The Evolution of Adiabatic Supernova Remnants in a Turbulent, Magnetized Medium

(Abridged) We present the results of three dimensional calculations for the MHD evolution of an adiabatic supernova remnant in both a uniform and turbulent interstellar medium using the RIEMANN framework of Balsara. In the uniform case, which contains an initially uniform magnetic field, the density structure of the shell remains largely spherical, while the magnetic pressure and synchrotron emissivity are enhanced along the plane perpendicular to the field direction. This produces a bilateral or barrel-type morphology in synchrotron emission for certain viewing angles. We then consider a case with a turbulent external medium as in Balsara & Pouquet, characterized by $v_{A}(rms)/c_{s}=2$. Several important changes are found. First, despite the presence of a uniform field, the overall synchrotron emissivity becomes approximately spherically symmetric, on the whole, but is extremely patchy and time-variable, with flickering on the order of a few computational time steps. We suggest that the time and spatial variability of emission in early phase SNR evolution provides information on the turbulent medium surrounding the remnant. The shock-turbulence interaction is also shown to be a strong source of helicity-generation and, therefore, has important consequences for magnetic field generation. We compare our calculations to the Sedov-phase evolution, and discuss how the emission characteristics of SNR may provide a diagnostic on the nature of turbulence in the pre-supernova environment.Comment: ApJ, in press, 5 color figure

Second Order Accurate Schemes for Magnetohydrodynamics With Divergence-Free Reconstruction

In this paper we study the problem of divergence-free numerical MHD and show that the work done so far still has four key unresolved issues. We resolve those issues in this paper. The problem of reconstructing MHD flow variables with spatially second order accuracy is also studied. The other goal of this paper is to show that the same well-designed second order accurate schemes can be formulated for more complex geometries such as cylindrical and spherical geometry. Being able to do divergence-free reconstruction in those geometries also resolves the problem of doing AMR in those geometries. The resulting MHD scheme has been implemented in Balsara's RIEMANN framework for parallel, self-adaptive computational astrophysics. The present work also shows that divergence-free reconstruction and the divergence-free time-update can be done for numerical MHD on unstructured meshes. All the schemes designed here are shown to be second order accurate. Several stringent test problems are presented to show that the methods work, including problems involving high velocity flows in low plasma-b magnetospheric environments.Comment: 85 pages, 6 figure

Dust Settling in Magnetorotationally-Driven Turbulent Discs II: The Pervasiveness of the Streaming Instability and its Consequences

We present a series of simulations of turbulent stratified protostellar discs with the goal of characterizing the settling of dust throughout a minimum-mass solar nebula. We compare the evolution of both compact spherical grains, as well as highly fractal grains. Our simulations use a shearing-box formulation to study the evolution of dust grains locally within the disc, and collectively our simulations span the entire extent of a typical accretion disc. The dust is stirred by gas that undergoes MRI-driven turbulence. This establishes a steady state scale height for the dust that is different for dust of different sizes. This sedimentation of dust is an important first step in planet formation and we predict that ALMA should be able to observationally verify its existence. When significant sedimentation occurs, the dust will participate in a streaming instability that significantly enhances the dust density. We show that the streaming instability is pervasive in the outer disc. We characterize the scale heights of dust whose size ranges from a few microns to a few centimeters. We find that for spherical grains, a power-law relationship develops for the scale height with grain size, with a slope that is slightly steeper than -1/2. The sedimentation is strongest in the outer disc and increases for large grains. The results presented here show that direct measurements of grain settling can be made by ALMA and we present favorable conditions for observability. The streaming instability should also be directly observable and we provide conditions for directly observing it. We calculate collision rates and growth rates for the dust grains in our simulations of various sizes colliding with other grains, and find that these rates are significantly enhanced through the density enhancement arising from the streaming instability.Comment: 39 pages, 13 figures, submitted to MNRAS. Abstract is abridge

Measurement of Three Transport Coefficients and the Thermodynamic Factor in Block Copolymer Electrolytes with Different Morphologies.

The design and engineering of composite materials is one strategy to satisfy the materials needs of systems with multiple orthogonal property requirements. In the case of rechargeable batteries with lithium metal anodes, the system requires a separator with fast lithium ion transport and good mechanical strength. In this work, we focus on the system polystyrene-block-poly(ethylene oxide) (SEO) with bis(trifluoromethane)sulfonimide lithium salt (LiTFSI). Ion transport occurs in the salt-containing poly(ethylene oxide)-rich domains. Mechanical rigidity arises due to the glassy nature of polystyrene (PS). If we assume that the salt does not interact with the PS-rich domains, we can describe ion transport in the electrolyte by three transport parameters (ionic conductivity, κ, salt diffusion coefficient, D, and cation transference number, t+0) and a thermodynamic factor, Tf. By systematically varying the volume fraction of the conducting phase, ϕc between 0.29 and 1.0, and chain length, N between 80 and 8000, we elucidate the role of morphology on ion transport. We find that κ is the strongest function of morphology, varying by three full orders of magnitude, while D is a weaker function of morphology. To calculate t+0 and Tf, we measure the current fraction, ρ+, and the open circuit potential, U, of concentration cells. We find that ρ+ and U follow universal trends as a function of salt concentration, regardless of chain length, morphology, or ϕc, allowing us to calculate t+0 for any SEO/LiTFSI or PEO/LiTFSI mixture when κ and D are known. The framework developed in this paper enables predicting the performance of any block copolymer electrolyte in a rechargeable battery