968 research outputs found
The Price of Anarchy for Selfish Ring Routing is Two
We analyze the network congestion game with atomic players, asymmetric
strategies, and the maximum latency among all players as social cost. This
important social cost function is much less understood than the average
latency. We show that the price of anarchy is at most two, when the network is
a ring and the link latencies are linear. Our bound is tight. This is the first
sharp bound for the maximum latency objective.Comment: Full version of WINE 2012 paper, 24 page
Convex Hull of Arithmetic Automata
Arithmetic automata recognize infinite words of digits denoting
decompositions of real and integer vectors. These automata are known expressive
and efficient enough to represent the whole set of solutions of complex linear
constraints combining both integral and real variables. In this paper, the
closed convex hull of arithmetic automata is proved rational polyhedral.
Moreover an algorithm computing the linear constraints defining these convex
set is provided. Such an algorithm is useful for effectively extracting
geometrical properties of the whole set of solutions of complex constraints
symbolically represented by arithmetic automata
Parameters of the Magnetic Flux inside Coronal Holes
Parameters of magnetic flux distribution inside low-latitude coronal holes
(CHs) were analyzed. A statistical study of 44 CHs based on Solar and
Heliospheric Observatory (SOHO)/MDI full disk magnetograms and SOHO/EIT 284\AA
images showed that the density of the net magnetic flux, , does
not correlate with the associated solar wind speeds, . Both the area and
net flux of CHs correlate with the solar wind speed and the corresponding
spatial Pearson correlation coefficients are 0.75 and 0.71, respectively. A
possible explanation for the low correlation between and
is proposed. The observed non-correlation might be rooted in the structural
complexity of the magnetic field. As a measure of complexity of the magnetic
field, the filling factor, , was calculated as a function of spatial
scales. In CHs, was found to be nearly constant at scales above 2 Mm,
which indicates a monofractal structural organization and smooth temporal
evolution. The magnitude of the filling factor is 0.04 from the Hinode SOT/SP
data and 0.07 from the MDI/HR data. The Hinode data show that at scales smaller
than 2 Mm, the filling factor decreases rapidly, which means a mutlifractal
structure and highly intermittent, burst-like energy release regime. The
absence of necessary complexity in CH magnetic fields at scales above 2 Mm
seems to be the most plausible reason why the net magnetic flux density does
not seem to be related to the solar wind speed: the energy release dynamics,
needed for solar wind acceleration, appears to occur at small scales below 1
Mm.Comment: 6 figures, approximately 23 pages. Accepted in Solar Physic
An Ab Initio Approach to the Solar Coronal Heating Problem
We present an ab initio approach to the solar coronal heating problem by
modelling a small part of the solar corona in a computational box using a 3D
MHD code including realistic physics. The observed solar granular velocity
pattern and its amplitude and vorticity power spectra, as reproduced by a
weighted Voronoi tessellation method, are used as a boundary condition that
generates a Poynting flux in the presence of a magnetic field. The initial
magnetic field is a potential extrapolation of a SOHO/MDI high resolution
magnetogram, and a standard stratified atmosphere is used as a thermal initial
condition. Except for the chromospheric temperature structure, which is kept
fixed, the initial conditions are quickly forgotten because the included
Spitzer conductivity and radiative cooling function have typical timescales
much shorter than the time span of the simulation. After a short initial start
up period, the magnetic field is able to dissipate 3-4 10^6 ergs cm^{-2} s^{-1}
in a highly intermittent corona, maintaining an average temperature of K, at coronal density values for which emulated images of the Transition
Region And Coronal Explorer(TRACE) 171 and 195 pass bands reproduce observed
photon count rates.Comment: 12 pages, 14 figures. Submitted to Ap
Nonlinear force-free and potential field models of active-region and global coronal fields during the Whole Heliospheric Interval
Between 2008/3/24 and 2008/4/2, the three active regions NOAA active regions
10987, 10988 and 10989 were observed daily by the Synoptic Optical Long-term
Investigations of the Sun (SOLIS) Vector Spectro-Magnetograph (VSM) while they
traversed the solar disk. We use these measurements and the nonlinear
force-free magnetic field code XTRAPOL to reconstruct the coronal magnetic
field for each active region and compare model field lines with images from the
Solar Terrestrial RElations Observatory (STEREO) and Hinode X-ray Telescope
(XRT) telescopes. Synoptic maps made from continuous, round-the-clock Global
Oscillations Network Group (GONG) magnetograms provide information on the
global photospheric field and potential-field source-surface models based on
these maps describe the global coronal field during the Whole Heliospheric
Interval (WHI) and its neighboring rotations. Features of the modeled global
field, such as the coronal holes and streamer belt locations, are discussed in
comparison with extreme ultra-violet and coronagraph observations from STEREO.
