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In this paper we consider an initial-boundary value problem with a Caputo time derivative of order $\alpha\in(0,1)$. The solution typically exhibits a weak singularity near the initial time and this causes a reduction in the orders of convergence of standard schemes. To deal with this singularity, the solution is computed with a fitted difference scheme on a graded mesh. The convergence of this scheme is analysed using a discrete maximum principle and carefully chosen barrier functions. Sharp error estimates are proved, which show an enhancement in the convergence rate compared with the standard L1 approximation on uniform meshes, and also indicate an optimal choice for the mesh grading. This optimal mesh grading is less severe than the optimal grading for the standard L1 scheme. Furthermore, the dependence of the error on the final time forms part of our error estimate. Numerical experiments are presented which corroborate our theoretical results.

Pointwise accurate numerical methods are constructed and analysed for three classes of singularly perturbed first order transport problems. The methods involve piecewise-uniform Shishkin meshes and the numerical approximations are shown to be parameter-uniformly convergent in the maximum norm. A transport problem from the modelling of fluid-particle interaction is formulated and used as a test problem for these numerical methods. Numerical results are presented to illustrate the performance of the numerical methods and to confirm the theoretical error bounds established in the paper., Comment: 29 pages, 2 figures and 5 tables

The domain wall dynamics driven by an out of plane magnetic field was measured for a series of magnetic trilayers with different strengths of the interfacial Dzyaloshinskii-Moriya interaction (DMI). The features of the field-driven domain wall velocity curves strongly depend on the amplitude of the HD field stabilising chiral N\'eel walls. The measured Walker velocity, which in systems with large DMI is maintained after the Walker field giving rise to a velocity plateau up to the Slonczewski field HS, can be easily related to the DMI strength. Yet, when the DMI field HD and the domain wall demagnetising field HDW have comparable values, a careful analysis needs to be done in order to evaluate the impact of the DMI on the domain wall velocity. By means of a one-dimensional model and 2D simulations, we successfully extend this method to explain experimental results to cases where HD and HDW are comparable., Comment: 9 pages, 3 Figures

We present two new planetary systems found around cool dwarf stars with data from the K2 mission. The first system was found in K2-239 (EPIC 248545986), char- acterized in this work as M3.0V and observed in the 14th campaign of K2. It consists of three Earth-size transiting planets with radii of 1.1, 1.0 and 1.1 R Earth, showing a compact configuration with orbital periods of 5.24, 7.78 and 10.1 days, close to 2:3:4 resonance. The second was found in K2-240 (EPIC 249801827), characterized in this work as M0.5V and observed in the 15th campaign. It consists of two transiting super-Earths with radii 2.0 and 1.8 R Earth and orbital periods of 6.03 and 20.5 days. The equilibrium temperatures of the atmospheres of these planets are estimated to be in the range of 380-600 K and the amplitudes of signals in transmission spectroscopy are estimated at ~10 ppm., Comment: Accepted for publication in MNRAS letters

We report on the design, construction and operation of a low background x-ray detection line composed of a shielded Micromegas (micromesh gaseous structure) detector of the microbulk technique. The detector is made from radiopure materials and is placed at the focal point of a $\sim$~5 cm diameter, 1.3 m focal-length, cone-approximation Wolter I x-ray telescope (XRT) comprised of thermally-formed (or "slumped") glass substrates deposited with multilayer coatings. The system has been conceived as a technological pathfinder for the future International Axion Observatory (IAXO), as it combines two of the techniques (optic and detector) proposed in the conceptual design of the project. It is innovative for two reasons: it is the first time an x-ray optic has been designed and fabricated specifically for axion research, and the first time a Micromegas detector has been operated with an x-ray optic. The line has been installed at one end of the CERN Axion Solar Telescope (CAST) magnet and is currently looking for solar axions. The combination of the XRT and Micromegas detector provides the best signal-to-noise ratio obtained so far by any detection system of the CAST experiment with a background rate of 5.4$\times$10$^{-3}\;$counts per hour in the energy region-of-interest and signal spot area., Comment: 21 pages, 16 figures

