Computing Matveev's complexity via crystallization theory: the boundary case

The notion of Gem-Matveev complexity has been introduced within crystallization theory, as a combinatorial method to estimate Matveev's complexity of closed 3-manifolds; it yielded upper bounds for interesting classes of such manifolds. In this paper we extend the definition to the case of non-empty boundary and prove that for each compact irreducible and boundary-irreducible 3-manifold it coincides with the modified Heegaard complexity introduced by Cattabriga, Mulazzani and Vesnin. Moreover, via Gem-Matveev complexity, we obtain an estimation of Matveev's complexity for all Seifert 3-manifolds with base $\mathbb D^2$ and two exceptional fibers and, therefore, for all torus knot complements.Comment: 27 pages, 14 figure

Combinatorial properties of the G-degree

A strong interaction is known to exist between edge-colored graphs (which encode PL pseudo-manifolds of arbitrary dimension) and random tensor models (as a possible approach to the study of Quantum Gravity). The key tool is the "G-degree" of the involved graphs, which drives the 1/N expansion in the tensor models context. In the present paper - by making use of combinatorial properties concerning Hamiltonian decompositions of the complete graph - we prove that, in any even dimension d greater or equal to 4, the G-degree of all bipartite graphs, as well as of all (bipartite or non-bipartite) graphs representing singular manifolds, is an integer multiple of (d-1)!. As a consequence, in even dimension, the terms of the 1/N expansion corresponding to odd powers of 1/N are null in the complex context, and do not involve colored graphs representing singular manifolds in the real context. In particular, in the 4-dimensional case, where the G-degree is shown to depend only on the regular genera with respect to an arbitrary pair of "associated" cyclic permutations, several results are obtained, relating the G-degree or the regular genus of 5-colored graphs and the Euler characteristic of the associated PL 4-manifolds

An In-Depth Computational Study of Alkene Cyclopropanation Catalyzed by Fe(porphyrin)(OCH3) Complexes. The Environmental Effects on the Energy Barriers

Iron porphyrin methoxy complexes, of the general formula [Fe(porphyrin)(OCH3)], are able to catalyze the reaction of diazo compounds with alkenes to give cyclopropane products with very high efficiency and selectivity. The overall mechanism of these reactions was thoroughly investigated with the aid of a computational approach based on density functional theory calculations. The energy profile for the processes catalyzed by the oxidized [FeIII(Por)(OCH3)] (Por = porphine) as well as the reduced [FeII(Por)(OCH3)]- forms of the iron porphyrin was determined. The main reaction step is the same in both of the cases, that is, the one leading to the terminal-carbene intermediate [Fe(Por)(OCH3)(CHCO2Et)] with simultaneous dinitrogen loss; however, the reduced species performs much better than the oxidized one. Contrarily to the iron(III) profile in which the carbene intermediate is directly obtained from the starting reactant complex, the favored iron(II) process is more intricate. The initially formed reactant adduct between [FeII(Por)(OCH3)]- and ethyl diazoacetate (EDA) is converted into a closer reactant adduct, which is in turn converted into the terminal iron porphyrin carbene [Fe(Por)(OCH3)(CHCO2Et)]-. The two corresponding transition states are almost isoenergetic, thus raising the question of whether the rate-determining step corresponds to dinitrogen loss or to the previous structural and electronic rearrangement. The ethylene addition to the terminal carbene is a downhill process, which, on the open-shell singlet surface, presents a defined but probably short-living diradicaloid intermediate, though other spin-state surfaces do not show this intermediate allowing a direct access to the cyclopropane product. For the crucial stationary points, the more complex catalyst [Fe(2)(OCH3)], in which a sterically hindered chiral bulk is mounted onto the porphyrin, was investigated. The corresponding computational data disclose the very significant effect of the porphyrin skeleton on the reaction energy profile. Though the geometrical features around the reactive core of the system remain unchanged, the energy barriers become much lower, thus revealing the profound effects that can be exerted by the three-dimensional organic scaffold surrounding the reaction site.

The Infrared Surface Brightness Fluctuation Distances to the Hydra and Coma Clusters

We present IR surface brightness fluctuation (SBF) distance measurements to NGC 4889 in the Coma cluster and to NGC 3309 and NGC 3311 in the Hydra cluster. We explicitly corrected for the contributions to the fluctuations from globular clusters, background galaxies, and residual background variance. We measured a distance of 85 +/- 10 Mpc to NGC 4889 and a distance of 46 +/- 5 Mpc to the Hydra cluster. Adopting recession velocities of 7186 +/- 428 km/s for Coma and 4054 +/- 296 km/s for Hydra gives a mean Hubble constant of H_0 = 87 +/- 11 km/s/Mpc. Corrections for residual variances were a significant fraction of the SBF signal measured, and, if underestimated, would bias our measurement towards smaller distances and larger values of H_0. Both NICMOS on the Hubble Space Telescope and large-aperture ground-based telescopes with new IR detectors will make accurate SBF distance measurements possible to 100 Mpc and beyond.Comment: 24 pages, 4 PostScript figures, 2 JPEG images; accepted for publication in Ap

