Universality in Blow-Up for Nonlinear Heat Equations

We consider the classical problem of the blowing-up of solutions of the nonlinear heat equation. We show that there exist infinitely many profiles around the blow-up point, and for each integer $k$, we construct a set of codimension $2k$ in the space of initial data giving rise to solutions that blow-up according to the given profile.Comment: 38 page

New accurate measurement of 36ArH+ and 38ArH+ ro-vibrational transitions by high resolution IR absorption spectroscopy

The protonated Argon ion, $^{36}$ArH$^{+}$, has been identified recently in the Crab Nebula (Barlow et al. 2013) from Herschel spectra. Given the atmospheric opacity at the frequency of its $J$=1-0 and $J$=2-1 rotational transitions (617.5 and 1234.6 GHz, respectively), and the current lack of appropriate space observatories after the recent end of the Herschel mission, future studies on this molecule will rely on mid-infrared observations. We report on accurate wavenumber measurements of $^{36}$ArH$^{+}$ and $^{38}$ArH$^{+}$ rotation-vibration transitions in the $v$=1-0 band in the range 4.1-3.7 $\mu$m (2450-2715 cm$^{-1}$). The wavenumbers of the $R$(0) transitions of the $v$=1-0 band are 2612.50135$\pm$0.00033 and 2610.70177$\pm$0.00042 cm$^{-1}$ ($\pm3\sigma$) for $^{36}$ArH$^{+}$ and $^{38}$ArH$^{+}$, respectively. The calculated opacity for a gas thermalized at a temperature of 100 K and a linewidth of 1 km.s$^{-1}$ of the $R$(0) line is $1.6\times10^{-15}\times N$($^{36}$ArH$^+$). For column densities of $^{36}$ArH$^+$ larger than $1\times 10^{13}$ cm$^{-2}$, significant absorption by the $R$(0) line can be expected against bright mid-IR sources

Analyzing the external social capital of family firms

We examine an important yet overlooked aspect in research on social capital: the familial bonding that interorganizational relations may hold. We argue that the social identity of a family member is likely to reframe how they behave within social relations and towards actors outside the firm that are within or not within the family, changing the conditions for trust, knowledge exchange, and value creation. Drawing on a family and nonfamily classification of interorganizational relations, we examine: 1) theoretically and empirically the extent to which relationships with family members located in other related firms, which we define as external family social capital (EFSC), affect firm performance; (2) its interaction with relationships with members of other firms not bearing a family connection, referred to as external organizational social capital (EOSC); and (3) the varying levels of trust required to extract value from EFSC and EOSC

Improved determination of the 1(0)-0(0) rotational frequency of NH3D+ from the high resolution spectrum of the v4 infrared band

The high resolution spectrum of the v4 band of NH3D+ has been measured by difference frequency IR laser spectroscopy in a multipass hollow cathode discharge cell. From the set of molecular constants obtained from the analysis of the spectrum, a value of 262817(6) MHz (3sigma) has been derived for the frequency of the 1(0)-0(0) rotational transition. This value supports the assignment to NH3D+ of lines at 262816.7 MHz recorded in radio astronomy observations in Orion-IRc2 and the cold prestellar core B1-bS.Comment: Accepted for publication in the Astrophysical Journal Letters 04 June 201

Testing Supersymmetry with Lepton Flavor Violating tau and mu decays

In this work the following lepton flavor violating $\tau$ and $\mu$ decays are studied: $\tau^- \to \mu^- \mu^- \mu^+$, $\tau^- \to e^- e^- e^+$, $\mu^- \to e^- e^- e^+$, $\tau^- \to \mu^- \gamma$, $\tau^- \to e^- \gamma$ and $\mu^- \to e^- \gamma$. We work in a supersymmetric scenario consisting of the minimal supersymmetric standard model particle content, extended by the addition of three heavy right handed Majorana neutrinos and their supersymmetric partners, and where the generation of neutrino masses is done via the seesaw mechanism. Within this context, a significant lepton flavor mixing is generated in the slepton sector due to the Yukawa neutrino couplings, which is transmited from the high to the low energies via the renormalization group equations. This slepton mixing then generates via loops of supersymmetric particles significant contributions to the rates of $l_j \to 3 l_i$ and the correlated $l_j \to l_i \gamma$ decays. We analize here in full detail these rates in terms of the relevant input parameters, which are the usual minimal supergravity parameters and the seesaw parameters. For the $l_j \to 3 l_i$ decays, a full one-loop analytical computation of all the contributing supersymmetric loops is presented. This completes and corrects previous computations in the literature. In the numerical analysis compatibility with the most recent experimental upper bounds on all these $\tau$ and $\mu$ decays, with the neutrino data, and with the present lower bounds on the supersymmetric particle masses are required. Two typical scenarios with degenerate and hierarchical heavy neutrinos are considered. We will show here that the minimal supergravity and seesaw parameters do get important restrictions from these $\tau$ and $\mu$ decays in the hierarchical neutrino case.Comment: Version to appear in Physical Review

