Similarity Measure Development for Case-Based Reasoning- A Data-driven Approach

In this paper, we demonstrate a data-driven methodology for modelling the local similarity measures of various attributes in a dataset. We analyse the spread in the numerical attributes and estimate their distribution using polynomial function to showcase an approach for deriving strong initial value ranges of numerical attributes and use a non-overlapping distribution for categorical attributes such that the entire similarity range [0,1] is utilized. We use an open source dataset for demonstrating modelling and development of the similarity measures and will present a case-based reasoning (CBR) system that can be used to search for the most relevant similar cases

Comparing Numerical Methods for Isothermal Magnetized Supersonic Turbulence

We employ simulations of supersonic super-Alfvenic turbulence decay as a benchmark test problem to assess and compare the performance of nine astrophysical MHD methods actively used to model star formation. The set of nine codes includes: ENZO, FLASH, KT-MHD, LL-MHD, PLUTO, PPML, RAMSES, STAGGER, and ZEUS. We present a comprehensive set of statistical measures designed to quantify the effects of numerical dissipation in these MHD solvers. We compare power spectra for basic fields to determine the effective spectral bandwidth of the methods and rank them based on their relative effective Reynolds numbers. We also compare numerical dissipation for solenoidal and dilatational velocity components to check for possible impacts of the numerics on small-scale density statistics. Finally, we discuss convergence of various characteristics for the turbulence decay test and impacts of various components of numerical schemes on the accuracy of solutions. We show that the best performing codes employ a consistently high order of accuracy for spatial reconstruction of the evolved fields, transverse gradient interpolation, conservation law update step, and Lorentz force computation. The best results are achieved with divergence-free evolution of the magnetic field using the constrained transport method, and using little to no explicit artificial viscosity. Codes which fall short in one or more of these areas are still useful, but they must compensate higher numerical dissipation with higher numerical resolution. This paper is the largest, most comprehensive MHD code comparison on an application-like test problem to date. We hope this work will help developers improve their numerical algorithms while helping users to make informed choices in picking optimal applications for their specific astrophysical problems.Comment: 17 pages, 5 color figures, revised version to appear in ApJ, 735, July 201

The Effects of Large-Scale Magnetic Fields on Disk Formation and Evolution

This is a draft chapter for a book, entitled Physical Processes in Circumstellar Disks around Young Stars, which is scheduled for publication by the University of Chicago Press as one of its Theoretical Astrophysics Series volumes. Sect. 1 presents the motivation for considering the effects of a large-scale, ordered magnetic field on the formation and evolution of protostellar disks. Sect. 2 outlines the physical principles that underlie the magnetohydrodynamics of disks that are threaded by such a field. Sect. 3 discusses the formation and early evolution of disks that result from the collapse of a rotating molecular cloud core that is coupled to the insterstellar magnetic field. Sect. 4 reviews the observational evidence for the disk--wind connection and describes the structure of magnetically accelerated disk outflows, focusing on centrifugally driven winds; it then goes on to discuss the equilibrium and stability properties of weakly ionized protostellar accretion disks in which the transport of angular momentum is dominated by a wind of this type. Sect. 5 considers the coupling between the central protostar and the surrounding disk through the protostellar magnetic field, covering, in turn, the phenomenology, basic concepts, and results of numerical simulations. The chapter is summarized in Sect. 6, which also contains a discussion of future research directions.Comment: 68 pages, 8 figures, to appear in Physical Processes in Circumstellar Disks around Young Stars, ed. P. J. V. Garcia (Chicago: University of Chicago Press), uses svmult.cl