From refined estimates for spherical harmonics to a sharp multiplier theorem on the Grushin sphere

We prove a sharp multiplier theorem of Mihlin–Hörmander type for the Grushin operator on the unit sphere in R 3 , and a corresponding boundedness result for the associated Bochner–Riesz means. The proof hinges on precise pointwise bounds for spherical harmonics

Palomar 13: a velocity dispersion inflated by binaries ?

Recently, combining radial velocities from Keck/HIRES echelle spectra with published proper motion membership probabilities, Cote et al (2002) observed a sample of 21 stars, probable members of Palomar 13, a globular cluster in the Galactic halo. Their projected velocity dispersion sigma_p = 2.2 +/-0.4 km/s gives a mass-to-light ratio M/L_V = 40 +24/-17, about one order of magnitude larger than the usual estimate for globular clusters. We present here radial velocities measured from three different CCD frames of commissioning observations obtained with the new ESO/VLT instrument FLAMES (Fibre Large Array Multi Element Spectrograph). From these data, now publicly available, we measure the homogeneous radial velocities of eight probable members of this globular cluster. A new projected velocity dispersion sigma_p = 0.6-0.9 +/-0.3 km/s implies Palomar 13 mass-to-light ratio M/L_V = 3-7, similar to the usual value for globular clusters. We discuss briefly the two most obvious reasons for the previous unusual mass-to-light ratio finding: binaries, now clearly detected, and more homogeneous data from the multi-fibre FLAMES spectrograph.Comment: 9 pages, 2 Postscript figure

Uncertainty inequalities on groups and homogeneous spaces via isoperimetric inequalities

We prove a family of $L^p$ uncertainty inequalities on fairly general groups and homogeneous spaces, both in the smooth and in the discrete setting. The crucial point is the proof of the $L^1$ endpoint, which is derived from a general weak isoperimetric inequality.Comment: 17 page

The Blue Straggler and Main-sequence Binary Population of the Low-Mass Globular Cluster Palomar 13

We present high-precision VI photometry of stars from the middle of the giant branch to about 5 magnitudes below the main-sequence turnoff in the globular cluster Palomar 13 based on images obtained with the Keck II 10m telescope. We tabulate a complete sample of blue stragglers in the cluster out to about 18 core radii. The blue straggler population is significantly more centrally concentrated than the giant star sample, which is in turn significantly more centrally concentrated than the main-sequence star sample. Palomar 13 has one of the highest specific frequencies of blue stragglers of any known globular cluster, but the specific frequency of blue stragglers in the outskirts of the cluster does not increase as has been seen in denser clusters. We also identify a group of faint blue stragglers (bluer than the turnoff, but having about the same magnitude) that outnumbers the brighter stragglers by more than a factor of 2. The cluster's color-magnitude diagram shows a large excess of stars to the red of the main sequence, indicating that the cluster's binary fraction is at least 30% +/- 4%, which appears to be similar to that of the low-mass cluster E3 but significantly higher than that of the more massive clusters Pal 5 and NGC 288.Comment: 36 pages, 13 figures, 1 electronic table, accepted to A

Tilted implants for full-arch rehabilitations in completely edentulous maxilla : a retrospective study

Purpose. The aims of this study were to assess the treatment outcome of immediately loaded full-arch fixed bridges anchored to both tilted and axially placed implants in the edentulous maxilla and to evaluate the incidence of biological and prosthetic complications. Materials and Methods. Thirty-four patients (18 women and 16 men) were included in the study. Each patient received a maxillary full-arch fixed bridge supported by two axial implants and two distal tilted implants. A total of 136 implants were inserted. Loading was applied within 48 hours of surgery and definitive restorations were placed 4 to 6 months later. Patients were scheduled for followup at 6, 12, 18, and 24 months and annually up to 5 years. At each followup plaque level and bleeding scores were assessed and every complication was recorded. Results. The overall follow-up range was 12 to 73 months (mean 38.8 months). No implant failures were recorded to date, leading to a cumulative implant survival rate of 100. Biological complications were recorded such as alveolar mucositis (11.8 patients), peri-implantitis (5.9 patients), and temporomandibular joint pain (5.9 patients). The most common prosthetic complications were the fracture or detachment of one or multiple acrylic teeth in both the temporary (20.6 patients) and definitive (17.7 patients) prosthesis and the minor acrylic fractures in the temporary (14.7 patients) and definitive (2.9 patients) prosthesis. Hygienic complications occurred in 38.2 patients. No patients' dissatisfactions were recorded. Conclusions. The high cumulative implant survival rate indicates that this technique could be considered a viable treatment option. An effective recall program is important to early intercept and correct prosthetic and biologic complications in order to avoid implant and prosthetic failures

