Convergence Rates for Newton’s Method at Singular Points

If Newton’s method is employed to find a root of a map from a Banach space into itself and the derivative is singular at that root, the convergence of the Newton iterates to the root is linear rather than quadratic. In this paper we give a detailed analysis of the linear convergence rates for several types of singular problems. For some of these problems we describe modifications of Newton’s method which will restore quadratic convergence

Oxygen-related traps in pentacene thin films: Energetic position and implications for transistor performance

We studied the influence of oxygen on the electronic trap states in a pentacene thin film. This was done by carrying out gated four-terminal measurements on thin-film transistors as a function of temperature and without ever exposing the samples to ambient air. Photooxidation of pentacene is shown to lead to a peak of trap states centered at 0.28 eV from the mobility edge, with trap densities of the order of 10(18) cm(-3). These trap states need to be occupied at first and cause a reduction in the number of free carriers, i.e. a consistent shift of the density of free holes as a function of gate voltage. Moreover, the exposure to oxygen reduces the mobility of the charge carriers above the mobility edge. We correlate the change of these transport parameters with the change of the essential device parameters, i.e. subthreshold performance and effective field-effect mobility. This study supports the assumption of a mobility edge for charge transport, and contributes to a detailed understanding of an important degradation mechanism of organic field-effect transistors. Deep traps in an organic field-effect transistor reduce the effective field-effect mobility by reducing the number of free carriers and their mobility above the mobility edge.Comment: 13 pages, 14 figures, to be published in Phys. Rev.

Sequencing and analysis of the gastrula transcriptome of the brittle star Ophiocoma wendtii

Background The gastrula stage represents the point in development at which the three primary germ layers diverge. At this point the gene regulatory networks that specify the germ layers are established and the genes that define the differentiated states of the tissues have begun to be activated. These networks have been well-characterized in sea urchins, but not in other echinoderms. Embryos of the brittle star Ophiocoma wendtii share a number of developmental features with sea urchin embryos, including the ingression of mesenchyme cells that give rise to an embryonic skeleton. Notable differences are that no micromeres are formed during cleavage divisions and no pigment cells are formed during development to the pluteus larval stage. More subtle changes in timing of developmental events also occur. To explore the molecular basis for the similarities and differences between these two echinoderms, we have sequenced and characterized the gastrula transcriptome of O. wendtii. Methods Development of Ophiocoma wendtii embryos was characterized and RNA was isolated from the gastrula stage. A transcriptome data base was generated from this RNA and was analyzed using a variety of methods to identify transcripts expressed and to compare those transcripts to those expressed at the gastrula stage in other organisms. Results Using existing databases, we identified brittle star transcripts that correspond to 3,385 genes, including 1,863 genes shared with the sea urchin Strongylocentrotus purpuratus gastrula transcriptome. We characterized the functional classes of genes present in the transcriptome and compared them to those found in this sea urchin. We then examined those members of the germ-layer specific gene regulatory networks (GRNs) of S. purpuratus that are expressed in the O. wendtii gastrula. Our results indicate that there is a shared ‘genetic toolkit’ central to the echinoderm gastrula, a key stage in embryonic development, though there are also differences that reflect changes in developmental processes. Conclusions The brittle star expresses genes representing all functional classes at the gastrula stage. Brittle stars and sea urchins have comparable numbers of each class of genes and share many of the genes expressed at gastrulation. Examination of the brittle star genes in which sea urchin orthologs are utilized in germ layer specification reveals a relatively higher level of conservation of key regulatory components compared to the overall transcriptome. We also identify genes that were either lost or whose temporal expression has diverged from that of sea urchins

Density of bulk trap states in organic semiconductor crystals: discrete levels induced by oxygen in rubrene

The density of trap states in the bandgap of semiconducting organic single crystals has been measured quantitatively and with high energy resolution by means of the experimental method of temperature-dependent space-charge-limited-current spectroscopy (TD-SCLC). This spectroscopy has been applied to study bulk rubrene single crystals, which are shown by this technique to be of high chemical and structural quality. A density of deep trap states as low as ~ 10^{15} cm^{-3} is measured in the purest crystals, and the exponentially varying shallow trap density near the band edge could be identified (1 decade in the density of states per ~25 meV). Furthermore, we have induced and spectroscopically identified an oxygen related sharp hole bulk trap state at 0.27 eV above the valence band.Comment: published in Phys. Rev. B, high quality figures: http://www.cpfs.mpg.de/~krellner

Milli-second Oscillations in the Persistent and Bursting Flux of Aql X-1 During an Outburst

