Formal deduction of the Saint-Venant-Exner model including arbitrarily sloping sediment beds and associated energy

In this work we present a deduction of the Saint-Venant-Exner model through an asymptotic analysis of the Navier-Stokes equations. A multi-scale analysis is performed in order to take into account that the velocity of the sediment layer is smaller than the one of the fluid layer. This leads us to consider a shallow water type system for the fluid layer and a lubrication Reynolds equation for the sediment one. This deduction provides some improvements with respect to the classical Saint-Venant-Exner model: (i) the deduced model has an associated energy. Moreover, it allows us to explain why classical models do not have an associated energy and how to modify them in order to recover a model with this property. (ii) The model incorporates naturally a necessary modification that must be taken into account in order to be applied to arbitrarily sloping beds. Furthermore, we show that this modification is different of the ones considered classically, and that it coincides with a classical one only if the solution has a constant free surface. (iii) The deduced solid transport discharge naturally depends on the thickness of the moving sediment layer, what allows to ensure sediment mass conservation. Moreover, we include a simplified version of the model for the case of quasi-stationary regimes. Some of these simplified models correspond to the generalization of classical ones such as Meyer-Peter$\&$M\"uller and Ashida-Michiue models. Three numerical tests are presented to study the evolution of a dune for several definition of the repose angle, to see the influence of the proposed definition of the effective shear stress in comparison with the classical one, and by comparing with experimental data.Comment: 44 pages, sumbitted to Advances in Water Resources 17 july 201

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

A two-layer shallow water model for bedload sediment transport: convergence to Saint-Venant-Exner model

A two-layer shallow water type model is proposed to describe bedload sediment transport. The upper layer is filled by water and the lower one by sediment. The key point falls on the definition of the friction laws between the two layers, which are a generalization of those introduced in Fern\'andez-Nieto et al. (ESAIM: M2AN, 51:115-145, 2017). This definition allows to apply properly the two-layer shallow water model for the case of intense and slow bedload sediment transport. Moreover, we prove that the two-layer model converges to a Saint-Venant-Exner system (SVE) including gravitational effects when the ratio between the hydrodynamic and morphodynamic time scales is small. The SVE with gravitational effects is a degenerated nonlinear parabolic system. This means that its numerical approximation is very expensive from a computational point of view, see for example T. Morales de Luna et al. (J. Sci. Comp., 48(1): 258-273, 2011). In this work, gravitational effects are introduced into the two-layer system without such extra computational cost. Finally, we also consider a generalization of the model that includes a non-hydrostatic pressure correction for the fluid layer and the boundary condition at the sediment surface. Numerical tests show that the model provides promising results and behave well in low transport rate regimes as well as in many other situations

Evidence Propagation and Consensus Formation in Noisy Environments

We study the effectiveness of consensus formation in multi-agent systems where there is both belief updating based on direct evidence and also belief combination between agents. In particular, we consider the scenario in which a population of agents collaborate on the best-of-n problem where the aim is to reach a consensus about which is the best (alternatively, true) state from amongst a set of states, each with a different quality value (or level of evidence). Agents' beliefs are represented within Dempster-Shafer theory by mass functions and we investigate the macro-level properties of four well-known belief combination operators for this multi-agent consensus formation problem: Dempster's rule, Yager's rule, Dubois & Prade's operator and the averaging operator. The convergence properties of the operators are considered and simulation experiments are conducted for different evidence rates and noise levels. Results show that a combination of updating on direct evidence and belief combination between agents results in better consensus to the best state than does evidence updating alone. We also find that in this framework the operators are robust to noise. Broadly, Yager's rule is shown to be the better operator under various parameter values, i.e. convergence to the best state, robustness to noise, and scalability.Comment: 13th international conference on Scalable Uncertainty Managemen

Short- and long- term consequences of developmental saline stress: impacts on anuran respiration and behaviour

Secondary salinization has been identified as a major stressor to amphibians. Exposure to elevated salinity necessitates physiological adjustments and biochemical changes that may be energetically demanding. As such, exposure to non-lethal levels of salinity during development could potentially alter anuran metabolic rates and individual performance in both pre- and post-metamorphic life stages. We investigated the effects of non-lethal levels of salinity on metamorphic traits (time to reach metamorphosis and metamorphic mass), tadpole oxygen consumption, escape response behaviour (pre- and post-metamorphosis) and foraging ability post-metamorphosis in two native Australian frog species, the southern brown tree frog (Litoria ewingii) and the striped marsh frog (Limnodynastes peronii). We found that both Lit. ewingii and Lim. peronii exhibited differences in metamorphic traits in response to elevated salinity. Neither species showed significant change in oxygen consumption during development in response to salinity, relative to freshwater controls. Both species displayed impaired escape response behaviours in response to salinity during larval development, but flow-on effects to adult escape response behaviours and foraging performance were species-specific. Our results show that the influence of stressors during development can have consequences for anuran physiology and behaviour at multiple life stages, and emphasize the need for studies that examine the energetics of anuran responses in order to better understand the responses of biota to stressful environments

