Network growth model with intrinsic vertex fitness

© 2013 American Physical SocietyWe study a class of network growth models with attachment rules governed by intrinsic node fitness. Both the individual node degree distribution and the degree correlation properties of the network are obtained as functions of the network growth rules. We also find analytical solutions to the inverse, design, problems of matching the growth rules to the required (e.g., power-law) node degree distribution and more generally to the required degree correlation function. We find that the design problems do not always have solutions. Among the specific conditions on the existence of solutions to the design problems is the requirement that the node degree distribution has to be broader than a certain threshold and the fact that factorizability of the correlation functions requires singular distributions of the node fitnesses. More generally, the restrictions on the input distributions and correlations that ensure solvability of the design problems are expressed in terms of the analytical properties of their generating functions

Why Matrix theory works for oddly shaped membranes

We give a simple proof of why there is a Matrix theory approximation for a membrane shaped like an arbitrary Riemann surface. As corollaries, we show that noncompact membranes cannot be approximated by matrices and that the Poisson algebra on any compact phase space is U(infinity). The matrix approximation does not appear to work properly in theories such as IIB string theory or bosonic membrane theory where there is no conserved 3-form charge to which the membranes couple.Comment: 8 pages, 4 figures, revtex; references adde

Fractionation of sulfur isotopes during heterogeneous oxidation of SO₂ on sea salt aerosol: a new tool to investigate non-sea salt sulfate production in the marine boundary layer

The oxidation of SO₂ to sulfate on sea salt aerosols in the marine environment is highly important because of its effect on the size distribution of sulfate and the potential for new particle nucleation from H₂SO₄ (g). However, models of the sulfur cycle are not currently able to account for the complex relationship between particle size, alkalinity, oxidation pathway and rate – which is critical as SO₂ oxidation by O₃ and Cl catalysis are limited by aerosol alkalinity, whereas oxidation by hypohalous acids and transition metal ions can continue at low pH once alkalinity is titrated. We have measured ³⁴S/³²S fractionation factors for SO₂ oxidation in sea salt, pure water and NaOCl aerosol, as well as the pH dependency of fractionation. <br><br> Oxidation of SO₂ by NaOCl aerosol was extremely efficient, with a reactive uptake coefficient of ≈0.5, and produced sulfate that was enriched in ³²S with &alpha;_OCl = 0.9882±0.0036 at 19 °C. Oxidation on sea salt aerosol was much less efficient than on NaOCl aerosol, suggesting alkalinity was already exhausted on the short timescale of the experiments. Measurements at pH = 2.1 and 7.2 were used to calculate fractionation factors for each step from SO₂(g) → multiple steps → SO_OCl^2&minus;. Oxidation on sea salt aerosol resulted in a lower fractionation factor than expected for oxidation of SO₃^2&minus; by O₃ (&alpha;_seasalt = 1.0124±0.0017 at 19 °C). Comparison of the lower fractionation during oxidation on sea salt aerosol to the fractionation factor for high pH oxidation shows HOCl contributed 29% of S(IV) oxidation on sea salt in the short experimental timescale, highlighting the potential importance of hypohalous acids in the marine environment. <br><br> The sulfur isotope fractionation factors measured in this study allow differentiation between the alkalinity-limited pathways – oxidation by O₃ and by Cl catalysis (&alpha;₃₄ = 1.0163&plusmn;0.0018 at 19 °C in pure water or 1.0199&plusmn;0.0024 at pH = 7.2) – which favour the heavy isotope, and the alkalinity non-limited pathways – oxidation by transition metal catalysis (&alpha;₃₄ = 0.9905±0.0031 at 19 °C, Harris et al., 2012a) and by hypohalites (&alpha;₃₄ = 0.9882±0.0036 at 19 °C) – which favour the light isotope. In combination with field measurements of the oxygen and sulfur isotopic composition of SO₂ and sulfate, the fractionation factors presented in this paper may be capable of constraining the relative importance of different oxidation pathways in the marine boundary layer

Primary cosmic ray particles with z 35 (VVH particles)

Large areas of nuclear emulsions and plastic detectors were exposed to the primary cosmic radiation during high altitude balloon flights. From the analysis of 141 particle tracks recorded during a total exposure of 1.3 x 10 to the 7th power sq m ster.sec., a charge spectrum of the VVH particles has been derived

Carbon-rich presolar grains from massive stars : subsolar ¹²C/¹³C and ¹⁴N/¹⁵N ratios and the mystery of ¹⁵N

Carbon-rich grains with isotopic anomalies compared to the Sun are found in primitive meteorites. They were made by stars, and carry the original stellar nucleosynthesis signature. Silicon carbide grains of Type X and C and low-density (LD) graphites condensed in the ejecta of core-collapse supernovae. We present a new set of models for the explosive He shell and compare them with the grains showing ¹²C/¹³C and ¹⁴N/¹⁵N ratios lower than solar. In the stellar progenitor H was ingested into the He shell and not fully destroyed before the explosion. Different explosion energies and H concentrations are considered. If the supernova shock hits the He-shell region with some H still present, the models can reproduce the C and N isotopic signatures in C-rich grains. Hot-CNO cycle isotopic signatures are obtained, including a large production of ¹³C and ¹⁵N. The short-lived radionuclides ²²Na and ²⁶Al are increased by orders of magnitude. The production of radiogenic ²²Ne from the decay of ²²Na in the He shell might solve the puzzle of the Ne-E(L) component in LD graphite grains. This scenario is attractive for the SiC grains of type AB with ¹⁴N/¹⁵N ratios lower than solar, and provides an alternative solution for SiC grains originally classified as nova grains. Finally, this process may contribute to the production of ¹⁴N and ¹⁵N in the Galaxy, helping to produce the ¹⁴N/¹⁵N ratio in the solar system

