Derivation of a multilayer approach to model suspended sediment transport: application to hyperpycnal and hypopycnal plumes

We propose a multi-layer approach to simulate hyperpycnal and hypopycnal plumes in flows with free surface. The model allows to compute the vertical profile of the horizontal and the vertical components of the velocity of the fluid flow. The model can describe as well the vertical profile of the sediment concentration and the velocity components of each one of the sediment species that form the turbidity current. To do so, it takes into account the settling velocity of the particles and their interaction with the fluid. This allows to better describe the phenomena than a single layer approach. It is in better agreement with the physics of the problem and gives promising results. The numerical simulation is carried out by rewriting the multi-layer approach in a compact formulation, which corresponds to a system with non-conservative products, and using path-conservative numerical scheme. Numerical results are presented in order to show the potential of the model

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

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

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

Distorted Heisenberg Algebra and Coherent States for Isospectral Oscillator Hamiltonians

The dynamical algebra associated to a family of isospectral oscillator Hamiltonians is studied through the analysis of its representation in the basis of energy eigenstates. It is shown that this representation becomes similar to that of the standard Heisenberg algebra, and it is dependent of a parameter $w\geq 0$. We name it {\it distorted Heisenberg algebra}, where $w$ is the distortion parameter. The corresponding coherent states for an arbitrary $w$ are derived, and some particular examples are discussed in full detail. A prescription to produce the squeezing, by adequately selecting the initial state of the system, is given.Comment: 21 pages, Latex, 3 figures available as hard copies upon request from the first Autho

Threading Through Macrocycles Enhances the Performance of Carbon Nanotubes as Polymer Fillers

In this work we study the reinforcement of polymers by mechanically interlocked derivatives of single-walled carbon nanotubes (SWNTs). We compare the mechanical properties of fibers made of polymers and of composites with pristine single-walled carbon nanotubes (SWNTs), mechanically interlocked derivatives of SWNTs (MINTs) and the corresponding supramolecular models. Improvements of both Young's modulus and tensile strength of up to 200 % were observed for the polystyrene-MINTs samples with an optimized loading of just 0.01 wt.%, while the supramolecular models with identical chemical composition and loading showed negligible or even detrimental influence. This behavior is found for three different types of SWNTs and two types of macrocycles. Molecular dynamics simulations show that the polymer adopts an elongated conformation parallel to the SWNT when interacting with MINT fillers, irrespective of the macrocycle chemical nature, whereas a more globular structure is taken upon facing with either pristine SWNTs or supramolecular models. The MINT composite architecture thus leads to a more efficient exploitation of the axial properties of the SWNTs and of the polymer chain at the interface, in agreement with experimental results. Our findings demonstrate that the mechanical bond imparts distinctive advantageous properties to SWNT derivatives as polymer fillers.Comment: 39 pages, 19 figure

Second Order Darboux Displacements

The potentials for a one dimensional Schroedinger equation that are displaced along the x axis under second order Darboux transformations, called 2-SUSY invariant, are characterized in terms of a differential-difference equation. The solutions of the Schroedinger equation with such potentials are given analytically for any value of the energy. The method is illustrated by a two-soliton potential. It is proven that a particular case of the periodic Lame-Ince potential is 2-SUSY invariant. Both Bloch solutions of the corresponding Schroedinger equation equation are found for any value of the energy. A simple analytic expression for a family of two-gap potentials is derived

Geometric Phases and Mielnik's Evolution Loops

The cyclic evolutions and associated geometric phases induced by time-independent Hamiltonians are studied for the case when the evolution operator becomes the identity (those processes are called {\it evolution loops}). We make a detailed treatment of systems having equally-spaced energy levels. Special emphasis is made on the potentials which have the same spectrum as the harmonic oscillator potential (the generalized oscillator potentials) and on their recently found coherent states.Comment: 11 pages, harvmac, 2 figures available upon request; CINVESTAV-FIS GFMR 11/9

Production of new neutron-rich isotopes of heavy elements in fragmentation reactions of 238^{238}U projectiles at 1 A GeV

The production of heavy neutron-rich nuclei has been investigated using cold fragmentation reactions of $^{238}$U projectiles at relativistic energies. The experiment performed at the high-resolving-power magnetic spectrometer FRS at GSI allowed to identify 45 new heavy neutron-rich nuclei: $^{205}$Pt, $^{207-210}$Au, $^{211-216}$Hg, $^{213-217}$Tl, $^{215-220}$Pb, $^{219-224}$Bi, $^{221-227}$Po, $^{224-229}$At, $^{229-231}$Rn and $^{233}$Fr. The production cross sections of these nuclei were also determined and used to benchmark reaction codes that predict the production of nuclei far from stability.Comment: 5 pages, 2 figure

INTEGRATION OF DYNAMIC INFORMATION ON ENERGY PARAMETERS IN HBIM MODELS

The conservation of cultural heritage can be affected by different changes in temperature and humidity within architectural spaces, so energy performance and interior microclimate of historic buildings require adaptation to new maintenance and prevention studies. The search for these new investigations brings cultural heritage closer to new digital technologies such as Historic Building Information Modelling (HBIM). In this work, a new interdisciplinary methodology is developed between energy operators and BIM operators, so that a new framework is created to monitor energy parameters through intelligent sensors that measure temperature and humidity in the fully interoperable and semantically enriched 3D model itself. The study's commitment involves solving the interoperability workflow between sensors and the BIM platform, taking advantage of this new interconnectivity. For the study, a methodology applied to the Church of the Sacred Heart of Jesus in Seville was carried out, where from a survey through a georeferenced terrestrial laser scanner with topographic equipment, it is modelled from the point cloud, incorporating the sensors in the HBIM Project. In the workflow, it has been shown that the integration of microclimate data inside churches can be managed directly in the environment of an HBIM-based model and transfer a reverse flow in the process