Constraining Cosmic Evolution of Type Ia Supernovae

We present the first large-scale effort of creating composite spectra of high-redshift type Ia supernovae (SNe Ia) and comparing them to low-redshift counterparts. Through the ESSENCE project, we have obtained 107 spectra of 88 high-redshift SNe Ia with excellent light-curve information. In addition, we have obtained 397 spectra of low-redshift SNe through a multiple-decade effort at Lick and Keck Observatories, and we have used 45 UV spectra obtained by HST/IUE. The low-redshift spectra act as a control sample when comparing to the ESSENCE spectra. In all instances, the ESSENCE and Lick composite spectra appear very similar. The addition of galaxy light to the Lick composite spectra allows a nearly perfect match of the overall spectral-energy distribution with the ESSENCE composite spectra, indicating that the high-redshift SNe are more contaminated with host-galaxy light than their low-redshift counterparts. This is caused by observing objects at all redshifts with the same slit width, which corresponds to different projected distances. After correcting for the galaxy-light contamination, subtle differences in the spectra remain. We have estimated the systematic errors when using current spectral templates for K-corrections to be ~0.02 mag. The variance in the composite spectra give an estimate of the intrinsic variance in low-redshift maximum-light SN spectra of ~3% in the optical and growing toward the UV. The difference between the maximum light low and high-redshift spectra constrain SN evolution between our samples to be < 10% in the rest-frame optical.Comment: 22 pages, 22 figures, submitted to ApJ. Composite spectra can be downloaded from http://astro.berkeley.edu/~rfoley/composite

Understanding the unsteady pressure field inside combustion chambers of compression-ignited engines using a computational fluid dynamics approach

