On a conjecture regarding the upper graph box dimension of bounded subsets of the real line

Let X \subset R be a bounded set; we introduce a formula that calculates the upper graph box dimension of X (i.e.the supremum of the upper box dimension of the graph over all uniformly continuous functions defined on X). We demonstrate the strength of the formula by calculating the upper graph box dimension for some sets and by giving an "one line" proof, alternative to the one given in [1], of the fact that if X has finitely many isolated points then its upper graph box dimension is equal to the upper box dimension plus one. Furthermore we construct a collection of sets X with infinitely many isolated points, having upper box dimension a taking values from zero to one while their graph box dimension takes any value in [max{2a,1},a + 1], answering this way, negatively to a conjecture posed in [1]

Photometry of Irregular Satellites of Uranus and Neptune

We present BVR photometric colors of six Uranian and two Neptunian irregular satellites, collected using the Magellan Observatory (Las Campanas, Chile) and the Keck Observatory, (Manua Kea, Hawaii). The colors range from neutral to light red, and like the Jovian and the Saturnian irregulars (Grav et al. 2003) there is an apparent lack of the extremely red objects found among the Centaurs and Kuiper belt objects. The Uranian irregulars can be divided into three possible dynamical families, but the colors collected show that two of these dynamical families, the Caliban and Sycorax-clusters, have heterogeneous colors. Of the third possible family, the 168-degree cluster containing two objects with similar average inclinations but quite different average semi-major axis, only one object (U XXI Trinculo) was observed. The heterogeneous colors and the large dispersion of the average orbital elements leads us to doubt that they are collisional families. We favor single captures as a more likely scenario. The two neptunians observed (N II Nereid and S/2002 N1) both have very similar neutral, sun-like colors. Together with the high collisional probability between these two objects over the age of the solar system (Nesvorny et al. 2003, Holman et al. 2004), this suggests that S/2002 N1 be a fragment of Nereid, broken loose during a collision or cratering event with an undetermined impactor.Comment: 13 pages (including 3 figures and 2 tables). Submitted to ApJ Letter

Continued monitoring of LMXBs with the Faulkes Telescopes

The Faulkes Telescope Project is an educational and research arm of the Las Cumbres Observatory Global Telescope Network (LCOGTN). It has two 2-metre robotic telescopes, located at Haleakala on Maui (FT North) and Siding Spring in Australia (FT South). It is planned for these telescopes to be complemented by a research network of eighteen 1-metre telescopes, along with an educational network of twenty-eight 0.4-metre telescopes, providing 24 hour coverage of both northern and southern hemispheres. We have been conducting a monitoring project of 13 low-mass X-ray binaries (LMXBs) using FT North since early 2006. The introduction of FT South has allowed us to extend this to monitor a total of 30 LMXBs (see target list, Section 4). New instrumentation will allow us to expand this project to include both infrared wavelengths (z and y band) and spectroscopy. Brighter targets (~ 16 - 18 mag.) are imaged weekly in V, R and i’ bands (SNR ~ 50), while fainter ones (> 18 mag.) are observed only in i’ band (SNR ~ 20). We alter this cadence in response to our own analysis or Astronomers Telegrams (ATels)

Thermal Desorption of Water-Ice in the Interstellar Medium

Water (H2O) ice is an important solid constituent of many astrophysical environments. To comprehend the role of such ices in the chemistry and evolution of dense molecular clouds and comets, it is necessary to understand the freeze-out, potential surface reactivity, and desorption mechanisms of such molecular systems. Consequently, there is a real need from within the astronomical modelling community for accurate empirical molecular data pertaining to these processes. Here we give the first results of a laboratory programme to provide such data. Measurements of the thermal desorption of H2O ice, under interstellar conditions, are presented. For ice deposited under conditions that realistically mimic those in a dense molecular cloud, the thermal desorption of thin films (~50 molecular layers) is found to occur with zero order kinetics characterised by a surface binding energy, E_{des}, of 5773 +/- 60 K, and a pre-exponential factor, A, of 10^(30 +/- 2) molecules cm^-2 s^-1. These results imply that, in the dense interstellar medium, thermal desorption of H2O ice will occur at significantly higher temperatures than has previously been assumed.Comment: 9 pages, 4 figures, accepted for publication in MNRA

First-passage theory of exciton population loss in single-walled carbon nanotubes reveals micron-scale intrinsic diffusion lengths

One-dimensional crystals have long range translational invariance which manifests as long exciton diffusion lengths, but such intrinsic properties are often obscured by environmental perturbations. We use a first-passage approach to model single-walled carbon nanotube (SWCNT) exciton dynamics (including exciton-exciton annihilation and end effects) and compare it to results from both continuous-wave and multi-pulse ultrafast excitation experiments to extract intrinsic SWCNT properties. Excitons in suspended SWCNTs experience macroscopic diffusion lengths, on the order of the SWCNT length, (1.3-4.7 um) in sharp contrast to encapsulated samples. For these pristine samples, our model reveals intrinsic lifetimes (350-750 ps), diffusion constants (130-350 cm^2/s), and absorption cross-sections (2.1-3.6 X 10^-17 cm^2/atom) among the highest previously reported.and diffusion lengths for SWCNTs.Comment: 6 pages, 3 figure

Axisymmetric filamentary structures

Axisymmetric filamentary structure