We explore the possibility to develop a new axion helioscope type, sensitive to the higher axion mass region favored by axion models. We propose to use a low background large volume TPC immersed in an intense magnetic field. Contrary to traditional tracking helioscopes, this detection technique takes advantage of the capability to directly detect the photons converted on the buffer gas which defines the axion mass sensitivity region, and does not require pointing the magnet to the Sun. The operation flexibility of a TPC to be used with different gas mixtures (He, Ne, Xe, etc) and pressures (from 10 mbar to 10 bar) will allow to enhance sensitivity for axion masses from few meV to several eV. We present different helioscope data taking scenarios, considering detection efficiency and axion absorption probability, and show the sensitivities reachable with this technique to be few $\times$ 10$^{-11}\,$GeV$^{-1}$ for a 5$\,$T$\,$m$^3$ scale TPC. We show that a few years program taking data with such setup would allow to probe the KSVZ axion model for axion masses above 100 meV., Comment: prepared for submission to JCAP

Here we focus on the description of the mechanisms behind the process of information aggregation and decision making, a basic step to understand emergent phenomena in society, such as trends, information spreading or the wisdom of crowds. In many situations, agents choose between discrete options. We analyze experimental data on binary opinion choices in humans. The data consists of two separate experiments in which humans answer questions with a binary response, where one is correct and the other is incorrect. The questions are answered without and with information on the answers of some previous participants. We find that a Bayesian approach captures the probability of choosing one of the answers. The influence of peers is uncorrelated with the difficulty of the question. The data is inconsistent with Weber's law, which states that the probability of choosing an option depends on the proportion of previous answers choosing that option and not on the total number of those answers. Last, the present Bayesian model fits reasonably well to the data as compared to some other previously proposed functions although the latter sometime perform slightly better than the Bayesian model. The asset of the present model is the simplicity and mechanistic explanation of the behavior., Comment: 8 pages, 6 figures, 1 table

NEXT-MM is a general-purpose high pressure (10 bar, $\sim25$ l active volume) Xenon-based TPC, read out in charge mode with an 8 cm $\times$8 cm-segmented 700 cm$^2$ plane (1152 ch) of the latest microbulk-Micromegas technology. It has been recently commissioned at University of Zaragoza as part of the R&D of the NEXT $0\nu\beta\beta$ experiment, although the experiment's first stage is currently being built based on a SiPM/PMT-readout concept relying on electroluminescence. Around 2 million events were collected during the last months, stemming from the low energy $\gamma$-rays emitted by a $^{241}$Am source when interacting with the Xenon gas ($\epsilon$ = 26, 30, 59.5 keV). The localized nature of such events above atmospheric pressure, the long drift times, as well as the possibility to determine their production time from the associated $\alpha$ particle in coincidence, allow the extraction of primordial properties of the TPC filling gas, namely the drift velocity, diffusion and attachment coefficients. In this work we focus on the little explored combination of Xe and trimethylamine (TMA) for which, in particular, such properties are largely unknown. This gas mixture offers potential advantages over pure Xenon when aimed at Rare Event Searches, mainly due to its Penning characteristics, wave-length shifting properties and reduced diffusion, and it is being actively investigated by our collaboration. The chamber is currently operated at 2.7 bar, as an intermediate step towards the envisaged 10 bar. We report here its performance as well as a first implementation of the calibration procedures that have allowed the extension of the previously reported energy resolution to the whole readout plane (10.6%FWHM@30keV)., Comment: 22 pages, 13 figures

Motivated by the idea that some characteristics are specific to the relations between individuals and not of the individuals themselves, we study a prototype model for the dynamics of the states of the links in a fixed network of interacting units. Each link in the network can be in one of two equivalent states. A majority link-dynamics rule is implemented, so that in each dynamical step the state of a randomly chosen link is updated to the state of the majority of neighboring links. Nodes can be characterized by a link heterogeneity index, giving a measure of the likelihood of a node to have a link in one of the two states. We consider this link-dynamics model on fully connected networks, square lattices and Erd \"os-Renyi random networks. In each case we find and characterize a number of nontrivial asymptotic configurations, as well as some of the mechanisms leading to them and the time evolution of the link heterogeneity index distribution. For a fully connected network and random networks there is a broad distribution of possible asymptotic configurations. Most asymptotic configurations that result from link-dynamics have no counterpart under traditional node dynamics in the same topologies., Comment: 9 pages, 13 figures

We present self-consistent global, steady-state MHD models and synthetic optically thin synchrotron emission maps for the jet of M87. The model consist of two distinct zones: an inner relativistic outflow, which we identify with the observed jet, and an outer cold disk-wind. While the former does not self-collimate efficiently due to its high effective inertia, the latter fulfills all the conditions for efficient collimation by the magneto-centrifugal mechanism. Given the right balance between the effective inertia of the inner flow and the collimation efficiency of the outer disk wind, the relativistic flow is magnetically confined into a well collimated beam and matches the measurements of the opening angle of M87 over several orders of magnitude in spatial extent. The synthetic synchrotron maps reproduce the morphological structure of the jet of M87, i.e. center-bright profiles near the core and limb-bright profiles away from the core. At the same time, they also show a local increase of brightness at some distance along the axis associated to a recollimation shock in the MHD model. Its location coincides with the position of the optical knot HST-1. In addition our best fitting model is consistent with a number of observational constraints such as the magnetic field in the knot HST-1, and the jet-to-counterjet brightness ratio., Comment: 9 pages, 9 figures, accepted by ApJ