Hydrogen and muonium in diamond: A path-integral molecular dynamics simulation

Isolated hydrogen, deuterium, and muonium in diamond have been studied by path-integral molecular dynamics simulations in the canonical ensemble. Finite-temperature properties of these point defects were analyzed in the range from 100 to 800 K. Interatomic interactions were modeled by a tight-binding potential fitted to density-functional calculations. The most stable position for these hydrogenic impurities is found at the C-C bond center. Vibrational frequencies have been obtained from a linear-response approach, based on correlations of atom displacements at finite temperatures. The results show a large anharmonic effect in impurity vibrations at the bond center site, which hardens the vibrational modes with respect to a harmonic approximation. Zero-point motion causes an appreciable shift of the defect level in the electronic gap, as a consequence of electron-phonon interaction. This defect level goes down by 70 meV when replacing hydrogen by muonium.Comment: 11 pages, 8 figure

Outflows of hot molecular gas in ultra-luminous infra-red galaxies mapped with VLT-SINFONI

We present the detection and morphological characterization of hot molecular gas outflows in nearby ultra-luminous infrared galaxies, using the near-IR integral-field spectrograph SINFONI on the VLT. We detect outflows observed in the 2.12 micron H$_{2}$ 1-0 S(1) line for three out of four ULIRGs analyzed; IRAS 12112+0305, 14348-1447, and 22491-1808. The outflows are mapped on scales of 0.7-1.6 kpc, show typical outflow velocities of 300-500 km/s, and appear to originate from the nuclear region. The outflows comprise hot molecular gas masses of ~6-8x10$^3$ M(sun). Assuming a hot-to-cold molecular gas mass ratio of 6x10$^{-5}$, as found in nearby luminous IR galaxies, the total (hot+cold) molecular gas mass in these outflows is expected to be ~1x10$^{8}$ M(sun). This translates into molecular mass outflow rates of ~30-85 M(sun)/yr, which is a factor of a few lower than the star formation rate in these ULIRGs. In addition, most of the outflowing molecular gas does not reach the escape velocity of these merger systems, which implies that the bulk of the outflowing molecular gas is re-distributed within the system and thus remains available for future star formation. The fastest H$_{2}$ outflow is seen in the Compton-thick AGN of IRAS 14348-1447, reaching a maximum outflow velocity of ~900 km/s. Another ULIRG, IRAS 17208-0014, shows asymmetric H$_{2}$ line profiles different from the outflows seen in the other three ULIRGs. We discuss several alternative explanations for its line asymmetries, including a very gentle galactic wind, internal gas dynamics, low-velocity gas outside the disk, or two superposed gas disks. We do not detect the hot molecular counterpart to the outflow previously detected in CO(2-1) in IRAS 17208-0014, but we note that our SINFONI data are not sensitive enough to detect this outflow if it has a small hot-to-cold molecular gas mass ratio of < 9x10$^{-6}$.Comment: Accepted for publication in A&A (11 pages, 10 figures

Kinetic growth walks on complex networks

Kinetically grown self-avoiding walks on various types of generalized random networks have been studied. Networks with short- and long-tailed degree distributions $P(k)$ were considered ($k$, degree or connectivity), including scale-free networks with $P(k) \sim k^{-\gamma}$. The long-range behaviour of self-avoiding walks on random networks is found to be determined by finite-size effects. The mean self-intersection length of non-reversal random walks, , scales as a power of the system size $N$: $ \sim N^{\beta}$, with an exponent $\beta = 0.5$ for short-tailed degree distributions and $\beta < 0.5$ for scale-free networks with $\gamma < 3$. The mean attrition length of kinetic growth walks, , scales as $\sim N^{\alpha}$, with an exponent $\alpha$ which depends on the lowest degree in the network. Results of approximate probabilistic calculations are supported by those derived from simulations of various kinds of networks. The efficiency of kinetic growth walks to explore networks is largely reduced by inhomogeneity in the degree distribution, as happens for scale-free networks.Comment: 10 pages, 8 figure

Detection of the Ammonium Ion in Space

We report on the detection of a narrow feature at 262816.73 MHz towards Orion and the cold prestellar core B1-bS, that we attribute to the 1(0)-0(0) line of the deuterated Ammonium ion, NH3D+. The observations were performed with the IRAM 30m radio telescope. The carrier has to be a light molecular species as it is the only feature detected over 3.6 GHz of bandwidth. The hyperfine structure is not resolved indicating a very low value for the electric quadrupolar coupling constant of Nitrogen which is expected for NH3D+ as the electric field over the N nucleus is practically zero. Moreover, the feature is right at the predicted frequency for the 1(0)-0(0) transition of the Ammonium ion, 262817(6) MHz (3sigma), using rotational constants derived from new infrared data obtained in our laboratory in Madrid. The estimated column density is 1.1(0.2)e12 cm-2. Assuming a deuterium enhancement similar to that of NH2D, we derive N(NH4+) sim 2.6e13 cm-2, i.e., an abundance for Ammonium of a few 1e(-11).Comment: Accepted for publication in the Astrophysical Journal Letters 04 June 201