A note on the γ\gamma-coefficients of the "tree Eulerian polynomial"

We consider the generating polynomial of the number of rooted trees on the set $\{1,2,\dots,n\}$ 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 $n$-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 $\gamma$-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$\alpha$ 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$\alpha$ 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 $\Omega$-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 $\Omega$-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

On the (co)homology of the poset of weighted partitions

We consider the poset of weighted partitions $\Pi_n^w$, introduced by Dotsenko and Khoroshkin in their study of a certain pair of dual operads. The maximal intervals of $\Pi_n^w$ provide a generalization of the lattice $\Pi_n$ of partitions, which we show possesses many of the well-known properties of $\Pi_n$. 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 $\{1,2,\dots,n\}$ having a fixed number of descents, we find combinatorial bases for homology and cohomology, and we give an explicit sign twisted $\mathfrak{S}_n$-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 $\Pi_n^w$ has a nice factorization analogous to that of $\Pi_n$.Comment: 50 pages, final version, to appear in Trans. AM

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