Hiring Practices in the Newborough Unified School District

This case was commissioned by Public Education Network (PEN) and prepared by the Rennie Center for Education Research and Policy. This case was designed for use at PEN's 2006 annual conference, and focuses on hiring practices within a fictitious city's school system

Educational Choice or Unfair Competition: Charter Schools in Benton

This case was commissioned by Public Education Network (PEN) and prepared by the Rennie Center for Education Research and Policy. This case was designed for use at PEN's 2006 annual conference, and focuses on the topic of charter schools and school choice in a fictitious large city

Educating English Language Learners in Dexter

This case was commissioned by Public Education Network (PEN) and prepared by the Rennie Center for Education Research and Policy. This case was designed for use at PEN's 2006 annual conference, and focuses on meeting the educational needs of English Language Learners (ELLs) in a fictitious community

A Time for Change: The Search for a New Superintendent in Carlton City

This case was commissioned by Public Education Network (PEN) and prepared by the Rennie Center for Education Research and Policy. This case was designed for use at PEN's 2006 annual conference, and focuses on a fictitious capital city's search for a new superintendent of schools

A filamentation instability for streaming cosmic-rays

We demonstrate that cosmic rays form filamentary structures in the precursors of supernova remnant shocks due to their self-generated magnetic fields. The cosmic-ray filamentation results in the growth of a long wavelength instability, and naturally couples the rapid non-linear amplification on small scales to larger length scales. Hybrid magnetohydrodynamics--particle simulations are performed to confirm the effect. The resulting large scale magnetic field may facilitate the scattering of high energy cosmic rays as required to accelerate protons beyond the knee in the cosmic-ray spectrum at supernova remnant shocks. Filamentation far upstream of the shock may also assist in the escape of cosmic rays from the accelerator.Comment: Accepted for publication in MNRA

Computation of synthetic spectra from simulations of relativistic shocks

Particle-in-cell (PIC) simulations of relativistic shocks are in principle capable of predicting the spectra of photons that are radiated incoherently by the accelerated particles. The most direct method evaluates the spectrum using the fields given by the Lienard-Wiechart potentials. However, for relativistic particles this procedure is computationally expensive. Here we present an alternative method, that uses the concept of the photon formation length. The algorithm is suitable for evaluating spectra both from particles moving in a specific realization of a turbulent electromagnetic field, or from trajectories given as a finite, discrete time series by a PIC simulation. The main advantage of the method is that it identifies the intrinsic spectral features, and filters out those that are artifacts of the limited time resolution and finite duration of input trajectories.Comment: Accepted for publication in the Astrophysical Journa

Modified Friedmann equations via conformal Bohm -- De Broglie gravity

We use an alternative interpretation of quantum mechanics, based on the Bohmian trajectory approach, and show that the quantum effects can be included in the classical equation of motion via a conformal transformation on the background metric. We apply this method to the Robertson-Walker metric to derive a modified version of Friedmann's equations for a Universe consisting of scalar, spin-zero, massive particles. These modified equations include additional terms that result from the non-local nature of matter and appear as an acceleration in the expansion of the Universe. We see that the same effect may also be present in the case of an inhomogeneous expansion.Comment: Accepted for publication in Ap

On the Cosmic Ray Driven Firehose Instability

The role of the non-resonant firehose instability in conditions relevant to the precursors of supernova remnant shocks is considered. Using a second order tensor expansion of the Vlasov-Fokker-Planck equation we illustrate the necessary conditions for the firehose to operate. It is found that for very fast shocks, the diffusion approximation predicts that the linear firehose growth rate is marginally faster than its resonant counterpart. Preliminary hybrid MHD-Vlasov-Fokker-Planck simulation results using young supernova relevant parameters are presented.Comment: Contribution to the 6th International Symposium on High Energy Gamma-Ray Astronomy (Gamma2016), Heidelberg, Germany. To be published in the AIP Conference Proceeding

Scaling of Magneto-Quantum-Radiative Hydrodynamic Equations: From Laser-produced Plasmas to Astrophysics

We introduce here the equations of magneto-quantum-radiative hydrodynamics. By rewriting them in a dimensionless form, we obtain a set of parameters that describe scale-dependent ratios of all the characteristic hydrodynamic quantities. We discuss how these dimensionless parameters relate to the scaling between astrophysical observations and laboratory experiments.Comment: 12 page