785 research outputs found
Adaptive Mesh Refinement for Supersonic Molecular Cloud Turbulence
We performed a series of three-dimensional numerical simulations of
supersonic homogeneous Euler turbulence with adaptive mesh refinement (AMR) and
effective grid resolution up to 1024^3 zones. Our experiments describe
non-magnetized driven supersonic turbulent flows with an isothermal equation of
state. Mesh refinement on shocks and shear is implemented to cover dynamically
important structures with the highest resolution subgrids and calibrated to
match the turbulence statistics obtained from the equivalent uniform grid
simulations.
We found that at a level of resolution slightly below 512^3, when a
sufficient integral/dissipation scale separation is first achieved, the
fraction of the box volume covered by the AMR subgrids first becomes smaller
than unity. At the higher AMR levels subgrids start covering smaller and
smaller fractions of the whole volume, which scale with the Reynolds number as
Re^{-1/4}. We demonstrate the consistency of this scaling with a hypothesis
that the most dynamically important structures in intermittent supersonic
turbulence are strong shocks with a fractal dimension of two. We show that
turbulence statistics derived from AMR simulations and simulations performed on
uniform grids agree surprisingly well, even though only a fraction of the
volume is covered by AMR subgrids. Based on these results, we discuss the
signature of dissipative structures in the statistical properties of supersonic
turbulence and their role in overall flow dynamics.Comment: 5 pages, 5 figures, revised versio
The Two States of Star Forming Clouds
We examine the effects of self-gravity and magnetic fields on supersonic
turbulence in isothermal molecular clouds with high resolution simulations and
adaptive mesh refinement. These simulations use large root grids (512^3) to
capture turbulence and four levels of refinement to capture high density, for
an effective resolution of 8,196^3. Three Mach 9 simulations are performed, two
super-Alfv\'enic and one trans-Alfv\'enic. We find that gravity splits the
clouds into two populations, one low density turbulent state and one high
density collapsing state. The low density state exhibits properties similar to
non-self-gravitating in this regime, and we examine the effects of varied
magnetic field strength on statistical properties: the density probability
distribution function is approximately lognormal; velocity power spectral
slopes decrease with field strength; alignment between velocity and magnetic
field increases with field; the magnetic field probability distribution can be
fit to a stretched exponential. The high density state is characterized by
self-similar spheres; the density PDF is a power-law; collapse rate decreases
with increasing mean field; density power spectra have positive slopes,
P({\rho},k) \propto k; thermal-to-magnetic pressure ratios are unity for all
simulations; dynamic-to-magnetic pressure ratios are larger than unity for all
simulations; magnetic field distribution is a power-law. The high Alfv\'en Mach
numbers in collapsing regions explain recent observations of magnetic influence
decreasing with density. We also find that the high density state is found in
filaments formed by converging flows, consistent with recent Herschel
observations. Possible modifications to existing star formation theories are
explored.Comment: 19 pages, 20 figure
Dispersion of Observed Position Angles of Submillimeter Polarization in Molecular Clouds
One can estimate the characteristic magnetic field strength in GMCs by
comparing submillimeter polarimetric observations of these sources with
simulated polarization maps developed using a range of different values for the
assumed field strength. The point of comparison is the degree of order in the
distribution of polarization position angles. In a recent paper by H. Li and
collaborators, such a comparison was carried out using SPARO observations of
two GMCs, and employing simulations by E. Ostriker and collaborators. Here we
reexamine this same question, using the same data set and the same simulations,
but using an approach that differs in several respects. The most important
difference is that we incorporate new, higher angular resolution observations
for one of the clouds, obtained using the Hertz polarimeter. We conclude that
the agreement between observations and simulations is best when the total
magnetic energy (including both uniform and fluctuating field components) is at
least as large as the turbulent kinetic energy.Comment: revised, accepted version; to appear in The Astrophysical Journal; 20
pages, 2 figures, 2 table
Voices and Colors of Murano, Italy
Title: Voices and Colors of Murano, Italy
Author: Stefano G. Padoan
This collection of poetry displays the voices and colors of Murano, Italy, where I have spent a lifetime of summers. With this collection, I hope to capture the details of the island as well of the hearts of its’ people
Scaling Laws and Intermittency in Highly Compressible Turbulence
We use large-scale three-dimensional simulations of supersonic Euler
turbulence to study the physics of a highly compressible cascade. Our numerical
experiments describe non-magnetized driven turbulent flows with an isothermal
equation of state and an rms Mach number of 6. We find that the inertial range
velocity scaling deviates strongly from the incompressible Kolmogorov laws. We
propose an extension of Kolmogorov's K41 phenomenology that takes into account
compressibility by mixing the velocity and density statistics and preserves the
K41 scaling of the density-weighted velocity v=rho^{1/3}u. We show that
low-order statistics of 'v' are invariant with respect to changes in the Mach
number. For instance, at Mach 6 the slope of the power spectrum of 'v' is -1.69
and the third-order structure function of 'v' scales linearly with separation.
We directly measure the mass dimension of the "fractal" density distribution in
the inertial subrange, D_m=2.4, which is similar to the observed fractal
dimension of molecular clouds and agrees well with the cascade phenomenology.Comment: 7 pages, 3 figures; in press, AIP Conference Proceedings: "Turbulence
and Nonlinear Processes in Astrophysical Plasmas", Waikiki Beach, Hawaii,
March 21, 200
Multivariate Nonparametric Estimation of the Pickands Dependence Function using Bernstein Polynomials
Many applications in risk analysis, especially in environmental sciences,
require the estimation of the dependence among multivariate maxima. A way to do
this is by inferring the Pickands dependence function of the underlying
extreme-value copula. A nonparametric estimator is constructed as the sample
equivalent of a multivariate extension of the madogram. Shape constraints on
the family of Pickands dependence functions are taken into account by means of
a representation in terms of a specific type of Bernstein polynomials. The
large-sample theory of the estimator is developed and its finite-sample
performance is evaluated with a simulation study. The approach is illustrated
by analyzing clusters consisting of seven weather stations that have recorded
weekly maxima of hourly rainfall in France from 1993 to 2011
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
Simulating Supersonic Turbulence in Magnetized Molecular Clouds
We present results of large-scale three-dimensional simulations of weakly
magnetized supersonic turbulence at grid resolutions up to 1024^3 cells. Our
numerical experiments are carried out with the Piecewise Parabolic Method on a
Local Stencil and assume an isothermal equation of state. The turbulence is
driven by a large-scale isotropic solenoidal force in a periodic computational
domain and fully develops in a few flow crossing times. We then evolve the flow
for a number of flow crossing times and analyze various statistical properties
of the saturated turbulent state. We show that the energy transfer rate in the
inertial range of scales is surprisingly close to a constant, indicating that
Kolmogorov's phenomenology for incompressible turbulence can be extended to
magnetized supersonic flows. We also discuss numerical dissipation effects and
convergence of different turbulence diagnostics as grid resolution refines from
256^3 to 1024^3 cells.Comment: 10 pages, 3 figures, to appear in the proceedings of the DOE/SciDAC
2009 conferenc
- …