Energy distribution and equation of state of the early Universe: matching the end of inflation and the onset of radiation domination

We study the energy distribution and equation of state of the universe between the end of inflation and the onset of radiation domination (RD), considering observationally consistent single-field inflationary scenarios, with a potential 'flattening' at large field values, and a monomial shape $V(\phi) \propto |\phi|^p$ around the origin. As a proxy for (p)reheating, we include a quadratic interaction $g^2\phi^2X^2$ between the inflaton $\phi$ and a light scalar 'daughter' field $X$, with $g^2>0$. We capture the non-perturbative and non-linear nature of the system dynamics with lattice simulations, obtaining that: $i)$ the final energy transferred to $X$ depends only on $p$, not on $g^2$, ; $ii)$ the final transfer of energy is always negligible for $2 \leq p < 4$, and of order $\sim 50\%$ for $p \geq 4$; $iii)$ the system goes at late times to matter-domination for $p = 2$, and always to RD for $p > 2$. In the latter case we calculate the number of e-folds until RD, significantly reducing the uncertainty in the inflationary observables $n_s$ and $r$.Comment: 7 pages + references, 5 figures. It matches published versio

How a trainee mathematics teacher develops teacher self-efficacy

This research contributes new understanding of how teacher self-efficacy is acquired and developed by a preservice teacher during a one-year programme of initial teacher education (ITE). Our findings are consistent with previous studies in confirming that self-efficacy is acquired through vicarious experience, verbal persuasion and mastery experience while being undermined by negative physiological and affective states. In this study, however, we consider three separate subdomains of teacher self-efficacy: efficacy in classroom management, efficacy in student engagement and efficacy in instructional strategies. Based on a qualitative analysis of a trainee’s weekly reflections, this research shows that efficacy development is phased, initially dominated by developing efficacy in classroom management and efficacy in student engagement and, only at a significantly later stage, in instructional strategies. This is an important contribution to understanding how trainee teachers develop professional efficacy. Based on these findings, we tentatively offer a new self-efficacy development trajectory framework which can be used to inform the development of ITE programmes or continuing professional development programmes

Theory of Drop Formation

We consider the motion of an axisymmetric column of Navier-Stokes fluid with a free surface. Due to surface tension, the thickness of the fluid neck goes to zero in finite time. After the singularity, the fluid consists of two halves, which constitute a unique continuation of the Navier-Stokes equation through the singular point. We calculate the asymptotic solutions of the Navier-Stokes equation, both before and after the singularity. The solutions have scaling form, characterized by universal exponents as well as universal scaling functions, which we compute without adjustable parameters

Geochemical evidence for mélange melting in global arcs

© The Author(s), 2017. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Science Advances 3 (2017): e1602402, doi:10.1126/sciadv.1602402.In subduction zones, sediments and hydrothermally altered oceanic crust, which together form part of the subducting slab, contribute to the chemical composition of lavas erupted at the surface to form volcanic arcs. Transport of this material from the slab to the overlying mantle wedge is thought to involve discreet melts and fluids that are released from various portions of the slab. We use a meta-analysis of geochemical data from eight globally representative arcs to show that melts and fluids from individual slab components cannot be responsible for the formation of arc lavas. Instead, the data are compatible with models that first invoke physical mixing of slab components and the mantle wedge, widely referred to as high-pressure mélange, before arc magmas are generated.This work was supported by the NSF (EAR-1119373 to S.G.N., EAR-1427310 to S.G.N. and H.R.M., and EAR-1348063 to H.R.M. and G. Gaetani) and Woods Hole Oceanographic Institution–Ocean Exploration Institute (to H.R.M. and G. Gaetani)

Teachers’ perspectives on homework: manifestations of culturally situated common sense

This paper presents an exploratory study of English and Swedish teachers’ perspectives on the role of homework in year-one children’s learning of number. In order to ensure cultural integrity, data were analysed independently by two colleagues in each context. Analyses yielded three broad but cross-culturally common themes reflecting culturally situated notions of common sense. These concerned the existence of homework, the purpose of homework and the role of parents in homework’s completion. While homework was unproblematic for all English teachers, half the Swedish cohort spoke against it, arguing that variation in home background would compromise principles of equity. All teachers who set homework, whether English or Swedish, spoke of homework as a means of supporting children at risk of falling behind their peers, a process by which children practice routine skills. English teachers’ homework-related justifications were located in a discourse of target setting that was invisible in the Swedish

Deafferentation as a cause of hallucinations

PURPOSE OF REVIEW: The association between hallucinations and sensory loss, especially vision- and hearing-impairment, has been firmly established over the past years. The deafferentation theory, a decrease of the threshold for activation in the brain and the consequential imbalance between excitatory and inhibitory brain networks, is hypothesized to underly this relationship. Here we review the studies investigating this theory with a focus on the most recent literature to better understand the contribution of sensory loss to hallucinations. RECENT FINDINGS: A large cross-sectional study has recently confirmed the relationship between auditory impairment and deafferentation. However, the underlying mechanisms of deafferentation are still under debate, with hyperexcitability and deviations in bottom-up and top-down processes being the most likely explanations. Social isolation following sensory impairment increases the risk for hallucinations. Better knowledge and awareness about the contribution of deafferentation and loneliness would benefit diagnosis and treatment of hallucinations. SUMMARY: Studies imply activity in higher order areas, corresponding to the functional mapping of sensory system, and a general state of higher excitability as neurobiological explanation. Auditory deafferentation, tinnitus and other auditory hallucinations, likely lie on a continuum. Social isolation mediates psychotic symptoms in sensory-impaired individuals. Currently, there is no standard treatment for deafferentation hallucinations

Simulation of Ablating Hypersonic Vehicles with Finite-Rate Surface Chemistry

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/140434/1/6.2014-2124.pd