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

Propagating, evanescent, and localized states in carbon nanotube-graphene junctions

We study the electronic structure of the junctions between a single graphene layer and carbon nanotubes, using a tight-binding model and the continuum theory based on Dirac fermion fields. The latter provides a unified description of different lattice structures with curvature, which is always localized at six heptagonal carbon rings around each junction. When these are evenly spaced, we find that it is possible to curve the planar lattice into armchair (6n,6n) as well as zig-zag (6n,0) nanotubes. We show that the junctions fall into two different classes, regarding the low-energy electronic behavior. One of them, constituted by the junctions made of the armchair nanotubes and the zig-zag (6n,0) geometries when n is a multiple of 3, is characterized by the presence of two quasi-bound states at the Fermi level, which are absent for the rest of the zig-zag nanotubes. These states, localized at the junction, are shown to arise from the effective gauge flux induced by the heptagonal carbon rings, which has a direct reflection in the local density of states around the junction. Furthermore, we also analyze the band structure of the arrays of junctions, finding out that they can also be classified into two different groups according to the low-energy behavior. In this regard, the arrays made of armchair and (6n,0) nanotubes with n equal to a multiple of 3 are characterized by the presence of a series of flat bands, whose number grows with the length of the nanotubes. We show that such flat bands have their origin in the formation of states confined to the nanotubes in the array. This is explained in the continuum theory from the possibility of forming standing waves in the mentioned nanotube geometries, as a superposition of modes with opposite momenta and the same quantum numbers under the C_6v symmetry of the junction.Comment: 13 pages, 8 figure

Molar volume of solid isotopic helium mixtures

Solid isotopic helium mixtures have been studied by path-integral Monte Carlo simulations in the isothermal-isobaric ensemble. This method allowed us to study the molar volume as a function of temperature, pressure, and isotopic composition. At 25 K and 0.2 GPa, the relative difference between molar volumes of isotopically-pure crystals of 3He and 4He is found to be about 3%. This difference decreases under pressure, and for 12 GPa it is smaller than 1%. For isotopically-mixed crystals, a linear relation between lattice parameters and concentrations of helium isotopes is found, in agreement with Vegard's law. The virtual crystal approximation, valid for isotopic mixtures of heavier atoms, does not give reliable results for solid solutions of helium isotopes.Comment: 7 pages, 5 figure

Solid helium at high pressure: A path-integral Monte Carlo simulation

Solid helium (3He and 4He) in the hcp and fcc phases has been studied by path-integral Monte Carlo. Simulations were carried out in the isothermal-isobaric (NPT) ensemble at pressures up to 52 GPa. This allows one to study the temperature and pressure dependences of isotopic effects on the crystal volume and vibrational energy in a wide parameter range. The obtained equation of state at room temperature agrees with available experimental data. The kinetic energy, E_k, of solid helium is found to be larger than the vibrational potential energy, E_p. The ratio E_k/E_p amounts to about 1.4 at low pressures, and decreases as the applied pressure is raised, converging to 1, as in a harmonic solid. Results of these simulations have been compared with those yielded by previous path integral simulations in the NVT ensemble. The validity range of earlier approximations is discussed.Comment: 7 pages, 5 figure

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

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

The OPTX Project I: The Flux and Redshift Catalogs for the CLANS, CLASXS, and CDF-N fields

We present the redshift catalogs for the X-ray sources detected in the Chandra Deep Field North (CDF-N), the Chandra Large Area Synoptic X-ray Survey (CLASXS), and the Chandra Lockman Area North Survey (CLANS). The catalogs for the CDF-N and CLASXS fields include redshifts from previous work, while the redshifts for the CLANS field are all new. For fluxes above 10^-14 ergs cm^-2 s^-1 (2-8 keV) we have redshifts for 76% of the sources. We extend the redshift information for the full sample using photometric redshifts. The goal of the OPTX Project is to use these three surveys, which are among the most spectroscopically complete surveys to date, to analyze the effect of spectral type on the shape and evolution of the X-ray luminosity functions and to compare the optical spectral types with the X-ray spectral properties. We also present the CLANS X-ray catalog. The nine ACIS-I fields cover a solid angle of ~0.6 square degrees and reach fluxes of 7x10^-16 ergs cm^-2 s^-1 (0.5-2 keV) and 3.5x10^-15 ergs cm^-2 s^-1 (2-8 keV). We find a total of 761 X-ray point sources. Additionally, we present the optical and infrared photometric catalog for the CLANS X-ray sources, as well as updated optical and infrared photometric catalogs for the X-ray sources in the CLASXS and CDF-N fields. The CLANS and CLASXS surveys bridge the gap between the ultradeep pencil-beam surveys, such as the CDFs, and the shallower, very large-area surveys. As a result, they probe the X-ray sources that contribute the bulk of the 2-8 keV X-ray background and cover the flux range of the observed break in the logN-logS distribution. We construct differential number counts for each individual field and for the full sample.Comment: Published in The Astrophysical Journal Supplement. 18 pages, 16 figures, 14 table

Preoperative digital three-dimensional planning for rhinoplasty

BACKGROUND: This report describes preoperative digital planning for rhinoplasty using a new three-dimensional (3D) radiologic viewer that allows both patients and surgeons to visualize on a common monitor the 3D real aspect of the nose in its inner and outer sides. METHODS: In the period 2002 to 2008, 210 patients underwent rhinoplasty procedures in the authors' clinic. The patients were randomly divided into three groups according to the type of preoperative planning used: photos only, a simulated result by Adobe Photoshop, or the 3D radiologic viewer. The parameters evaluated included the number of patients that underwent surgery after the first consultation, the number of patients who asked for a reintervention, patient satisfaction (according to a test given to the patients 12 months postoperatively), the surgical time required for a functional intervention, and the improvement in nasal function by postoperative rhinomanometry and subjective evaluation. RESULTS: Computer-aided technologies led to a higher number of patients deciding to undergo a rhinoplasty. Simulation of the postoperative results was not as useful in the postoperative period due to the higher number of reintervention requests. CONCLUSION: The patients undergoing rhinoplasties preferred new technologies in the preoperative period. The advantages of using the 3D radiologic viewer included improved preoperative planning, reduction in intraoperative stress, a higher number of patients undergoing surgery, reduction in postoperative surgical corrections, reduction in surgical time for the functional intervention, a higher rate of improvement in nasal function, a higher percentage of postoperative satisfaction, and reduced costs