We present a self-consistent MHD model for the jet of M87. The model consist of two distinct zones: an inner relativistic outflow, which we identify with the observed jet, and an outer cold disk-wind. While the former does not self-collimate efficiently due to its high effective inertia, the latter fulfills all the conditions for efficient collimation by the magneto-centrifugal mechanism. Given the right balance between the effective inertia of the inner flow and the collimation efficiency of the outer disk wind, the relativistic flow is magnetically confined into a well collimated beam for a wide range of parameters and matches the measurements of the opening angle of M87 over several orders of magnitude in spatial extent. In the second part of this work, we present synthetic synchrotron emission maps for our MHD models. In principle the two-zone model can reproduce the morphological structure seen in radio observations, as central-peaked profiles across the jet close the the source, limb-bright further down the jet, and a bright knot close to the position of HST-1. However it is difficult to reconcile all features into a single set of parameters., Comment: 4 pages, 5 figures, to appear in the proceedings of the HEPRO conference, September 24-28, 2007, Dublin, Ireland

We report on a densely time sampled polarimetric flux density monitoring of the BL Lac object S5 0716+71 at 86 GHz and 229 GHz with the IRAM 30 m telescope within a coordinated broad spectral band campaign, centred around an INTEGRAL observation during November 10 to 16, 2003. Our aim was to search for signatures of inverse-Compton "catastrophes". At 86 GHz, making use of a new calibration strategy, we reach a relative rms accuracy of the flux density measurements of 1.2%. At this frequency, S5 0716+71 showed no intra-day variability, but showed remarkable inter-day variability with a flux density increase of 34% during the first four observing days, which can not be explained by source extrinsic causes. The 86 GHz linear polarization fraction of S5 0716+71 was unusually large 15.0+-1.8%. Inter-day variability in linear polarization at 86 GHz, with significance level >~95%; sigma_P/=15% and sigma_chi=6 deg., was also observed. From the emission variations at the synchrotron turnover frequency (~86 GHz) we compute an apparent brightness temperature T_B,app>1.4x10^14K at a redshift of 0.3, which exceeds by two orders of magnitude the inverse-Compton limit. A relativistic correction for T_B,app with a Doppler factor delta > 7.8 brings the observed brightness temperature down to the inverse Compton limit. A more accurate lower limit of delta > 14.0, is obtained from the comparison of the 86 GHz synchrotron flux density and the upper limits for the synchrotron self-Compton flux density obtained from the INTEGRAL observations. The relativistic beaming of the emission by this high Doppler factor explains the non-detection of "catastrophic" inverse-Compton avalanches by INTEGRAL., Comment: Accepted for publication in A&A. 16 pages, 11 figures

Recent gamma-ray observations of the blazar 1ES 1101-232 (redshift z=0.186) reveal that the unabsorbed TeV spectrum is hard, with spectral index $\alpha \lesssim 0.5$ [$F(\nu) \propto \nu^{-\alpha}$]. We show that simple one-zone synchrotron self-Compton model can explain such hard spectra if we assume a power law energy distribution of the emitting electrons with a relatively high minimum energy. In this case the intrinsic TeV spectrum can be as hard as $F(\nu)\propto \nu^{1/3}$, while the predicted X-ray spectrum can still be much softer. The observations of 1ES 1101-232 can therefore be reconciled with relatively high intensities of the infrared background, even if some extreme background levels can indeed be excluded. We show that the other TeV sources (Mrk 421, Mrk 501 and PKS 2155-304) can be interpreted in the same framework, with a somewhat larger minimum energy., Comment: 5 pages, 3 figures, accepted for publication as a letter in MNRAS

