On the rooted Tutte polynomial

The Tutte polynomial is a generalization of the chromatic polynomial of graph colorings. Here we present an extension called the rooted Tutte polynomial, which is defined on a graph where one or more vertices are colored with prescribed colors. We establish a number of results pertaining to the rooted Tutte polynomial, including a duality relation in the case that all roots reside around a single face of a planar graph. The connection with the Potts model is also reviewed.Comment: plain latex, 14 pages, 2 figs., to appear in Annales de l'Institut Fourier (1999

Turbulent mixing of a slightly supercritical Van der Waals fluid at Low-Mach number

Supercritical fluids near the critical point are characterized by liquid-like densities and gas-like transport properties. These features are purposely exploited in different contexts ranging from natural products extraction/fractionation to aerospace propulsion. Large part of studies concerns this last context, focusing on the dynamics of supercritical fluids at high Mach number where compressibility and thermodynamics strictly interact. Despite the widespread use also at low Mach number, the turbulent mixing properties of slightly supercritical fluids have still not investigated in detail in this regime. This topic is addressed here by dealing with Direct Numerical Simulations (DNS) of a coaxial jet of a slightly supercritical Van der Waals fluid. Since acoustic effects are irrelevant in the Low Mach number conditions found in many industrial applications, the numerical model is based on a suitable low-Mach number expansion of the governing equation. According to experimental observations, the weakly supercritical regime is characterized by the formation of finger-like structures-- the so-called ligaments --in the shear layers separating the two streams. The mechanism of ligament formation at vanishing Mach number is extracted from the simulations and a detailed statistical characterization is provided. Ligaments always form whenever a high density contrast occurs, independently of real or perfect gas behaviors. The difference between real and perfect gas conditions is found in the ligament small-scale structure. More intense density gradients and thinner interfaces characterize the near critical fluid in comparison with the smoother behavior of the perfect gas. A phenomenological interpretation is here provided on the basis of the real gas thermodynamics properties.Comment: Published on Physics of Fluid

SN 1997bs in M66: Another Extragalactic Eta Carinae Analog?

We report on SN 1997bs in NGC 3627 (M66), the first supernova discovered by the Lick Observatory Supernova Search using the 0.75-m Katzman Automatic Imaging Telescope (KAIT). Based on its early-time optical spectrum, SN 1997bs was classified as Type IIn. However, from the BVRI light curves obtained by KAIT early in the supernova's evolution, and F555W and F814W light curves obtained from Hubble Space Telescope archival WFPC2 images at late times, we question the identification of SN 1997bs as a bona fide supernova. We believe that it is more likely a super-outburst of a very massive luminous blue variable star, analogous to Eta Carinae, and similar to SN 1961V in NGC 1058 (Filippenko et al. 1995 [AJ, 110, 2261]) and SN 1954J (``Variable 12'') in NGC 2403 (Humphreys & Davidson 1994 [PASP, 106, 1025]). The progenitor may have survived the outburst, since the SN is seen in early 1998 at m_F555W=23.4, about 0.5 mag fainter than the progenitor identified by Van Dyk et al. (1999, [AJ, 118, 2331]) in a pre-discovery image. Based on analysis of its environment in the Hubble Space Telescope images, the progenitor was not in an H II region or association of massive stars. The recent discovery of additional objects with properties similar to those of SN 1997bs suggests that the heterogeneous class of Type IIn supernovae consists in part of ``impostors.''Comment: 15 pages, 8 figures, to appear in the PASP (2000 Dec issue

Trimaximal neutrino mixing from vacuum alignment in A4 and S4 models

Recent T2K results indicate a sizeable reactor angle theta_13 which would rule out exact tri-bimaximal lepton mixing. We study the vacuum alignment of the Altarelli-Feruglio A4 family symmetry model including additional flavons in the 1' and 1" representations and show that it leads to trimaximal mixing in which the second column of the lepton mixing matrix consists of the column vector (1,1,1)^T/sqrt{3}, with a potentially large reactor angle. In order to limit the reactor angle and control the higher order corrections, we propose a renormalisable S4 model in which the 1' and 1" flavons of A4 are unified into a doublet of S4 which is spontaneously broken to A4 by a flavon which enters the neutrino sector at higher order. We study the vacuum alignment in the S4 model and show that it predicts accurate trimaximal mixing with approximate tri-bimaximal mixing, leading to a new mixing sum rule testable in future neutrino experiments. Both A4 and S4 models preserve form dominance and hence predict zero leptogenesis, up to renormalisation group corrections.Comment: 24 pages, 2 figures, version to be published in JHE

How Does Gender Stereotype Affect the Memory of Advertisements? A Behavioral and Electroencephalography Study.

Previous studies have shown equivocal results about whether atypical or unusual events, compared with typical ones, facilitate or inhibit memory. We suspect that the indefinite findings could be partly due to the recall task used in these studies, as the participants might have used inference instead of recall in their responses. In the present study, we tested the recognition memory for real (Experiment 1) and fabricated (Experiment 2) advertisements, which could be congruent or incongruent with gender stereotypes. In congruent advertisements, a female endorser presented a traditionally considered feminine product or a male endorser presented a traditionally considered masculine product, whereas the gender-product type matching reversed in incongruent advertisements. The results of both behavioral experiments revealed that the participants' memory performance for stereotype-incongruent advertisements was higher than for congruent ones. In the event-related potential (ERP) recordings in Experiment 3, larger positive amplitudes were found for stereotype-incongruent advertisements than for congruent advertisements on the left parietal sites, suggesting a deeper encoding process for stereotype-incongruent information than for stereotype-congruent information

Formation and observation of a quasi-two-dimensional dxyd_{xy} electron liquid in epitaxially stabilized Sr2−x_{2-x}Lax_{x}TiO4_{4} thin films

We report the formation and observation of an electron liquid in Sr$_{2-x}$La$_{x}$TiO$_4$, the quasi-two-dimensional counterpart of SrTiO$_3$, through reactive molecular-beam epitaxy and {\it in situ} angle-resolved photoemission spectroscopy. The lowest lying states are found to be comprised of Ti 3$d_{xy}$ orbitals, analogous to the LaAlO$_3$/SrTiO$_3$ interface and exhibit unusually broad features characterized by quantized energy levels and a reduced Luttinger volume. Using model calculations, we explain these characteristics through an interplay of disorder and electron-phonon coupling acting co-operatively at similar energy scales, which provides a possible mechanism for explaining the low free carrier concentrations observed at various oxide heterostructures such as the LaAlO$_3$/SrTiO$_3$ interface