The fractional Keller-Segel model

The Keller-Segel model is a system of partial differential equations modelling chemotactic aggregation in cellular systems. This model has blowing up solutions for large enough initial conditions in dimensions d >= 2, but all the solutions are regular in one dimension; a mathematical fact that crucially affects the patterns that can form in the biological system. One of the strongest assumptions of the Keller-Segel model is the diffusive character of the cellular motion, known to be false in many situations. We extend this model to such situations in which the cellular dispersal is better modelled by a fractional operator. We analyze this fractional Keller-Segel model and find that all solutions are again globally bounded in time in one dimension. This fact shows the robustness of the main biological conclusions obtained from the Keller-Segel model

Solid helium at high pressure: A path-integral Monte Carlo simulation

Solid helium (3He and 4He) in the hcp and fcc phases has been studied by path-integral Monte Carlo. Simulations were carried out in the isothermal-isobaric (NPT) ensemble at pressures up to 52 GPa. This allows one to study the temperature and pressure dependences of isotopic effects on the crystal volume and vibrational energy in a wide parameter range. The obtained equation of state at room temperature agrees with available experimental data. The kinetic energy, E_k, of solid helium is found to be larger than the vibrational potential energy, E_p. The ratio E_k/E_p amounts to about 1.4 at low pressures, and decreases as the applied pressure is raised, converging to 1, as in a harmonic solid. Results of these simulations have been compared with those yielded by previous path integral simulations in the NVT ensemble. The validity range of earlier approximations is discussed.Comment: 7 pages, 5 figure

Massive stars in the hinterland of the young cluster, Westerlund 2

Accepted for publication in MNRAS, 13 July 2018. 16 pages, plus one-page table in an appendix.An unsettled question concerning the formation and distribution of massive stars is whether they must be born in massive clusters and, if found in less dense environments, whether they must have migrated there. With the advent of wide-area digital photometric surveys, it is now possible to identify massive stars away from prominent Galactic clusters without bias. In this study we consider 40 candidate OB stars found in the field around the young massive cluster, Westerlund 2, by Mohr-Smith et al.: these are located inside a box of 1.5 × 1.5 deg 2 and are selected on the basis of their extinctions and K magnitudes.We present VLT/X-shooter spectra of two of the hottest O stars, respectively 11 and 22 arcmin from the centre of Westerlund 2. They are confirmed as O4V stars, with stellar masses likely to be in excess of 40 M ·. Their radial velocities relative to the non-binary reference object, MSP 182, in Westerlund 2 are -29.4 ± 1.7 and -14.4 ± 2.2 km s -1, respectively. Using Gaia DR2 proper motions we find that between 8 and 11 early O/WR stars in the studied region (including the two VLT targets, plus WR 20c and WR 20aa) could have been ejected fromWesterlund 2 in the last one million years. This represents an efficiency of massive-star ejection of up to ~ 25 per cent. On sky, the positions of these stars and their proper motions show a near N-S alignment. We discuss the possibility that these results are a consequence of prior sub-cluster merging combining with dynamical ejection.Peer reviewe

Optical detection of the radio supernova SN 2000ft in the circumnuclear region of the luminous infrared galaxy NGC 7469

SN 2000ft is detected in two independent Planetary Camera images (F547W and F814W) taken May 13, 2000, about two months before the predicted date of the explosion (July 19, 2000), based on the analysis of its radio light evolution by Alberdi and collaborators. The apparent optical magnitudes and red color of SN 2000ft indicate that it is observed through an extinction of at least A$_V$= 3.0 magnitudes. The extinction corrected lower limit to the absolute visual magnitude (M$_V$ $\leq -$ 18.0), identifies SN 2000ft as a luminous supernova in the optical, as other luminous radio supernovae before. SN 2000ft exploded in a region located at only 0.1 arcsec (i.e. 34 +/- 3 pc) west of a faint cluster (C24). No parent cluster is identified within the detection limits of the HST short exposures. The unambiguous detection of SN 2000ft in the visual shows that multi-epoch sub-arcsecond (FWHM less than 0.1 arcsec) optical imaging is also a valid tool that should be explored further to detect supernovae in the dusty (circum)nuclear regions of (U)LIRGs

Multiple peak aggregations for the Keller-Segel system

In this paper we derive matched asymptotic expansions for a solution of the Keller-Segel system in two space dimensions for which the amount of mass aggregation is $8\pi N$, where $N=1,2,3,...$ Previously available asymptotics had been computed only for the case in which N=1

Real Time Electron Tunneling and Pulse Spectroscopy in Carbon Nanotube Quantum Dots

We investigate a Quantum Dot (QD) in a Carbon Nanotube (CNT) in the regime where the QD is nearly isolated from the leads. An aluminum single electron transistor (SET) serves as a charge detector for the QD. We precisely measure and tune the tunnel rates into the QD in the range between 1 kHz and 1 Hz, using both pulse spectroscopy and real - time charge detection and measure the excitation spectrum of the isolated QD.Comment: 12 pages, 5 figure

Transmission spectroscopy of the inflated exo-Saturn HAT-P-19b

We observed the Saturn-mass and Jupiter-sized exoplanet HAT-P-19b to refine its transit parameters and ephemeris as well as to shed first light on its transmission spectrum. We monitored the host star over one year to quantify its flux variability and to correct the transmission spectrum for a slope caused by starspots. A transit of HAT-P-19b was observed spectroscopically with OSIRIS at the Gran Telescopio Canarias in January 2012. The spectra of the target and the comparison star covered the wavelength range from 5600 to 7600 AA. One high-precision differential light curve was created by integrating the entire spectral flux. This white-light curve was used to derive absolute transit parameters. Furthermore, a set of light curves over wavelength was formed by a flux integration in 41 wavelength channels of 50 AA width. We analyzed these spectral light curves for chromatic variations of transit depth. The transit fit of the combined white-light curve yields a refined value of the planet-to-star radius ratio of 0.1390 pm 0.0012 and an inclination of 88.89 pm 0.32 degrees. After a re-analysis of published data, we refine the orbital period to 4.0087844 pm 0.0000015 days. We obtain a flat transmission spectrum without significant additional absorption at any wavelength or any slope. However, our accuracy is not sufficient to significantly rule out the presence of a pressure-broadened sodium feature. Our photometric monitoring campaign allowed for an estimate of the stellar rotation period of 35.5 pm 2.5 days and an improved age estimate of 5.5^+1.8_-1.3 Gyr by gyrochronology.Comment: 14 pages, 9 figures, Accepted for publication in A&