12 research outputs found

### Gender gap and polarisation of physics on global courses

We extend on previous research on the Force Concept Inventory (FCI) given to
first year classical mechanics students (N=66 students, over four years) pre
and post score, for students on an international (global) course at Osaka
University. In particular, we revisit the notion of "polarisation" in
connection with the six polarisation-inducing questions in the FCI and examine
its gender aspect. Our data suggest that this phenomenon is not unique to one
gender. Furthermore, the extent by which it is exhibited by males may differ
from that of females at the beginning (pretest) but the gap closes upon
learning more about forces (posttest). These findings are for the most part,
complemented by our result for the FCI as a whole. Although the differences in
means for males and females suggest a gender gap, statistical analysis shows
that there is no gender difference at the 95% confidence level.Comment: 15 pages, 7 figure

### Polarization of physics on global courses

Since October 2010, the Chemistry-Biology Combined Major Program (CBCMP), an
international course taught in English at Osaka University, has been teaching
small classes (no more than 20 in size). We present data from the Force Concept
Inventory (FCI) given to first year classical mechanics students (N=47 students
over three years) pre and post score, for a class that predominantly uses
interactive engagement (IE), such as MasteringPhysics. Our findings show a
$G$-factor improved score of about $\sim$ 0.18, which is marginally about the
average of a traditional based course. Furthermore, we analyse in detail a set
of six questions from the FCI, involving the identification of forces acting on
a body. We find that student answers tend to cluster about "polarising
choices"-a pair of choices containing the correct choice and a wrong choice
with the latter corresponding to a superset of forces in the former. Our
results are suggestive that students have a good idea of the right set of
forces acting on a given system but the inclusion of extra force(s) brings
about confusion; something that may be explained by misleading ontological
categorisation of forces. In an appendix we also comment on possible
correlations between the pre/post score and the level of English ability on
entry to the course.Comment: 11 pages, 5 figures, 1 table; modified the discussion to focus on
polarisation; the discussion on English ability can now be found in the
appendix; added reference

### Logarithmic divergences in the $k$-inflationary power spectra computed through the uniform approximation

We investigate a calculation method for solving the Mukhanov-Sasaki equation
in slow-roll $k$-inflation based on the uniform approximation (UA) in
conjunction with an expansion scheme for slow-roll parameters with respect to
the number of $e$-folds about the so-called \textit{turning point}. Earlier
works on this method has so far gained some promising results derived from the
approximating expressions for the power spectra among others, up to second
order with respect to the Hubble and sound flow parameters, when compared to
other semi-analytical approaches (e.g., Green's function and WKB methods).
However, a closer inspection is suggestive that there is a problem when
higher-order parts of the power spectra are considered; residual logarithmic
divergences may come out that can render the prediction physically
inconsistent. Looking at this possibility, we map out up to what order with
respect to the mentioned parameters several physical quantities can be
calculated before hitting a logarithmically divergent result. It turns out that
the power spectra are limited up to second order, the tensor-to-scalar ratio up
to third order, and the spectral indices and running converge to all orders.
This indicates that the expansion scheme is incompatible with the working
equations derived from UA for the power spectra but compatible with that of the
spectral indices. For those quantities that involve logarithmically divergent
terms in the higher-order parts, existing results in the literature for the
convergent lower-order parts calculated in the equivalent fashion should be
viewed with some caution; they do not rest on solid mathematical ground.Comment: version 4 : extended Section 6 on remarks on logarithmic divergence

### Adiabatic regularisation of power spectra in $k$-inflation

We look at the question posed by Parker et al. about the effect of UV
regularisation on the power spectrum for inflation. Focusing on the slow-roll
$k$-inflation, we show that up to second order in the Hubble and sound flow
parameters, the adiabatic regularisation of such model leads to no difference
in the power spectrum apart from certain cases that violate near scale
invariant power spectra. Furthermore, extending to non-minimal $k$-inflation,
we establish the equivalence of the subtraction terms in the adiabatic
regularisation of the power spectrum in Jordan and Einstein frames.Comment: 17 pages; v2, typos corrected & reference added; v3, rewrote some
parts for clarit

### Percolation of 'Civilisation' in a Homogeneous Isotropic Universe

In this work, we consider the spread of a 'civilisation' in an idealised
homogeneous isotropic universe where all the planets of interest are habitable.
Following a framework that goes beyond the usual idea of percolation, we
investigate the behaviour of the number of colonised planets with time, and the
total colonisation time for three types of universes. These include static,
dark energy-dominated, and matter-dominated universes. For all these types of
universes, we find a remarkable fit with the Logistic Growth Function for the
number of colonised planets with time. This is in spite of the fact that for
the matter- and dark-energy dominated universes, the space itself is expanding.
For the total colonisation time, $T$, the case for a dark energy-dominated
universe is marked with divergence beyond the linear regime characterised by
small values of the Hubble parameter, $H$. Not all planets in a spherical
section of this universe can be 'colonised' due to the presence of a shrinking
Hubble sphere. In other words, the recession speeds of other planets go beyond
the speed of light making them impossible to reach. On the other hand, for a
matter-dominated universe, while there is an apparent horizon, the Hubble
sphere is growing instead of shrinking. This leads to a finite total
colonisation time that depends on the Hubble parameter characterising the
universe; in particular, we find $T\sim H$ for small $H$ and $T\sim H^2$ for
large $H$.Comment: 10 pages, 8 figure

### Extending the symmetry of the massless Klein-Gordon equation under the general disformal transformation

The Klein-Gordon equation, one of the most fundamental equations in field
theory, is known to be not invariant under conformal transformation. However,
its massless limit exhibits symmetry under Bekenstein's disformal
transformation, subject to some conditions on the disformal part of the metric
variation. In this study, we explore the symmetry of the Klein-Gordon equation
under the general disformal transformation encompassing that of Bekenstein and
a hierarchy of `sub-generalisations' explored in the literature (within the
context of inflationary cosmology and scalar-tensor theories). We find that the
symmetry in the massless limit can be extended under this generalisation
provided that the disformal factors takes a special form in relation to the
conformal factor. Upon settling the effective extension of symmetry, we
investigate the invertibility of the general disformal transformation to avoid
propagating non-physical degrees of freedom upon changing the metric. We derive
the inverse transformation and the accompanying restrictions that make this
inverse possible.Comment: 14 pages, accepted for publication in International Journal of Modern
Physics A, deleted some unimportant details, clarified that the
`orthogonality condition' does not make the field overdetermined, rewritten
parts for clarit