COVID-19: Open-data resources for monitoring, modeling, and forecasting the epidemic

We provide an insight into the open-data resources pertinent to the study of the spread of the Covid-19 pandemic and its control. We identify the variables required to analyze fundamental aspects like seasonal behavior, regional mortality rates, and effectiveness of government measures. Open-data resources, along with data-driven methodologies, provide many opportunities to improve the response of the different administrations to the virus. We describe the present limitations and difficulties encountered in most of the open-data resources. To facilitate the access to the main open-data portals and resources, we identify the most relevant institutions, on a global scale, providing Covid-19 information and/or auxiliary variables (demographics, mobility, etc.). We also describe several open resources to access Covid-19 datasets at a country-wide level (i.e., China, Italy, Spain, France, Germany, US, etc.). To facilitate the rapid response to the study of the seasonal behavior of Covid-19, we enumerate the main open resources in terms of weather and climate variables. We also assess the reusability of some representative open-data sources

Optimized Micro-Hydro Power Plants Layout Design Using Messy Genetic Algorithms

Micro Hydro-Power Plants (MHPP) represent a powerful and effective solution to address the problem of energy poverty in rural remote areas, with the ad vantage of preserving the natural resources and minimizing the impact on the environment. Nevertheless, the lack of resources and qualified manpower usu ally constitutes a big obstacle to its adequate application, generally translating into sub-optimal generation systems with poor levels of efficiency. Therefore, the study and development of expert, simple and efficient strategies to assist the design of these installations is of especial relevance. This work proposes a design methodology based on a tailored messy evolutionary computational approach, with the objective of finding the most suitable layout of MHPP, considering several constraints derived from a minimal power supply requirement, the max imum flow usage, and the physical feasibility of the plant in accordance with the real terrain profile. This profile is built on the basis of a discrete topographic survey, by means of a shape preserving interpolation, which permits the appli cation of a continuous variable length Messy Genetic Algorithm (MGA). The optimization problem is then formulated in both single-objective (cost minimiza tion) and multi-objective (cost minimization and power supply maximization) modes, including the study of the Pareto dominance. The algorithm is applied to a real scenario in a remote community in Honduras, obtaining a 56.96% of cost reduction with respect to previous work

B_s ---> \gamma \gamma decay in the model III and 3HDM(O_2) with CP violating effects

We analyse the CP asymmetry for B_{s} -->\gamma\gamma in the two Higgs doublet model with tree level flavor changing currents (model III) and three Higgs doublet model with O_2 symmetry in the Higgs sector, including O_{7} type long distance effects. Further, we study the dependencies of the branching ratio Br(B_{s} --> \gamma\gamma)$ and the ratio of CP-even and CP-odd amplitude squares, R=|A^{+}|^2/|A^{-}|^2, on the CP parameter sin \theta. We found that, there is a weak CP asymmetry, at the order of 10^{-4}. Besides, the branching ratio Br(B_{s} --> \gamma\gamma), and also R ratio, is not sensitive to the CP parameter for |\frac{\bar{\xi}^{U}_{N,tt}}{\bar{\xi}^{D}_{N,bb}}|<1.Comment: 17 pages, 11 figure

A well-balanced finite volume-augmented Lagrangian method for an integrated Herschel-Bulkley model

40 pages. 12 figures.International audienceWe are interested in the derivation of an integrated Herschel-Bulkley model for shallow flows, as well as in the design of a numerical algorithm to solve the resulting equations. The goal is to simulate the evolution of thin sheet of viscoplastic materials on inclined planes and, in particular, to be able to compute the evolution from dynamic to stationary states. The model involves a variational inequality and it is valid from null to moderate slopes. The proposed numerical scheme is well balanced and involves a coupling between a duality technique (to treat plasticity), a fixed point method (to handle the power law) and a finite volume discretization. Several numerical tests are done, including a comparison with an analytical solution, to confirm the well balanced property and the ability to cope with the various rheological regimes associated with the Herschel-Bulkley constitutive law