[EN] In this article, a numerical methodology for assessing combustion noise in compression ignition engines is described with the specific purpose of analysing the unsteady pressure field inside the combustion chamber. The numerical results show consistent agreement with experimental measurements in both the time and frequency domains. Nonetheless, an exhaustive analysis of the calculation convergence is needed to guarantee an independent solution. These results contribute to the understanding of in-cylinder unsteady processes, especially of those related to combustion chamber resonances, and their effects on the radiated noise levels. The method was applied to different combustion system configurations by modifying the spray angle of the injector, evidencing that controlling the ignition location through this design parameter, it is possible to decrease the combustion noise by minimizing the resonance contribution. Important efficiency losses were, however, observed due to the injector/bowl matching worsening which compromises the performance and emissions levels.The authors want to express their gratitude to CONVERGENT SCIENCE Inc. and Convergent Science GmbH for their kind support for performing the CFD calculations using CONVERGE software.Torregrosa, AJ.; Broatch, A.; Margot, X.; Gómez-Soriano, J. (2018). Understanding the unsteady pressure field inside combustion chambers of compression-ignited engines using a computational fluid dynamics approach. International Journal of Engine Research. 1-13. https://doi.org/10.1177/1468087418803030S113Benajes, J., Novella, R., De Lima, D., & Tribotté, P. (2014). Analysis of combustion concepts in a newly designed two-stroke high-speed direct injection compression ignition engine. International Journal of Engine Research, 16(1), 52-67. doi:10.1177/1468087414562867Costa, M., Bianchi, G. M., Forte, C., & Cazzoli, G. (2014). A Numerical Methodology for the Multi-objective Optimization of the DI Diesel Engine Combustion. Energy Procedia, 45, 711-720. doi:10.1016/j.egypro.2014.01.076Navid, A., Khalilarya, S., & Taghavifar, H. (2016). Comparing multi-objective non-evolutionary NLPQL and evolutionary genetic algorithm optimization of a DI diesel engine: DoE estimation and creating surrogate model. Energy Conversion and Management, 126, 385-399. doi:10.1016/j.enconman.2016.08.014Benajes, J., García, A., Pastor, J. M., & Monsalve-Serrano, J. (2016). Effects of piston bowl geometry on Reactivity Controlled Compression Ignition heat transfer and combustion losses at different engine loads. Energy, 98, 64-77. doi:10.1016/j.energy.2016.01.014Masterton, B., Heffner, H., & Ravizza, R. (1969). The Evolution of Human Hearing. The Journal of the Acoustical Society of America, 45(4), 966-985. doi:10.1121/1.1911574Strahle, W. C. (1978). Combustion noise. Progress in Energy and Combustion Science, 4(3), 157-176. doi:10.1016/0360-1285(78)90002-3Flemming, F., Sadiki, A., & Janicka, J. (2007). Investigation of combustion noise using a LES/CAA hybrid approach. Proceedings of the Combustion Institute, 31(2), 3189-3196. doi:10.1016/j.proci.2006.07.060Klos, D., & Kokjohn, S. L. (2014). Investigation of the sources of combustion instability in low-temperature combustion engines using response surface models. International Journal of Engine Research, 16(3), 419-440. doi:10.1177/1468087414556135Cyclic dispersion in engine combustion—Introduction by the special issue editors. (2015). International Journal of Engine Research, 16(3), 255-259. doi:10.1177/1468087415572740Hickling, R., Feldmaier, D. A., & Sung, S. H. (1979). Knock‐induced cavity resonances in open chamber diesel engines. The Journal of the Acoustical Society of America, 65(6), 1474-1479. doi:10.1121/1.382910Torregrosa, A. J., Broatch, A., Margot, X., Marant, V., & Beauge, Y. (2004). Combustion chamber resonances in direct injection automotive diesel engines: A numerical approach. International Journal of Engine Research, 5(1), 83-91. doi:10.1243/146808704772914264Broatch, A., Margot, X., Gil, A., & Christian Donayre, (José). (2007). Computational study of the sensitivity to ignition characteristics of the resonance in DI diesel engine combustion chambers. Engineering Computations, 24(1), 77-96. doi:10.1108/02644400710718583Eriksson, L. J. (1980). Higher order mode effects in circular ducts and expansion chambers. The Journal of the Acoustical Society of America, 68(2), 545-550. doi:10.1121/1.384768Broatch, A., Margot, X., Novella, R., & Gomez-Soriano, J. (2017). Impact of the injector design on the combustion noise of gasoline partially premixed combustion in a 2-stroke engine. Applied Thermal Engineering, 119, 530-540. doi:10.1016/j.applthermaleng.2017.03.081Tutak, W., & Jamrozik, A. (2016). Validation and optimization of the thermal cycle for a diesel engine by computational fluid dynamics modeling. Applied Mathematical Modelling, 40(13-14), 6293-6309. doi:10.1016/j.apm.2016.02.021Payri, F., Benajes, J., Margot, X., & Gil, A. (2004). CFD modeling of the in-cylinder flow in direct-injection Diesel engines. Computers & Fluids, 33(8), 995-1021. doi:10.1016/j.compfluid.2003.09.003Benajes, J., Novella, R., De Lima, D., & Thein, K. (2017). Impact of injection settings operating with the gasoline Partially Premixed Combustion concept in a 2-stroke HSDI compression