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

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

Logarithmic divergences in the kk-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 kk-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