Improved variational principle for bounds on energy dissipation in turbulent shear flow

We extend the Doering-Constantin approach to upper bounds on energy dissipation in turbulent flows by introducing a balance parameter into the variational principle. This parameter governs the relative weight of different contributions to the dissipation rate. Its optimization leads to improved bounds without entailing additional technical difficulties. For plane Couette flow, the high-Re-bounds obtainable with one-dimensional background flows are methodically lowered by a factor of 27/32.Comment: 15 pages, RevTeX, 3 postscript figure

(Non)Differentiability and Asymptotics for Potential Densities of Subordinators

For subordinators with positive drift we extend recent results on the structure of the potential measures and the renewal densities. Applying Fourier analysis a new representation of the potential densities is derived from which we deduce asymptotic results and show how the atoms of the Levy measure translate into points of (non)smoothness.Comment: 27 pages, appeared in Electronic Journal of Probability 201

Long-Term Student Experiences in a Hybrid, Open-Ended and Problem Based Adventure Learning Program

In this paper we investigate the experiences of elementary school children over a two-year period during which they engaged with a hybrid Adventure Learning program. In addition to delineating Adventure Learning experiences, we report on educational technology implementations in ecologically valid and complex environments, while drawing inferences on the design of sustainable and successful innovations. Our research indicates that the Adventure Learning experience over the two-year period was dynamic, participatory, engaging, collaborative, and social. Students eagerly became part of the experience both inside and outside of the classroom, and it quickly became apparent that they saw themselves as valued members of the unfolding storyline that mediated their learning. Our recommendations for future research and practice include a call to evaluate "authenticity," focus on the learner experience and narrative, and consider the interplay between pedagogy, technology, and design.Center for Learning and Memor