53,831 research outputs found
A note on the -coefficients of the "tree Eulerian polynomial"
We consider the generating polynomial of the number of rooted trees on the
set counted by the number of descending edges (a parent with
a greater label than a child). This polynomial is an extension of the descent
generating polynomial of the set of permutations of a totally ordered -set,
known as the Eulerian polynomial. We show how this extension shares some of the
properties of the classical one. B. Drake proved that this polynomial factors
completely over the integers. From his product formula it can be concluded that
this polynomial has positive coefficients in the -basis and we show
that a formula for these coefficients can also be derived. We discuss various
combinatorial interpretations of these positive coefficients in terms of
leaf-labeled binary trees and in terms of the Stirling permutations introduced
by Gessel and Stanley. These interpretations are derived from previous results
of the author and Wachs related to the poset of weighted partitions and the
free multibracketed Lie algebra.Comment: 13 pages, 6 figures, Interpretations derived from results in
arXiv:1309.5527 and arXiv:1408.541
High-resolution imaging spectroscopy of two micro-pores and an arch filament system in a small emerging-flux region
Aims. The purpose of this investigation is to characterize the temporal
evolution of an emerging flux region, the associated photospheric and
chromospheric flow fields, and the properties of the accompanying arch filament
system. Methods. This study is based on imaging spectroscopy with the
G\"ottingen Fabry-P\'erot Interferometer at the Vacuum Tower Telescope, on 2008
August 7. Cloud model (CM) inversions of line scans in the strong chromospheric
absorption H line yielded CM parameters, which describe the cool plasma
contained in the arch filament system. Results. The observations cover the
decay and convergence of two micro-pores with diameters of less than one
arcsecond and provide decay rates for intensity and area. The photospheric
horizontal flow speed is suppressed near the two micro-pores indicating that
the magnetic field is sufficiently strong to affect the convective energy
transport. The micro-pores are accompanied by an arch filament system, where
small-scale loops connect two regions with H line-core brightenings
containing an emerging flux region with opposite polarities. The chromospheric
velocity of the cloud material is predominantly directed downwards near the
footpoints of the loops with velocities of up to 12 km/s, whereas loop tops
show upward motions of about 3 km/s. Conclusions. Micro-pores are the smallest
magnetic field concentrations leaving a photometric signature in the
photosphere. In the observed case, they are accompanied by a miniature arch
filament system indicative of newly emerging flux in the form of
-loops. Flux emergence and decay take place on a time-scale of about
two days, whereas the photometric decay of the micro-pores is much more rapid
(a few hours), which is consistent with the incipient submergence of
-loops. The results are representative for the smallest emerging flux
regions still recognizable as such.Comment: 15 pages, 16 figures, 3 tables, published in A&
An event driven algorithm for fractal cluster formation
A new cluster based event-driven algorithm is developed to simulate the formation of clusters in a two dimensional gas: particles move freely until they collide and "stick" together irreversibly. These clusters aggregate into bigger structures in an isotompic way, forming fractal structures whose fractal dimension depends on the initial density of the system
Room temperature ferromagnetic-like behavior in Mn-implanted and post-annealed InAs layers deposited by Molecular Beam Epitaxy
We report on the magnetic and structural properties of Ar and Mn implanted
InAs epitaxial films grown on GaAs (100) by Molecular Beam Epitaxy (MBE) and
the effect of Rapid Thermal Annealing (RTA) for 30 seconds at 750C. Channeling
Particle Induced X- ray Emission (PIXE) experiments reveal that after Mn
implantation almost all Mn atoms are subsbtitutional in the In-site of the InAs
lattice, like in a diluted magnetic semiconductor (DMS). All of these samples
show diamagnetic behavior. But, after RTA treatment the Mn-InAs films exhibit
room-temperature magnetism. According to PIXE measurements the Mn atoms are no
longer substitutional. When the same set of experiments were performed with As
as implantation ion all of the layers present diamagnetism without exception.
This indicates that the appearance of room-temperature ferromagnetic-like
behavior in the Mn-InAs-RTA layer is not related to lattice disorder produce
during implantation, but to a Mn reaction produced after a short thermal
treatment. X-ray diffraction patterns (XRD) and Rutherford Back Scattering
(RBS) measurements evidence the segregation of an oxygen deficient-MnO2 phase
(nominally MnO1.94) in the Mn-InAs-RTA epitaxial layers which might be on the
origin of room temperature ferromagnetic-like response observed.Comment: 16 pages, 5 figures. Acepted in J. Appl. Phy
Unconventional quasiparticle lifetime in undoped graphene
We address the question of how small can the quasiparticle decay rate be at
low energies in undoped graphene, where kinematical constraints are known to
prevent the decay into particle-hole excitations. For this purpose, we study
the renormalization of the phonon dispersion by many-body effects, which turns
out to be very strong in the case of the out-of-plane phonons at the K point of
the spectrum. We show that these evolve into a branch of very soft modes that
provide the relevant channel for quasiparticle decay, at energies below the
scale of the optical phonon modes. In this regime, we find that the decay rate
is proportional to the cube of the quasiparticle energy. This implies that a
crossover should be observed in transport properties from the linear dependence
characteristic of the high-energy regime to the much slower decay rate due to
the soft phonon modes.Comment: 5 pages, 1 figur
On the (co)homology of the poset of weighted partitions
We consider the poset of weighted partitions , introduced by
Dotsenko and Khoroshkin in their study of a certain pair of dual operads. The
maximal intervals of provide a generalization of the lattice
of partitions, which we show possesses many of the well-known properties of
. In particular, we prove these intervals are EL-shellable, we show that
the M\"obius invariant of each maximal interval is given up to sign by the
number of rooted trees on on node set having a fixed number
of descents, we find combinatorial bases for homology and cohomology, and we
give an explicit sign twisted -module isomorphism from
cohomology to the multilinear component of the free Lie algebra with two
compatible brackets. We also show that the characteristic polynomial of
has a nice factorization analogous to that of .Comment: 50 pages, final version, to appear in Trans. AM
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