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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