Vortices in (2+1)d Conformal Fluids

We study isolated, stationary, axially symmetric vortex solutions in (2+1)-dimensional viscous conformal fluids. The equations describing them can be brought to the form of three coupled first order ODEs for the radial and rotational velocities and the temperature. They have a rich space of solutions characterized by the radial energy and angular momentum fluxes. We do a detailed study of the phases in the one-parameter family of solutions with no energy flux. This parameter is the product of the asymptotic vorticity and temperature. When it is large, the radial fluid velocity reaches the speed of light at a finite inner radius. When it is below a critical value, the velocity is everywhere bounded, but at the origin there is a discontinuity. We comment on turbulence, potential gravity duals, non-viscous limits and non-relativistic limits.Comment: 39 pages, 10 eps figures, v2: Minor changes, refs, preprint numbe

Cognitive Feedback and Behavioral Feedforward Automation Perspectives for Modeling and Validation in a Learning Context

State-of-the-art technologies have made it possible to provide a learner with immediate computer-assisted feedback by delivering a feedback targeting cognitive aspects of learning, (e.g. reflecting on a result, explaining a concept, i.e. improving understanding). Fast advancement of technology has recently generated increased interest for previously non-feasible approaches for providing feedback based on learning behavior observations by exploiting different traces of learning processes stored in information systems. Such learner behavior data makes it possible to observe different aspects of learning processes in which feedback needs of learners (e.g. difficulties, engagement issues, etc.) based on individual learning trajectories can be traced. By identifying problems earlier in a learning process it is possible to deliver individualized feedback helping learners to take control of their own learning, i.e. to become self-regulated learners, and teachers to understand individual feedback needs and/or adapt their teaching strategies. In this work we (i) propose cognitive computer-assisted feedback mechanisms using a combination of MDE based simulation augmented with automated feedback, and (ii) discuss perspectives for behavioral feedback, i.e. feedforward, that can be based on learning process analytics in the context of learning conceptual modeling. Aggregated results of our previous studies assessing the effective-ness of a proposed cognitive feedback method with respect to improved understanding on different dimension of knowledge, as well as feasibility of behavioural feedforward, are presented. Despite our focus on conceptual modeling and specific diagrams, the principles of the approach presented in this work can be used to support educational feedback automation for a broader spectrum of diagram types beyond the scope of conceptual modeling.status: accepte