Some intra-day variable, compact extra-galactic radio sources show brightness temperatures severely exceeding 10^{12} K, the limit set by catastrophic inverse-Compton (IC) cooling in sources of incoherent synchrotron radiation. The violation of the IC limit, possible under non-stationary conditions, would lead to IC avalanches in the soft-gamma-ray energy band during transient periods. For the first time, broadband signatures of possible IC catastrophes were searched for in S5 0716+71. A multifrequency observing campaign targetting S5 0716+71 was carried out in November 2003 under the framework of the European Network for the Investigation of Galactic nuclei through Multifrequency Analysis (ENIGMA) together with a campaign by the Whole Earth Blazar Telescope (WEBT), involving a pointing by the soft-gamma-ray satellite INTEGRAL, optical, near-infrared, sub-millimeter, millimeter, radio, and Very Long Baseline Array (VLBA) monitoring. S5 0716+71 was very bright at radio frequencies and in a rather faint optical state during the INTEGRAL pointing; significant inter-day and low intra-day variability was recorded in the radio regime, while typical fast variability features were observed in the optical band. No correlation was found between the radio and optical emission. The source was not detected by INTEGRAL, neither by the X-ray monitor JEM-X nor by the gamma-ray imager ISGRI, but upper limits to the source emission in the 3-200 keV energy band were estimated. A brightness temperature Tb>2.1x10^{14} K was inferred from the radio variability, but no corresponding signatures of IC avalanches were recorded at higher energies. The absence of IC-catastrophe signatures provides either a lower limit delta>8 to the Doppler factor affecting the radio emission or strong constraints for modelling of the Compton catastrophes in S5 0716+71., Comment: 15 pages, 3 EPS figures, 3 tables, to appear in A&A

We propose a new approximation for the cyclo-synchrotron emissivity of a single electron. In the second part of this work, we discuss a simple application for our approximation, and investigate the heating of electrons through the self-absorption process. Finally, we investigate the self-absorbed part of the spectrum produced by a power-law population of electrons. In comparison to earlier approximations, our formula provides a few significant advantages. Integration of the emissivity over the whole frequency range, starting from the proper minimal emitting frequency, gives the correct cooling rate for any energy particle. Further, the spectrum of the emission is well approximated over the whole frequency range, even for relatively low particle energies (beta << 0.1), where most of the power is emitted in the first harmonic. In order to test our continuous approximation, we compare it with a recently derived approximation of the first ten harmonics. Finally, our formula connects relatively smooth to the synchrotron emission at beta=0.9. We show that the self-absorption is a very efficient heating mechanism for low energy particles, independent of the shape of the particle distribution responsible for the self-absorbed synchrotron emission. We find that the energy gains for low energy particles are always higher than energy losses by cyclo-synchrotron emission. We show also that the spectral index of the self-absorbed part of the spectrum at very low frequencies differs significantly from the well known standard relation I(nu) ~ nu^(5/2)., Comment: 9 pages, 4 figures, accepted for publication in A&A

We apply a two-zone MHD model to the jet of M87. The model consists of an inner relativistic outflow, which is surrounded by a non-relativistic outer disk-wind. The outer disk-wind collimates very well through magnetic self-collimation and confines the inner relativistic jet into a narrow region around the rotation axis. Further, we show by example, that such models reproduce very accurately the observed opening angle of the M87 jet over a large range from the kiloparsec scale down to the sub-parsec scale., Comment: 4 pages, 2 figures, accepted by A&A Letters

We perform a numerical simulation of magnetohydrodynamic radially self-similar jets, whose prototype is the Blandford & Payne analytical example. The reached final steady state is valid close to the rotation axis and also at large distances above the disk where the classical analytical model fails to provide physically acceptable solutions. The outflow starts with a sub-slow magnetosonic speed which subsequently crosses all relevant MHD critical points and corresponding magnetosonic separatrix surfaces. The characteristics are plotted together with the Mach cones and the super-fast magnetosonic outflow satisfies MHD causality. The final solution remains close enough to the analytical one which is thus shown to be topologically stable and robust for various boundary conditions., Comment: 11 pages, 8 figures, minor changes to match the version accepted by MNRAS

We consider time-dependent models for rotating accretion flows onto black holes, where a transition takes place from an outer cooling-dominated disc to a radiatively inefficient flow in the inner region. In order to allow for a transition of this type we solve the energy equation, both, for the gas and for the radiation field, including a radiative cooling flux and a turbulent convective heat flux directed along the negative entropy gradient. The transition region is found to be highly variable, and a corresponding variation expected for the associated total luminosity. In particular, rapid oscillations of the transition radius are present on a timescale comparable with the local Keplerian rotation time. These oscillations are accompanied by a quasi-periodic modulation of the mass flux at the outer edge of the advection-dominated accretion flow (ADAF). We speculate about the relevance for the high-frequency QPO phenomenon., Comment: 6 pages, 3 figures. Revised version, added system of equations. Accepted for publication in MNRAS