ignition engine. Applied Energy, 193, 515-530. doi:10.1016/j.apenergy.2017.02.044Lesieur, M., Métais, O., & Comte, P. (2005). Large-Eddy Simulations of Turbulence. doi:10.1017/cbo9780511755507Pope, S. B. (2004). Ten questions concerning the large-eddy simulation of turbulent flows. New Journal of Physics, 6, 35-35. doi:10.1088/1367-2630/6/1/035Silva, C. F., Leyko, M., Nicoud, F., & Moreau, S. (2013). Assessment of combustion noise in a premixed swirled combustor via Large-Eddy Simulation. Computers & Fluids, 78, 1-9. doi:10.1016/j.compfluid.2010.09.034Jamrozik, A., Tutak, W., Kociszewski, A., & Sosnowski, M. (2013). Numerical simulation of two-stage combustion in SI engine with prechamber. Applied Mathematical Modelling, 37(5), 2961-2982. doi:10.1016/j.apm.2012.07.040Qin, W., Xie, M., Jia, M., Wang, T., & Liu, D. (2014). Large eddy simulation of in-cylinder turbulent flows in a DISI gasoline engine. Applied Mathematical Modelling, 38(24), 5967-5985. doi:10.1016/j.apm.2014.05.004Broatch, A., Margot, X., Novella, R., & Gomez-Soriano, J. (2016). Combustion noise analysis of partially premixed combustion concept using gasoline fuel in a 2-stroke engine. Energy, 107, 612-624. doi:10.1016/j.energy.2016.04.045Torregrosa, A. J., Broatch, A., Martín, J., & Monelletta, L. (2007). Combustion noise level assessment in direct injection Diesel engines by means of in-cylinder pressure components. Measurement Science and Technology, 18(7), 2131-2142. doi:10.1088/0957-0233/18/7/045Payri, F., Broatch, A., Margot, X., & Monelletta, L. (2008). Sound quality assessment of Diesel combustion noise using in-cylinder pressure components. Measurement Science and Technology, 20(1), 015107. doi:10.1088/0957-0233/20/1/015107Ihlenburg, F. (2003). The Medium-Frequency Range in Computational Acoustics: Practical and Numerical Aspects. Journal of Computational Acoustics, 11(02), 175-193. doi:10.1142/s0218396x03001900Lapuerta, M., Armas, O., & Hernández, J. J. (1999). Diagnosis of DI Diesel combustion from in-cylinder pressure signal by estimation of mean thermodynamic properties of the gas. Applied Thermal Engineering, 19(5), 513-529. doi:10.1016/s1359-4311(98)00075-1Payri, F., Olmeda, P., Martín, J., & García, A. (2011). A complete 0D thermodynamic predictive model for direct injection diesel engines. Applied Energy, 88(12), 4632-4641. doi:10.1016/j.apenergy.2011.06.005Payri, F., Broatch, A., Tormos, B., & Marant, V. (2005). New methodology for in-cylinder pressure analysis in direct injection diesel engines—application to combustion noise. Measurement Science and Technology, 16(2), 540-547. doi:10.1088/0957-0233/16/2/029Shahlari, A. J., Hocking, C., Kurtz, E., & Ghandhi, J. (2013). Comparison of Compression Ignition Engine Noise Metrics in Low-Temperature Combustion Regimes. SAE International Journal of Engines, 6(1), 541-552. doi:10.4271/2013-01-1659Yakhot, V., & Orszag, S. A. (1986). Renormalization group analysis of turbulence. I. Basic theory. Journal of Scientific Computing, 1(1), 3-51. doi:10.1007/bf01061452Redlich, O., & Kwong, J. N. S. (1949). On the Thermodynamics of Solutions. V. An Equation of State. Fugacities of Gaseous Solutions. Chemical Reviews, 44(1), 233-244. doi:10.1021/cr60137a013Issa, R. . (1986). Solution of the implicitly discretised fluid flow equations by operator-splitting. Journal of Computational Physics, 62(1), 40-65. doi:10.1016/0021-9991(86)90099-9Dukowicz, J. K. (1980). A particle-fluid numerical model for liquid sprays. Journal of Computational Physics, 35(2), 229-253. doi:10.1016/0021-9991(80)90087-xReitz, R. D., & Beale, J. C. (1999). MODELING SPRAY ATOMIZATION WITH THE KELVIN-HELMHOLTZ/RAYLEIGH-TAYLOR HYBRID MODEL. Atomization and Sprays, 9(6), 623-650. doi:10.1615/atomizspr.v9.i6.40Babajimopoulos, A., Assanis, D. N., Flowers, D. L., Aceves, S. M., & Hessel, R. P. (2005). A fully coupled computational fluid dynamics and multi-zone model with detailed chemical kinetics for the simulation of premixed charge compression ignition engines. International Journal of Engine Research, 6(5), 497-512. doi:10.1243/146808705x30503Pal, P., Keum, S., & Im, H. G. (2015). Assessment of flamelet versus multi-zone combustion modeling approaches for stratified-charge compression ignition engines. International Journal of Engine Research, 17(3), 280-290. doi:10.1177/1468087415571006Torregrosa, A. J., Broatch, A., Gil, A., & Gomez-Soriano, J. (2018). Numerical approach for assessing combustion noise in compression-ignited Diesel engines. Applied Acoustics, 135, 91-100. doi:10.1016/j.apacoust.2018.02.006Torregrosa, A., Olmeda, P., Degraeuwe, B., & Reyes, M. (2006). A concise wall temperature model for DI Diesel engines. Applied Thermal Engineering, 26(11-12), 1320-1327. doi:10.1016/j.applthermaleng.2005.10.021Broatch, A., Javier Lopez, J., García-Tíscar, J., & Gomez-Soriano, J. (2018). Experimental Analysis of Cyclical Dispersion in Compression-Ignited Versus Spark-Ignited Engines and Its Significance for Combustion Noise Numerical Modeling. Journal of Engineering for Gas Turbines and Power, 140(10). doi:10.1115/1.4040287Molina, S., García, A., Pastor, J. M., Belarte, E., & Balloul, I. (2015). Operating range extension of RCCI combustion concept from low to full load in a heavy-duty engine. Applied Energy, 143, 211-227. doi:10.1016/j.apenergy.2015.01.03

