A critical branching process model for biodiversity

Motivated as a null model for comparison with data, we study the following model for a phylogenetic tree on $n$ extant species. The origin of the clade is a random time in the past, whose (improper) distribution is uniform on $(0,\infty)$. After that origin, the process of extinctions and speciations is a continuous-time critical branching process of constant rate, conditioned on having the prescribed number $n$ of species at the present time. We study various mathematical properties of this model as $n \to \infty$ limits: time of origin and of most recent common ancestor; pattern of divergence times within lineage trees; time series of numbers of species; number of extinct species in total, or ancestral to extant species; and "local" structure of the tree itself. We emphasize several mathematical techniques: associating walks with trees, a point process representation of lineage trees, and Brownian limits.Comment: 31 pages, 7 figure

Glass Transition in a Two-Dimensional Electron System in Silicon in a Parallel Magnetic Field

Studies of low-frequency resistance noise show that the glassy freezing of the two-dimensional electron system (2DES) in Si in the vicinity of the metal-insulator transition (MIT) persists in parallel magnetic fields B of up to 9 T. At low B, both the glass transition density $n_g$ and $n_c$, the critical density for the MIT, increase with B such that the width of the metallic glass phase ($n_c<n_s<n_g$) increases with B. At higher B, where the 2DES is spin polarized, $n_c$ and $n_g$ no longer depend on B. Our results demonstrate that charge, as opposed to spin, degrees of freedom are responsible for glassy ordering of the 2DES near the MIT.Comment: 4 pages, 5 figure

Metal-insulator transition and glassy behavior in two-dimensional electron systems

Studies of low-frequency resistance noise demonstrate that glassy freezing occurs in a two-dimensional electron system in silicon in the vicinity of the metal-insulator transition (MIT). The width of the metallic glass phase, which separates the 2D metal and the (glassy) insulator, depends strongly on disorder, becoming extremely small in high-mobility (low-disorder) samples. The glass transition is manifested by a sudden and dramatic slowing down of the electron dynamics, and by a very abrupt change to the sort of statistics characteristic of complicated multistate systems. In particular, the behavior of the second spectrum, an important fourth-order noise statistic, indicates the presence of long-range correlations between fluctuators in the glassy phase, consistent with the hierarchical picture of glassy dynamics.Comment: Contribution to conference on "Noise as a tool for studying materials" (SPIE), Santa Fe, New Mexico, June 2003; 15 pages, 12 figs. (includes some low-quality figs; send e-mail to get high-quality figs.

The influence of microlensing on the shape of the AGN Fe K-alpha line

We study the influence of gravitational microlensing on the AGN Fe K-alpha line confirming that unexpected enhancements recently detected in the iron line of some AGNs can be produced by this effect. We use a ray tracing method to study the influence of microlensing in the emission coming from a compact accretion disc considering both geometries, Schwarzschild and Kerr. Thanks to the small dimensions of the region producing the AGN Fe K-alpha line, the Einstein Ring Radii associated to even very small compact objects have size comparable to the accretion disc hence producing noticeable changes in the line profiles. Asymmetrical enhancements contributing differently to the peaks or to the core of the line are produced by a microlens, off-centered with respect to the accretion disc. In the standard configuration of microlensing by a compact object in an intervening galaxy, we found that the effects on the iron line are two orders of magnitude larger than those expected in the optical or UV emission lines. In particular, microlensing can satisfactorily explain the excess in the iron line emission found very recently in two gravitational lens systems, H 1413+117 and MG J0414+0534. Exploring other physical {scenario} for microlensing, we found that compact objects (of the order of one Solar mass) which belong to {the bulge or the halo} of the host galaxy can also produce significant changes in the Fe K$_\alpha$ line profile of an AGN. However, the optical depth estimated for this type of microlensing is {very small, $\tau\sim 0.001$, even in a favorable case.Comment: Astron. Astrophys. accepte

The flux ratio of the [OIII] 5007,4959 lines in AGN: Comparison with theoretical calculations

By taking into account relativistic corrections to the magnetic dipole operator, the theoretical [OIII] 5006.843/4958.511 line intensity ratio of 2.98 is obtained. In order to check this new value using AGN spectra we present the measurements of the flux ratio of the [OIII] 4959,5007 emission lines for a sample of 62 AGN, obtained from the Sloan Digital Sky Survey (SDSS) Database and from published observations. We select only high signal-to-noise ratio spectra for which the line shapes of the [OIII] 4959,5007 lines are the same. We obtained an averaged flux ratio of 2.993 +/- 0.014, which is in a good agreement with the theoretical one.Comment: Accepted for publication in the MNRA

First evidence for charge ordering in NaV2_2O5_5 from Raman spectroscopy

We argue on the basis of symmetry selection rules and Raman scattering spectra that NaV$_2$O$_5$ undergoes a charge ordering phase transition at T$_c$=34 K. Such a transition is characterized by the redistribution of the charges at the phase transition and corresponds to the change of the vanadium ions, from uniform V$^{4.5+}$ to two different V$^{4+}$ and V$^{5+}$ states. In the low temperature phase the V$^{4+}$ ions are forming a "zig-zag" ladder structure along the {\bf b}-axis, consistent with the symmetry of the P2/b space group.Comment: to be published in solid state communication