388 research outputs found
Entropy Stable Finite Volume Approximations for Ideal Magnetohydrodynamics
This article serves as a summary outlining the mathematical entropy analysis
of the ideal magnetohydrodynamic (MHD) equations. We select the ideal MHD
equations as they are particularly useful for mathematically modeling a wide
variety of magnetized fluids. In order to be self-contained we first motivate
the physical properties of a magnetic fluid and how it should behave under the
laws of thermodynamics. Next, we introduce a mathematical model built from
hyperbolic partial differential equations (PDEs) that translate physical laws
into mathematical equations. After an overview of the continuous analysis, we
thoroughly describe the derivation of a numerical approximation of the ideal
MHD system that remains consistent to the continuous thermodynamic principles.
The derivation of the method and the theorems contained within serve as the
bulk of the review article. We demonstrate that the derived numerical
approximation retains the correct entropic properties of the continuous model
and show its applicability to a variety of standard numerical test cases for
MHD schemes. We close with our conclusions and a brief discussion on future
work in the area of entropy consistent numerical methods and the modeling of
plasmas
Ideal GLM-MHD - a new mathematical model for simulating astrophysical plasmas
Magnetic fields are ubiquitous in space. As there is strong evidence that magnetic fields play an important role in a variety of astrophysical processes, they should not be neglected recklessly. However, analytic models in astrophysical either do often not take magnetic fields into account or can do this after limiting simplifications reducing their overall predictive power. Therefore, computational astrophysics has evolved as a modern field of research using sophisticated computer simulations to gain insight into physical processes.
The ideal MHD equations, which are the most often used basis for simulating magnetized plasmas, have two critical drawbacks: Firstly, they do not limit the growth of numerically caused magnetic monopoles, and, secondly, most numerical schemes built from the ideal MHD equations are not conformable with thermodynamics.
In my work, at the interplay of math and physics, I developed and presented the first thermodynamically consistent model with effective inbuilt divergence cleaning. My new Galilean-invariant model is suitable for simulating magnetized plasmas under extreme conditions as those typically encountered in astrophysical scenarios. The new model is called the "ideal GLM-MHD" equations and supports nine wave solutions.
The accuracy and robustness of my numerical implementation are demonstrated with a number of tests, including comparisons to other schemes available within in the multi-physics, multi-scale adaptive mesh refinement (AMR) simulation code FLASH. A possible astrophysical application scenario is discussed in detail
The SILCC (SImulating the LifeCycle of molecular Clouds) project: I. Chemical evolution of the supernova-driven ISM
The SILCC project (SImulating the Life-Cycle of molecular Clouds) aims at a
more self-consistent understanding of the interstellar medium (ISM) on small
scales and its link to galaxy evolution. We simulate the evolution of the
multi-phase ISM in a 500 pc x 500 pc x 10 kpc region of a galactic disc, with a
gas surface density of .
The Flash 4.1 simulations include an external potential, self-gravity, magnetic
fields, heating and radiative cooling, time-dependent chemistry of H and CO
considering (self-) shielding, and supernova (SN) feedback. We explore SN
explosions at different (fixed) rates in high-density regions (peak), in random
locations (random), in a combination of both (mixed), or clustered in space and
time (clustered). Only random or clustered models with self-gravity (which
evolve similarly) are in agreement with observations. Molecular hydrogen forms
in dense filaments and clumps and contributes 20% - 40% to the total mass,
whereas most of the mass (55% - 75%) is in atomic hydrogen. The ionised gas
contributes <10%. For high SN rates (0.5 dex above Kennicutt-Schmidt) as well
as for peak and mixed driving the formation of H is strongly suppressed.
Also without self-gravity the H fraction is significantly lower (
5%). Most of the volume is filled with hot gas (90% within 2 kpc).