Supernovae with "Super-Hipparcos"

GAIA is the ``super-Hipparcos'' satellite scheduled for launch in 2010 by the European Space Agency. It is a scanning satellite that carries out multi-colour, multi-epoch photometry on all objects brighter than 20th magnitude. We conduct detailed simulations of supernovae (SNe) detection by GAIA. Supernovae of each type are chosen according to the observed distributions of absolute magnitudes, and located in nearby galaxies according to the local large-scale structure. Using an extinction model of the Galaxy and the scanning law of the GAIA satellite, we calculate how many SNe are detectable as a function of the phase of the lightcurve. Our study shows that GAIA will report data on 21400 SNe during the five-year mission lifetime, of which 14300 are SNe Ia, 1400 are SNe Ib/c and 5700 are SNe II. Using the simulations, we estimate that the numbers caught before maximum are 6300 SNe Ia, 500 SNe Ib/c and 1700 SNe II. GAIA will issue about 5 SNe alerts a day. The most distant SNe accessible to GAIA are at a redshift of 0.14 and so GAIA will provide a huge sample of local SNe. There will be many examples of the rarer subluminous events, over-luminous events, SNe Ib/c and SNe II-L. SNe rates will be found as a function of galaxy type, as well as extinction and position in the host galaxy. Amongst other applications, there may be about 26 SNe each year for which detection of gravitational waves is possible and about 180 SNe each year for which detection of gamma-rays is possible.Comment: 8 pages, 4 figures, version in press at MNRAS (small changes in section on neutrino detection

Palomar 13's Last Stand

We present a proper motion and CCD photometric study of stars in the distant halo globular cluster Palomar 13. The absolute proper motion of Pal 13 with respect to the background galaxies, derived from moderate scale photographic plates separated by a 40-year baseline, is $(\mu_{\alpha cos \delta}, \mu_{\delta}) = (+2.30, +0.27) \pm (0.26, 0.25)$ milliarc-seconds per year. The resultant total space velocity (315 km s$^{-1}$) implies that Pal 13 is in the inner part of its orbit near perigalacticon. Orbital integration reveals the cluster to possess an inclined, very eccentric, retrograde orbit. These data confirm that Pal 13 is a paradigm "young halo" globular cluster. The derived proper motions for cluster stars are used to produce membership probabilities and a cleaned CCD UBV catalogue for Pal 13. With this data set we have made small revisions to Pal 13's distance, metallicity, position and light profile. The membership of four previously reported RR Lyrae variables and a proportionally large group of blue straggler stars are confirmed. As expected, the blue stragglers are centrally concentrated. The small size of this cluster, combined with the shape of its light profile, which shows a clear departure from a classical King function beyond the tidal radius, suggests that Pal 13 is in the final throes of destruction. This could explain the large blue straggler specific frequency, as destructive processes would preferentially strip less massive stars.Comment: 54 pages, 9 figures, 7 tables, accapted for publication in February 2001 A