Exploring the mobile structural assessment tool: Concept maps for learning website: Concept Maps for Learning Website

In this paper, we describe how the pathfinder algorithm converts relatedness ratings of concept pairs to concept maps; we also present how this algorithm has been used to develop the Concept Maps for Learning website (www.conceptmapsforlearning.com) based on the principles of effective formative assessment. The pathfinder networks, one of the network representation tools, claim to help more students memorize and recall the relations between concepts than spatial representation tools (such as Multi- Dimensional Scaling). Therefore, the pathfinder networks have been used in various studies on knowledge structures, including identifying students’ misconceptions. To accomplish this, each student’s knowledge map and the expert knowledge map are compared via the pathfinder software, and the differences between these maps are highlighted. After misconceptions are identified, the pathfinder software fails to provide any feedback on these misconceptions. To overcome this weakness, we have been developing a mobile-based concept mapping tool providing visual, textual and remedial feedback (ex. videos, website links and applets) on the concept relations. This information is then placed on the expert concept map, but not on the student’s concept map. Additionally, students are asked to note what they understand from given feedback, and given the opportunity to revise their knowledge maps after receiving various types of feedback.

Non-radial instabilities and progenitor asphericities in core-collapse supernovae

Since core-collapse supernova simulations still struggle to produce robust neutrino-driven explosions in 3D, it has been proposed that asphericities caused by convection in the progenitor might facilitate shock revival by boosting the activity of non-radial hydrodynamic instabilities in the post-shock region. We investigate this scenario in depth using 42 relativistic 2D simulations with multigroup neutrino transport to examine the effects of velocity and density perturbations in the progenitor for different perturbation geometries that obey fundamental physical constraints (like the anelastic condition). As a framework for analysing our results, we introduce semi-empirical scaling laws relating neutrino heating, average turbulent velocities in the gain region, and the shock deformation in the saturation limit of non-radial instabilities. The squared turbulent Mach number, 〈Ma2〉, reflects the violence of aspherical motions in the gain layer, and explosive runaway occurs for 〈Ma2〉 ≳ 0.3, corresponding to a reduction of the critical neutrino luminosity by ∼25∼25 per cent compared to 1D. In the light of this theory, progenitor asphericities aid shock revival mainly by creating anisotropic mass flux on to the shock: differential infall efficiently converts velocity perturbations in the progenitor into density perturbations δρ/ρ at the shock of the order of the initial convective Mach number Maprog. The anisotropic mass flux and ram pressure deform the shock and thereby amplify post-shock turbulence. Large-scale (ℓ = 2, ℓ = 1) modes prove most conducive to shock revival, whereas small-scale perturbations require unrealistically high convective Mach numbers. Initial density perturbations in the progenitor are only of the order of Ma2progMaprog2 and therefore play a subdominant role.