The Rossi X-Ray Timing Explorer observed the soft X-Ray transient Aql X-1 during its outburst in February and March 1997. We report the discovery of quasi-periodic oscillations (QPOs) in its persistent flux with frequencies in the range of 740 to 830 Hz, Q-value of over 100, and a fractional RMS amplitude of (6.8 +- 0.6)%, and nearly coherent oscillations (NCOs) during a Type-I burst with a frequency of 549 Hz. The frequency of the QPOs in the persistent flux is correlated with the mass accretion rate on time scale of hours, but not on time scale of days. This is most likely the manifestation in a single source of the kHz QPO puzzle observed among many sources, i.e., on the one hand, individual sources show a correlation between the QPO frequency and the inferred mass accretion rate, on the other hand, the dozen or so sources with luminosities spanning two decades have essentially the same QPO frequencies. We propose that this multi-valued QPO frequency and mass accretion rate correlation indicates the existence of many similar regimes of the accretion disk. These regimes, with a very similar energy spectrum and QPO frequency, are distinguished from each other by the mass accretion rate or the total X-ray flux. The NCOs during the burst can be made almost perfectly coherent by taking into account a large frequency derivative. This strongly suggests that this frequency is related to the neutron star spin frequency. The large frequency derivative is attributable to the expansion or contraction of the neutron star photosphere during the burst.Comment: 6 pages, LaTex (aas2pp4), Accepted for publication in ApJ Let

Modifying the Einstein Equations off the Constraint Hypersuface

A new technique is presented for modifying the Einstein evolution equations off the constraint hypersurface. With this approach the evolution equations for the constraints can be specified freely. The equations of motion for the gravitational field variables are modified by the addition of terms that are linear and nonlocal in the constraints. These terms are obtained from solutions of the linearized Einstein constraints.Comment: 4 pages, 1 figure, uses REVTe

Multipole strength function of deformed superfluid nuclei made easy

We present an efficient method for calculating strength functions using the finite amplitude method (FAM) for deformed superfluid heavy nuclei within the framework of the nuclear density functional theory. We demonstrate that FAM reproduces strength functions obtained with the fully self-consistent quasi-particle random-phase approximation (QRPA) at a fraction of computational cost. As a demonstration, we compute the isoscalar and isovector monopole strength for strongly deformed configurations in $^{240}$Pu by considering huge quasi-particle QRPA spaces. Our approach to FAM, based on Broyden's iterative procedure, opens the possibility for large-scale calculations of strength distributions in well-bound and weakly bound nuclei across the nuclear landscape.Comment: 5 pages, 3 figure

Development of the post-injection propulsion system for the Mariner C spacecraft

Monopropellant hydrazine-fueled rocket used as post injection propulsion system for Mariner C spacecraf

The Radio Evolution of SN 2001gd

We present the results of observations of the radio emission from Supernova 2001gd in NGC 5033 from 2002 February 8 through 2006 September 25. The data were obtained using the Very Large Array at wavelengths of 1.3 cm (22.4 GHz), 2 cm (14.9 GHz), 3.6 cm (8.4 GHz), 6 cm (4.9 GHz), and 20 cm (1.5 GHz), with one upper limit at 90 cm (0.3 GHz). In addition, one detection has been provided by the Giant Metrewave Radio Telescope at 21 cm (1.4 GHz). SN 2001gd was discovered in the optical well past maximum light, so that it was not possible to obtain many of the early radio "turn-on" measurements which are important for estimating the local circumstellar medium (CSM) properties. Only at 20 cm were turn-on data available. However, our analysis and fitting of the radio light curves, and the assumption that the Type IIb SN 2001gd resembles the much better studied Type IIb SN 1993J, enables us to describe the radio evolution as being very regular through day ~550 and consistent with a nonthermal-emitting model with a thermal absorbing CSM. The presence of synchrotron-self absorption (SSA) at early times is implied by the data, but determination of the exact relationship between the SSA component from the emitting region and the free-free absorption component from the CSM is not possible as there are insufficient early measurements to distinguish between models. After day ~550, the radio emission exhibits a dramatically steeper decline rate which, assuming similarity to SN 1993J, can be described as an exponential decrease with an e-folding time of 500 days. We interpret this abrupt change in the radio flux density decline rate as implying a transition of the shock front into a more tenuous region of circumstellar material. A similar change in radio evolution has been seen earlier in other SNe such as SN 1988Z, SN 1980K, and SN 1993J.Comment: 3 tables, 2 figures, To appear in the Astrophysical Journa

Remote Sensing of Parasitic Nematodes in Plants

A method and apparatus for remote sensing of parasitic nematodes in plants, now undergoing development, is based on measurement of visible and infrared spectral reflectances of fields where the plants are growing. Initial development efforts have been concentrated on detecting reniform nematodes (Rotylenchulus reniformis) in cotton plants, because of the economic importance of cotton crops. The apparatus includes a hand-held spectroradiometer. The readings taken by the radiometer are processed to extract spectral reflectances at sixteen wavelengths between 451 and 949 nm that, taken together, have been found to be indicative of the presence of Rotylenchulus reniformis. The intensities of the spectral reflectances are used to estimate the population density of the nematodes in an area from which readings were taken