2D granular flows with the μ(I)\mu(I) rheology and side walls friction: a well balanced multilayer discretization

We present here numerical modelling of granular flows with the $\mu(I)$ rheology in confined channels. The contribution is twofold: (i) a model to approximate the Navier-Stokes equations with the $\mu(I)$ rheology through an asymptotic analysis. Under the hypothesis of a one-dimensional flow, this model takes into account side walls friction; (ii) a multilayer discretization following Fern\'andez-Nieto et al. (J. Fluid Mech., vol. 798, 2016, pp. 643-681). In this new numerical scheme, we propose an appropriate treatment of the rheological terms through a hydrostatic reconstruction which allows this scheme to be well-balanced and therefore to deal with dry areas. Based on academic tests, we first evaluate the influence of the width of the channel on the normal profiles of the downslope velocity thanks to the multilayer approach that is intrinsically able to describe changes from Bagnold to S-shaped (and vice versa) velocity profiles. We also check the well balance property of the proposed numerical scheme. We show that approximating side walls friction using single-layer models may lead to strong errors. Secondly, we compare the numerical results with experimental data on granular collapses. We show that the proposed scheme allows us to qualitatively reproduce the deposit in the case of a rigid bed (i. e. dry area) and that the error made by replacing the dry area by a small layer of material may be large if this layer is not thin enough. The proposed model is also able to reproduce the time evolution of the free surface and of the flow/no-flow interface. In addition, it reproduces the effect of erosion for granular flows over initially static material lying on the bed. This is possible when using a variable friction coefficient $\mu(I)$ but not with a constant friction coefficient

Testing models with non-minimal Higgs sector through the decay t->q+WZ

We study the contribution of charged Higgs boson to the rare decay of the top quark t->q+WZ (q=d,s,b) in models with Higgs sector that includes doublets and triplets. Higgs doublets are needed to couple charged Higgs with quarks, whereas the Higgs triplets are required to generate the non-standard vertex HWZ at tree-level. It is found that within a model that respect the custodial SU(2) symmetry and avoids flavour changing neutral currents by imposing discrete symmetries, the decay mode t->b+WZ, can reach a branching ratio of order 0.0178, whereas the decay modes t->(d,s)+WZ, can reach a similar branching ratio in models where flavour changing neutral currents are suppressed by flavour symmetries.Comment: Typeset using REVTEX and EPSF, 5 pag, 2 figure

A note on a gauge-gravity relation and functional determinants

We present a refinement of a recently found gauge-gravity relation between one-loop effective actions: on the gauge side, for a massive charged scalar in 2d dimensions in a constant maximally symmetric electromagnetic field; on the gravity side, for a massive spinor in d-dimensional (Euclidean) anti-de Sitter space. The inclusion of the dimensionally regularized volume of AdS leads to complete mapping within dimensional regularization. In even-dimensional AdS, we get a small correction to the original proposal; whereas in odd-dimensional AdS, the mapping is totally new and subtle, with the `holographic trace anomaly' playing a crucial role.Comment: 6 pages, io

Customer mobility and congestion in supermarkets

The analysis and characterization of human mobility using population-level mobility models is important for numerous applications, ranging from the estimation of commuter flows in cities to modeling trade flows between countries. However, almost all of these applications have focused on large spatial scales, which typically range between intra-city scales to inter-country scales. In this paper, we investigate population-level human mobility models on a much smaller spatial scale by using them to estimate customer mobility flow between supermarket zones. We use anonymized, ordered customer-basket data to infer empirical mobility flow in supermarkets, and we apply variants of the gravity and intervening-opportunities models to fit this mobility flow and estimate the flow on unseen data. We find that a doubly-constrained gravity model and an extended radiation model (which is a type of intervening-opportunities model) can successfully estimate 65--70\% of the flow inside supermarkets. Using a gravity model as a case study, we then investigate how to reduce congestion in supermarkets using mobility models. We model each supermarket zone as a queue, and we use a gravity model to identify store layouts with low congestion, which we measure either by the maximum number of visits to a zone or by the total mean queue size. We then use a simulated-annealing algorithm to find store layouts with lower congestion than a supermarket's original layout. In these optimized store layouts, we find that popular zones are often in the perimeter of a store. Our research gives insight both into how customers move in supermarkets and into how retailers can arrange stores to reduce congestion. It also provides a case study of human mobility on small spatial scales

The IACOB project. VI. On the elusive detection of massive O-type stars close to the ZAMS

The apparent lack of massive O-type stars near the zero-age main sequence (at ages < 2 Myr) is a topic widely discussed. Different explanations for this elusive detection have been proposed, but no firm conclusions have been reached yet. We reassess this empirical result benefiting from the high-quality spectroscopic observations of >400 Galactic O-type stars gathered by the IACOB and OWN surveys. We used temperatures and gravities from a iacob-gbat/fastwind spectroscopic analysis to locate our sample in the Kiel and spectroscopic HR diagrams. We evaluated the completeness of our sample of stars, observational biases using information from the Galactic O star catalog (GOSC), systematics of our methodology, and compare with other recent studies using smaller samples of Galactic O-type stars. We base our discussion on the spectroscopic HR diagram to avoid the use of uncertain distances. We performed a detailed study of the young cluster Trumpler-14 as an example of how Gaia cluster distances can help to construct the associated classical HR diagram. The apparent lack of massive O-type stars near the ZAMS with masses between 30 and 70 Msol persist even when spectroscopic results from a large, non-biased sample of stars are used. We do not find correlation between the dearth of stars and observational biases, limitations of our methodology, or the use of spectroscopic HR diagram instead of the classical one. Investigating the efficiency of mass accretion during the formation process we conclude that an adjustment of the accretion rate towards lower values could reconcile the hotter boundary of detected O-type stars and the theoretical birthline. Last, we discuss that the presence of a small sample of O2-O3.5 stars found closer to the ZAMS might be explained taking into account non-standard star evolution (e.g. binary interaction, mergers, or homogeneous evolution).Comment: 20 pages, 15 figures, accepted for publication in Astronomy & Astrophysic

Effect of Charged Scalar Loops on Photonic Decays of a Fermiophobic Higgs

Higgs bosons with very suppressed couplings to fermions ("Fermiophobic Higgs bosons", h_f) can decay to two photons (\gamma\gamma) with a branching ratio significantly larger than that expected for the Standard Model Higgs boson for m_{h_f}<150 GeV. Such a particle would give a clear signal at the LHC and can arise in the Two Higgs Doublet Model (type I) in which h_f -> \gamma\gamma is mediated by W^+ and charged Higgs boson (H^+) loops. We show that the H^+ loops can cause both constructive and destructive contributions with a magnitude considerably larger than the anticipated precision in the measurement of the photonic decay channel at future hadron and lepton colliders.Comment: 18 pages, 5 figures, clarifications added, one reference added, accepted by Physical Review