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

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

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

Subdiffractional focusing and guiding of polaritonic rays in a natural hyperbolic material

Uniaxial materials whose axial and tangential permittivities have opposite signs are referred to as indefinite or hyperbolic media. In such materials light propagation is unusual, leading to novel and often non-intuitive optical phenomena. Here we report infrared nano-imaging experiments demonstrating that crystals of hexagonal boron nitride (hBN), a natural mid-infrared hyperbolic material, can act as a "hyper-focusing lens" and as a multi-mode waveguide. The lensing is manifested by subdiffractional focusing of phonon-polaritons launched by metallic disks underneath the hBN crystal. The waveguiding is revealed through the modal analysis of the periodic patterns observed around such launchers and near the sample edges. Our work opens new opportunities for anisotropic layered insulators in infrared nanophotonics complementing and potentially surpassing concurrent artificial hyperbolic materials with lower losses and higher optical localization.Comment: 25 pages, 5 figure

Self-interactions of the lightest MSSM Higgs boson in the large pseudoscalar-mass limit

We investigate the decoupling properties of the Higgs-sector-induced one-loop corrections in the lightest Higgs-boson self-couplings, in the framework of the Minimal Supersymmetric Standard Model (MSSM). The renormalized n-point vertex functions with external Higgs particles in the MSSM and in the SM are derived to the one-loop level and compared in the MA >> MZ limit. The computation has been done in a general R_{xi} gauge and the on-shell renormalization scheme is chosen. By a comparison of the renormalized lightest Higgs-boson h^0 vertex functions with respect to the corresponding SM ones, we find that the differences between the predictions of both models are summarized in the lightest Higgs-boson mass correction Delta Mh. Consequently, the radiative corrections are absorbed in the Higgs-boson mass, and the trilinear and quartic h^0 self-couplings acquire the same structure as the couplings of the SM Higgs-boson. Therefore, decoupling of the heavy MSSM Higgs bosons occurs and the MSSM h^0 self-interactions converge to the SM ones in the MA >> MZ limit.Comment: LaTeX, 26 pages, 1 figure. Sections 4 and 5 summarized in one section. Some references added. Published version in Phys. Rev.

Testing Supersymmetry with Lepton Flavor Violating tau and mu decays

In this work the following lepton flavor violating $\tau$ and $\mu$ decays are studied: $\tau^- \to \mu^- \mu^- \mu^+$, $\tau^- \to e^- e^- e^+$, $\mu^- \to e^- e^- e^+$, $\tau^- \to \mu^- \gamma$, $\tau^- \to e^- \gamma$ and $\mu^- \to e^- \gamma$. We work in a supersymmetric scenario consisting of the minimal supersymmetric standard model particle content, extended by the addition of three heavy right handed Majorana neutrinos and their supersymmetric partners, and where the generation of neutrino masses is done via the seesaw mechanism. Within this context, a significant lepton flavor mixing is generated in the slepton sector due to the Yukawa neutrino couplings, which is transmited from the high to the low energies via the renormalization group equations. This slepton mixing then generates via loops of supersymmetric particles significant contributions to the rates of $l_j \to 3 l_i$ and the correlated $l_j \to l_i \gamma$ decays. We analize here in full detail these rates in terms of the relevant input parameters, which are the usual minimal supergravity parameters and the seesaw parameters. For the $l_j \to 3 l_i$ decays, a full one-loop analytical computation of all the contributing supersymmetric loops is presented. This completes and corrects previous computations in the literature. In the numerical analysis compatibility with the most recent experimental upper bounds on all these $\tau$ and $\mu$ decays, with the neutrino data, and with the present lower bounds on the supersymmetric particle masses are required. Two typical scenarios with degenerate and hierarchical heavy neutrinos are considered. We will show here that the minimal supergravity and seesaw parameters do get important restrictions from these $\tau$ and $\mu$ decays in the hierarchical neutrino case.Comment: Version to appear in Physical Review

Understanding the 8 micron vs. Pa-alpha relationship on sub-arcsecond scales in Luminous Infrared Galaxies

This work explores in detail the relation between the 8 micron and the Pa-alpha emissions for 122 HII regions identified in a sample of 10 low-z LIRGs with nearly constant metallicity (12 + log (O/H) ~ 8.8). We use Gemini/T-ReCS high-spatial resolution (<~ 0.4" ~ 120 pc for the average distance of 60 Mpc of our sample) mid-infrared imaging (at 8.7 micron or 10.3 micron) together with HST/NICMOS continuum and Pa-alpha images. The LIRG HII regions extend the L_8micron vs. L_Pa-alpha relation found for HII knots in the high-metallicity SINGS galaxies by about two orders of magnitude to higher luminosities. Since the metallicity of the LIRG sample is nearly constant, we can rule out this effect as a cause for the scatter seen in the relationship. In turn, it is attributed to two effects: age and PAH features. The L_8micron/L_Pa-alpha ratio, which varies by a factor of ten for the LIRG HII regions, is reproduced by a model with instantaneous star formation and ages ranging from ~ 4 to 7.5 Myr. The remaining dispersion around the model predictions for a given age is probably due to differential contributions of the PAH features (the 8.6 micron, in our case) to the 8 micron emission from galaxy to galaxy.Comment: 16 pages, 9 figures, accepted for publication in ApJ; paper with full-resolution figures can be found at: http://damir.iem.csic.es/extragalactic