Only for random or clustered driving, a vertically expanding warm component of
atomic hydrogen indicates a fountain flow. Magnetic fields have little impact
on the final disc structure. However, they affect dense gas () and delay H formation. We highlight that individual chemical
species, in particular atomic hydrogen, populate different ISM phases and
cannot be accurately accounted for by simple temperature-/density-based phase
cut-offs.Comment: 30 pages, 23 figures, submitted to MNRAS. Comments welcome! For
movies of the simulations and download of selected Flash data see the SILCC
website: http://www.astro.uni-koeln.de/silc
The SILCC project: III. Regulation of star formation and outflows by stellar winds and supernovae
We study the impact of stellar winds and supernovae on the multi-phase
interstellar medium using three-dimensional hydrodynamical simulations carried
out with FLASH. The selected galactic disc region has a size of (500 pc) x
5 kpc and a gas surface density of 10 M/pc. The simulations
include an external stellar potential and gas self-gravity, radiative cooling
and diffuse heating, sink particles representing star clusters, stellar winds
from these clusters which combine the winds from indi- vidual massive stars by
following their evolution tracks, and subsequent supernova explosions. Dust and
gas (self-)shielding is followed to compute the chemical state of the gas with
a chemical network. We find that stellar winds can regulate star (cluster)
formation. Since the winds suppress the accretion of fresh gas soon after the
cluster has formed, they lead to clusters which have lower average masses
(10 - 10 M) and form on shorter timescales (10 -
10 Myr). In particular we find an anti-correlation of cluster mass and
accretion time scale. Without winds the star clusters easily grow to larger
masses for ~5 Myr until the first supernova explodes. Overall the most massive
stars provide the most wind energy input, while objects beginning their
evolution as B-type stars contribute most of the supernova energy input. A
significant outflow from the disk (mass loading 1 at 1 kpc) can be
launched by thermal gas pressure if more than 50% of the volume near the disc
mid-plane can be heated to T > 3x10 K. Stellar winds alone cannot create a
hot volume-filling phase. The models which are in best agreement with observed
star formation rates drive either no outflows or weak outflows.Comment: 23 pages; submitted to MNRA
A Compact Linear Programming Relaxation for Binary Sub-modular MRF
We propose a novel compact linear programming (LP) relaxation for binary
sub-modular MRF in the context of object segmentation. Our model is obtained by
linearizing an -norm derived from the quadratic programming (QP) form of
the MRF energy. The resultant LP model contains significantly fewer variables
and constraints compared to the conventional LP relaxation of the MRF energy.
In addition, unlike QP which can produce ambiguous labels, our model can be
viewed as a quasi-total-variation minimization problem, and it can therefore
preserve the discontinuities in the labels. We further establish a relaxation
bound between our LP model and the conventional LP model. In the experiments,
we demonstrate our method for the task of interactive object segmentation. Our
LP model outperforms QP when converting the continuous labels to binary labels
using different threshold values on the entire Oxford interactive segmentation
dataset. The computational complexity of our LP is of the same order as that of
the QP, and it is significantly lower than the conventional LP relaxation
Lower Critical Dimension of Ising Spin Glasses
Exact ground states of two-dimensional Ising spin glasses with Gaussian and
bimodal (+- J) distributions of the disorder are calculated using a
``matching'' algorithm, which allows large system sizes of up to N=480^2 spins
to be investigated. We study domain walls induced by two rather different types
of boundary-condition changes, and, in each case, analyze the system-size
dependence of an appropriately defined ``defect energy'', which we denote by
DE. For Gaussian disorder, we find a power-law behavior DE ~ L^\theta, with
\theta=-0.266(2) and \theta=-0.282(2) for the two types of boundary condition
changes. These results are in reasonable agreement with each other, allowing
for small systematic effects. They also agree well with earlier work on smaller
sizes. The negative value indicates that two dimensions is below the lower
critical dimension d_c. For the +-J model, we obtain a different result, namely
the domain-wall energy saturates at a nonzero value for L\to \infty, so \theta
= 0, indicating that the lower critical dimension for the +-J model exactly
d_c=2.Comment: 4 pages, 4 figures, 1 table, revte
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