TOPOLOGY IN COLORED TENSOR MODELS

From a “geometric topology” point of view, the theory of manifold representation by means of edge-colored graphs has been deeply studied since 1975 and many results have been achieved: its great advantage is the possibility of encoding, in any dimension, every PL d-manifold by means of a totally combinatorial tool. Edge-colored graphs also play an important rôle within colored tensor models theory, considered as a possible approach to the study of Quantum Gravity: the key tool is the G-degree of the involved graphs, which drives the 1/N expansion in the higher dimensional tensor models context, exactly as it happens for the genus of surfaces in the two-dimensional matrix model setting. Therefore, topological and geometrical properties of the represented PL manifolds, with respect to the G-degree, have specific relevance in the tensor models framework, show- ing a direct fruitful interaction between tensor models and discrete geometry, via edge-colored graphs. In colored tensor models, manifolds and pseudomanifolds are (almost) on the same footing, since they constitute the class of polyhedra represented by edge-colored Feynman graphs arising in this context; thus, a promising research trend is to look for classification results concerning all pseudomanifolds - or, at least, singular d-manifolds, if d ≥ 4 - represented by graphs of a given G-degree. In dimension 4, the existence of colored graphs encoding different PL manifolds with the same underlying TOP manifold, suggests also to investigate the ability of ten- sor models to accurately reflect geometric degrees of freedom of Quantum Gravity

Uncovering Spiral Structure in Flocculent Galaxies

We present K'(2.1 micron) observations of four nearby flocculent spirals, which clearly show low-level spiral structure and suggest that kiloparsec-scale spiral structure is more prevalent in flocculent spirals than previously supposed. In particular, the prototypical flocculent spiral NGC 5055 is shown to have regular, two-arm spiral structure to a radius of 4 kpc in the near infrared, with an arm-interarm contrast of 1.3. The spiral structure in all four galaxies is weaker than that in grand design galaxies. Taken in unbarred galaxies with no large, nearby companions, these data are consistent with the modal theory of spiral density waves, which maintains that density waves are intrinsic to the disk. As an alternative, mechanisms for driving spiral structure with non-axisymmetric perturbers are also discussed. These observations highlight the importance of near infrared imaging for exploring the range of physical environments in which large-scale dynamical processes, such as density waves, are important.Comment: 12 pages AASTeX; 3 compressed PS figures can be retrieved from ftp://ftp.astro.umd.edu/pub/michele as file thornley.tar (1.6Mbytes). Accepted to Ap.J. Letters.(Figures now also available here, and from ftp://ftp.astro.umd.edu/pub/michele , in GIF format.

Comparing Star Formation on Large Scales in the c2d Legacy Clouds: Bolocam 1.1 mm Dust Continuum Surveys of Serpens, Perseus, and Ophiuchus

We have undertaken an unprecedentedly large 1.1 millimeter continuum survey of three nearby star forming clouds using Bolocam at the Caltech Submillimeter Observatory. We mapped the largest areas in each cloud at millimeter or submillimeter wavelengths to date: 7.5 sq. deg in Perseus (Paper I), 10.8 sq. deg in Ophiuchus (Paper II), and 1.5 sq. deg in Serpens with a resolution of 31", detecting 122, 44, and 35 cores, respectively. Here we report on results of the Serpens survey and compare the three clouds. Average measured angular core sizes and their dependence on resolution suggest that many of the observed sources are consistent with power-law density profiles. Tests of the effects of cloud distance reveal that linear resolution strongly affects measured source sizes and densities, but not the shape of the mass distribution. Core mass distribution slopes in Perseus and Ophiuchus (alpha=2.1+/-0.1 and alpha=2.1+/-0.3) are consistent with recent measurements of the stellar IMF, whereas the Serpens distribution is flatter (alpha=1.6+/-0.2). We also compare the relative mass distribution shapes to predictions from turbulent fragmentation simulations. Dense cores constitute less than 10% of the total cloud mass in all three clouds, consistent with other measurements of low star-formation efficiencies. Furthermore, most cores are found at high column densities; more than 75% of 1.1 mm cores are associated with Av>8 mag in Perseus, 15 mag in Serpens, and 20-23 mag in Ophiuchus.Comment: 32 pages, including 18 figures, accepted for publication in Ap

Low-Mass Star Formation and the Initial Mass Function in the Rho Ophiuchi Cloud Core

We have obtained moderate-resolution (R=800-1200) K-band spectra for ~100 stars within and surrounding the cloud core of rho Oph. We have measured spectral types and continuum veilings and have combined this information with results from new deep imaging. The IMF peaks at about 0.4 M_sun and slowly declines to the hydrogen burning limit with a slope of ~-0.5 in logarithmic units (Salpeter is +1.35). Our lower limits on the numbers of substellar objects demonstrate that the IMF probably does not fall more steeply below the hydrogen burning limit, at least down to ~0.02 M_sun. We then make the first comparison of mass functions of stars and pre-stellar clumps (Motte, Andre, & Neri) measured in the same region. The similar behavior of the two mass functions in rho Oph supports the suggestion of Motte et al. and Testi & Sargent that the stellar mass function in young clusters is a direct product of the process of cloud fragmentation. After considering the effect of extinction on the SED classifications of the sample, we find that ~17% of the rho Oph stars are Class I, implying ~0.1 Myr for the lifetime of this stage. In spectra separated by two years, we observe simultaneous variability in the Br gamma emission and K-band continuum veiling for two stars, where the hydrogen emission is brighter in the more heavily veiled data. This behavior indicates that the disk may contribute significantly to continuous K-band emission, in contrast to the proposal that the infalling envelope always dominates. Our detection of strong 2 micron veiling (r_K=1-4) in several Class II and III stars, which should have disks but little envelope material, further supports this proposition.Comment: 35 pages, 14 figures, accepted to Ap