Hybrid Entropy Stable HLL-Type Riemann Solvers for Hyperbolic Conservation Laws

It is known that HLL-type schemes are more dissipative than schemes based on characteristic decompositions. However, HLL-type methods offer greater flexibility to large systems of hyperbolic conservation laws because the eigenstructure of the flux Jacobian is not needed. We demonstrate in the present work that several HLL-type Riemann solvers are provably entropy stable. Further, we provide convex combinations of standard dissipation terms to create hybrid HLL-type methods that have less dissipation while retaining entropy stability. The decrease in dissipation is demonstrated for the ideal MHD equations with a numerical example.Comment: 6 page

Affordable, Entropy Conserving and Entropy Stable Flux Functions for the Ideal MHD Equations

In this work, we design an entropy stable, finite volume approximation for the ideal magnetohydrodynamics (MHD) equations. The method is novel as we design an affordable analytical expression of the numerical interface flux function that discretely preserves the entropy of the system. To guarantee the discrete conservation of entropy requires the addition of a particular source term to the ideal MHD system. Exact entropy conserving schemes cannot dissipate energy at shocks, thus to compute accurate solutions to problems that may develop shocks, we determine a dissipation term to guarantee entropy stability for the numerical scheme. Numerical tests are performed to demonstrate the theoretical findings of entropy conservation and robustness.Comment: arXiv admin note: substantial text overlap with arXiv:1509.06902; text overlap with arXiv:1007.2606 by other author

The effects of test-based retention on student outcomes over time: Regression discontinuity evidence from Florida

Many American states require that students lacking basic reading proficiency after third grade be retained and remediated. We exploit a discontinuity in retention probabilities under Florida's test-based promotion policy to study its effects on student outcomes through high school. We find large positive effects on achievement that fade out entirely when retained students are compared to their same-age peers, but remain substantial through grade 10 when compared to students in the same grade. Being retained in third grade due to missing the promotion standard increases students' grade point averages and leads them to take fewer remedial courses in high school but has no effect on their probability of graduating.We are grateful to the Florida Department of Education for providing the primary dataset for this study. We thank Stefan Bauernschuster, Matthew Chingos, Andrew Ho, Paul Peterson, Ludger Woessmann, and the seminar participants at the National Bureau of Economic Research, Harvard University, the Ifo Institute, Mathematica Policy Research, Stanford University, the European Economic Association Meeting in Gothenburg, the European Association of Labour Economists Meeting in Turin and the Swedish Institute for Social Research for helpful comments. The Helios Education Foundation provided financial support for this research. The views contained herein are not necessarily those of the Helios Education Foundation. Any errors are our own. (Helios Education Foundation)http://sites.bu.edu/marcuswinters/files/2017/09/NBER-Grade-Retention.pdfhttp://sites.bu.edu/marcuswinters/files/2017/09/NBER-Grade-Retention.pdfAccepted manuscrip

Investigations of the trapped magnetic field

Theoretical and experimental work on trapped magnetic field including diffusion time for frozen field and temperature dependence of trapped flux diffusion tim

Vanderbilt: The Challenge of Law Reform

A Review of The Challenge of Law Reform. By Arthur T. Vanderbilt

Edson R. Sunderland and Judicial Administration

The name of Edson R. Sunderland stands out as one of the great and forward-looking leaders of his generation and of all time in the improvement of the administration of justice

Trumbull: Materials on the Lawyer\u27s Professional Responsibility

A Review of Materials on the Lawyer\u27s Professional Responsibility. By William M. Trumbull