
In this talk, we will introduce the concept of
non-Archimedean fields with a brief motivation for their potential use
in Physics. Then we will review the algebraic and topological
structures of the Levi-Civita field which is the smallest
non-Archimedean ordered field extension of the real numbers that is
real closed and complete in the topology induced by the order.
Darren Flynn
On delta functions on the Levi-Civita field
In various
branches of physics, one encounters sources which are nearly
instantaneous (if time is the independent variable) or almost
localized (if the independent variable is a space coordinate). To
avoid the cumbersome studies of the detailed functional dependencies
of such sources, one would like to replace them with idealized sources
that are truly instantaneous or localized. Typical examples of such
sources are the concentrated forces and moments in solid mechanics,
the point masses in the theory of the gravitational potential, and the
point charges in electrostatics. The field of real numbers does not
permit a direct representation of the (improper) delta functions used
for the description of impulsive (instantaneous) or concentrated
(localized) sources. Of course, within the framework of distributions,
these concepts can be accounted for in a rigorous fashion, but at the
expense of the intuitive interpretation. The existence of infinitely
small numbers and infinitely large numbers in the Levi-Civita field
allows us to have well-behaved delta functions which, when restricted
to the real numbers, reduce to the Dirac delta function. Our current
work is in developing the foundations for a mathematically rigorous
theory of localized and instantaneous sources that has a clear and
unambiguous way of specifying a mathematically concentrated source.
Gidon Bookatz
On locally uniformly differentiable functions on the Levi-Civita field:
the inverse function theorem and the intermediate function theorem
In this talk we show, with examples, that the usual notion of
continuity and differentiability is too weak to extend many of the classical
results of the real calculus to the Levi-Civita field; this is due to the
total disconnectedness of the filed in the order topology. Then we present
a brief review of the properties of locally uniformly differentiable
functions on the field and state versions of the inverse function
theorem and the intermediate function theorem that hold for such functions.
William Grafton
Fourier analysis on the Levi-Civita field
The foundations for Fourier analysis on the Levi-Civita field will
be presented. We will show how to find the Fourier series for periodic
functions that satisfy Dirichlet-like conditions on a period where the
period may be finite, infinitely small, or infinitely large. We will then
apply these techniques to get Fourier series for non-periodic real-valued
functions on the field of real numbers R.