The global field is found to be far from a minimum, dipolar state. From the
nonlinear models we compute physical quantities for the active regions such as
the photospheric magnetic and electric current fluxes, the free magnetic energy
and the relative helicity for each region each day where observations permit.
The interconnectivity of the three regions is addressed in the context of the
potential-field source-surface model. Using local and global quantities derived
from the models, we briefly discuss the different observed activity levels of
the regions.Comment: Accepted for publication in the Solar Physics Whole Heliospheric
Interval (WHI) topical issue. We had difficulty squeezing this paper into
arXiv's 15 Mb limit. The full paper is available here
ftp://gong2.nso.edu/dsds_user/petrie/PetrieCanouAmari.pd
On Generalizations of Network Design Problems with Degree Bounds
Iterative rounding and relaxation have arguably become the method of choice
in dealing with unconstrained and constrained network design problems. In this
paper we extend the scope of the iterative relaxation method in two directions:
(1) by handling more complex degree constraints in the minimum spanning tree
problem (namely, laminar crossing spanning tree), and (2) by incorporating
`degree bounds' in other combinatorial optimization problems such as matroid
intersection and lattice polyhedra. We give new or improved approximation
algorithms, hardness results, and integrality gaps for these problems.Comment: v2, 24 pages, 4 figure
The Hilbert basis method for D-flat directions and the superpotential
We discuss, using the Hilbert basis method, how to efficiently construct a
complete basis for D-flat directions in supersymmetric Abelian and non-Abelian
gauge theories. We extend the method to discrete (R and non-R) symmetries. This
facilitates the construction of a basis of all superpotential terms in a theory
with given symmetries.Comment: 11 pages; a related mathematica code can be found at
http://einrichtungen.ph.tum.de/T30e/codes/NonAbelianHilbert
Stellar models of evolved secondaries in CVs
In this paper we study the impact of chemically evolved secondaries on CV
evolution. We find that when evolved secondaries are included a spread in the
secondary mass-orbital period plane comparable to that seen in the data is
produced for either the saturated prescription for magnetic braking or the
unsaturated model commonly used for CVs. We argue that in order to explain this
spread a considerable fraction of all CVs should have evolved stars as the
secondaries. The evolved stars become fully convective at lower orbital
periods. Therefore, even if there was an abrupt decrease in magnetic braking
for fully convective stars (contrary to open cluster data) it would not be
expected to produce a sharp break in the period distribution for CVs. We also
explore recent proposed revisions to the angular momentum loss rate for single
stars, and find that only modest increases over the saturated prescription are
consistent with the overall observed spindown pattern. We compare predictions
of our models with diagnostics of the mass accretion rate in WDs and find
results intermediate between the saturated and the older braking prescription.
Taken together these suggest that the angular momentum loss rate may be higher
in CV secondaries than in single stars of the same rotation period, but is
still significantly lower than in the traditional model. Alternative
explanations for the CV period gap are discussed.Comment: 24 pages, 9 figures. Submitted to Ap
Testing magnetofrictional extrapolation with the Titov-D\'emoulin model of solar active regions
We examine the nonlinear magnetofrictional extrapolation scheme using the
solar active region model by Titov and D\'emoulin as test field. This model
consists of an arched, line-tied current channel held in force-free equilibrium
by the potential field of a bipolar flux distribution in the bottom boundary. A
modified version, having a parabolic current density profile, is employed here.
We find that the equilibrium is reconstructed with very high accuracy in a
representative range of parameter space, using only the vector field in the
bottom boundary as input. Structural features formed in the interface between
the flux rope and the surrounding arcade-"hyperbolic flux tube" and "bald patch
separatrix surface"-are reliably reproduced, as are the flux rope twist and the
energy and helicity of the configuration. This demonstrates that force-free
fields containing these basic structural elements of solar active regions can
be obtained by extrapolation. The influence of the chosen initial condition on
the accuracy of reconstruction is also addressed, confirming that the initial
field that best matches the external potential field of the model quite
naturally leads to the best reconstruction. Extrapolating the magnetogram of a
Titov-D\'emoulin equilibrium in the unstable range of parameter space yields a
sequence of two opposing evolutionary phases which clearly indicate the
unstable nature of the configuration: a partial buildup of the flux rope with
rising free energy is followed by destruction of the rope, losing most of the
free energy.Comment: 14 pages, 10 figure
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