Dust in the Local Interstellar Wind

The gas-to-dust mass ratios found for interstellar dust within the Solar System, versus values determined astronomically for the cloud around the Solar System, suggest that large and small interstellar grains have separate histories, and that large interstellar grains preferentially detected by spacecraft are not formed exclusively by mass exchange with nearby interstellar gas. Observations by the Ulysses and Galileo satellites of the mass spectrum and flux rate of interstellar dust within the heliosphere are combined with information about the density, composition, and relative flow speed and direction of interstellar gas in the cloud surrounding the solar system to derive an in situ value for the gas-to-dust mass ratio, $R_{g/d} = 94^{+46}_{-38}$. Hubble observations of the cloud surrounding the solar system yield a gas-to-dust mass ratio of Rg/d=551+61-251 when B-star reference abundances are assumed. The exclusion of small dust grains from the heliosheath and heliosphere regions are modeled, increasing the discrepancy between interstellar and in situ observations. The shock destruction of interstellar grains is considered, and comparisons are made with interplanetary and presolar dust grains.Comment: 87 pages, 9 figures, 6 tables, accepted for publication in Astrophysical Journal. Uses AASTe

Structure Constants for New Infinite-Dimensional Lie Algebras of U(N+,N-) Tensor Operators and Applications

The structure constants for Moyal brackets of an infinite basis of functions on the algebraic manifolds M of pseudo-unitary groups U(N_+,N_-) are provided. They generalize the Virasoro and W_\infty algebras to higher dimensions. The connection with volume-preserving diffeomorphisms on M, higher generalized-spin and tensor operator algebras of U(N_+,N_-) is discussed. These centrally-extended, infinite-dimensional Lie-algebras provide also the arena for non-linear integrable field theories in higher dimensions, residual gauge symmetries of higher-extended objects in the light-cone gauge and C^*-algebras for tractable non-commutative versions of symmetric curved spaces.Comment: 8 pages, LaTeX, no figures; minor comments added; to appear in J. Phys A (Math. Gen.

Sulfur Isotopes in Gas-rich Impact-Melt Glasses in Shergottites

Large impact melt glasses in some shergottites contain huge amounts of Martian atmospheric gases and they are known as gas-rich impact-melt (GRIM) glasses. By studying the neutron-induced isotopic deficits and excesses in Sm-149 and Sm-150 isotopes resulting from Sm-149 (n,gamma) 150Sm reaction and 80Kr excesses produced by Br-79 (n,gamma) Kr-80 reaction in the GRIM glasses using mass-spectrometric techniques, it was shown that these glasses in shergottites EET79001 and Shergotty contain regolith materials irradiated by a thermal neutron fluence of approx.10(exp 15) n/sq cm near Martian surface. Also, it was shown that these glasses contain varying amounts of sulfates and sulfides based on the release patterns of SO2 (sulfate) and H2S (sulfide) using stepwise-heating mass-spectrometric techniques. Furthermore, EMPA and FE-SEM studies in basaltic-shergottite GRIM glasses EET79001, LithB (,507& ,69), Shergotty (DBS I &II), Zagami (,992 & ,994) showed positive correlation between FeO and "SO3" (sulfide + sulfate), whereas those belonging to olivine-phyric shergottites EET79001, LithA (,506, & ,77) showed positive correlation between CaO/Al2O3 and "SO3"

Aluminum-, Calcium- And Titanium-Rich Oxide Stardust In Ordinary Chondrite Meteorites

We report isotopic data for a total of 96 presolar oxide grains found in residues of several unequilibrated ordinary chondrite meteorites. Identified grain types include Al2O3, MgAl2O4, hibonite (CaAl12O19) and Ti oxide. This work greatly increases the presolar hibonite database, and is the first report of presolar Ti oxide. O-isotopic compositions of the grains span previously observed ranges and indicate an origin in red giant and asymptotic giant branch (AGB) stars of low mass (<2.5 MSun) for most grains. Cool bottom processing in the parent AGB stars is required to explain isotopic compositions of many grains. Potassium-41 enrichments in hibonite grains are attributable to in situ decay of now-extinct 41Ca. Inferred initial 41Ca/40Ca ratios are in good agreement with model predictions for low-mass AGB star envelopes, provided that ionization suppresses 41Ca decay. Stable Mg and Ca isotopic ratios of most of the hibonite grains reflect primarily the initial compositions of the parent stars and are generally consistent with expectations for Galactic chemical evolution, but require some local interstellar chemical inhomogeneity. Very high 17O/16O or 25Mg/24Mg ratios suggest an origin for some grains in binary star systems where mass transfer from an evolved companion has altered the parent star compositions. A supernova origin for the hitherto enigmatic 18O-rich Group 4 grains is strongly supported by multi-element isotopic data for two grains. The Group 4 data are consistent with an origin in a single supernova in which variable amounts of material from the deep 16O-rich interior mixed with a unique end-member mixture of the outer layers. The Ti oxide grains primarily formed in low-mass AGB stars. They are smaller and rarer than presolar Al2O3, reflecting the lower abundance of Ti than Al in AGB envelopes.Comment: Accepted for publication in ApJ; 47 pages, 13 figure