Utilisation d'un réseau de neurones pour appliquer le modèle de Muskingum aux réseaux d'assainissement

L'application du modèle de Muskingum pour simuler l'écoulement à surface libre dans les canaux d'irrigation a été largement utilisée et validée. Par extension, ce modèle est également employé pour simuler les écoulements en réseau d'assainissement. Or, nous avons pu montrer des erreurs allant jusqu'à 80% du débit de pointe entre le modèle de Muskingum à paramètres fixes et le modèle de référence de Barré de Saint-Venant. Nous proposons une nouvelle paramétrisation du modèle de Muskingum pour l'écoulement en collecteur circulaire en réseau d'assainissement et ceci pour un large domaine de longueurs, pentes et diamètres de collecteurs. Ce nouveau modèle non-linéaire a été calé par minimisation d'une fonction objectif traduisant la proximité du modèle proposé avec les résultats de la résolution des équations de Barré de Saint-Venant pour des hydrogrammes rectangulaires. Un réseau de neurones a été utilisé pour paramétrer le modèle. Cette nouvelle application des équations de Muskingum permet l'obtention d'erreurs relatives moyennes inférieures à 6% sur la valeur et l'instant du débit de pointe, ceci dans le cas de collecteurs ayant jusqu'à 6500 m de longueur, des pentes variant entre 0.5% et 1% et des diamètres entre 150 et 2500 mm et des hydrogrammes de débit de pointe proche de la capacité du collecteur. Le modèle a également été validé sur un hydrogramme de forme quelconque.Certain towns and cities frequently suffer from failures of their sewer networks, especially in rainy weather. Pollution of the host environment, as the direct consequence of occasionally untimely spills, is not appreciated by the natural environment or the human population. Improving the quality of the natural environment therefore involves an increasingly sophisticated control of the hydraulics and the pollutant load in drainage systems, and especially in sewer networks. Real-time management of sewer networks can provide a solution for the protection of the natural environment. In this case, control strategies are provided for the sluices and pumps of the sewer network during a rainy event to minimize the urban effluent. Moreover, a better understanding and modeling of the transport of pollution in the mains is required.To that end, not only must the hydraulic operation of the mains be correctly modeled (shape of the hydrograph, value and temporal position of the peak flow), but this numerical model must also be stable and converge towards the solution, irrespective of the initial conditions for modeling of the pollution, and the computer time must be compatible with the requirements of real-time management. The most representative model of unidimensional flows is that of Barré de Saint-Venant (1871). The non-linearity of the model, resulting in difficulties in solving these equations, together with the computer time required, are such that not all the criteria for a real-time application can be met. The conceptual equations model of Muskingum is another model that can be used.In the case of round sewerage mains with a slope ranging from practically nil to a few per-thousandths and a few kilometers long, the K and α coefficients traditionally used do not yield correct results with respect to the benchmark model of Barré de Saint-Venant. To keep the advantages of the simplification of the Muskingum equations, and to avoid having to solve the Barré de Saint Venant system, we propose new parameters for the Muskingum equations and we use optimization and correlation calculation techniques using neural networks.In modeling the mains of a sewer network, the discretization of their length, within the usual limits [50 m; 1000 m] is chosen empirically. This discretization plays an essential part in the propagation of the wave in a main. To take this effect into account, the round main of length L is discretized into N sections, and K is expressed on the basis of the maximum speed of the flow Vmax. The model setting parameters are now N and α, and will be calibrated for a wide range of slopes, lengths and flow rates for round mains with a constant roughness.The calculation procedure is as follows: - Setting of the optimal values of N and alpha giving results close to those calculated by Barré de Saint Venant; - Determination of correlations of the parameters N and alpha according to the slope, length and diameter; - Validation of the Muskingum model in relation to that of Barré de Saint-Venant. The parameters alpha and N are set by minimizing an objective function giving the agreement between the results of the hydraulic simulations by Barré de Saint-Venant and the simulations of the proposed model. The objective function is defined by the sum of the relative quadratic deviations of the values and times of maximum flow rates. The maximum errors are in fact reduced from 90% to 10% on peak flows and from 30% to 10% at a given point in time during the peak flow. The mean error is reduced forty-fold for peak flow, and five-fold in the temporal position, with a reduction of the same order for the standard deviations. Correlations of alpha and N are sought according to the slope, length and diameter of the mains modeled. As linear type relations failed to provide satisfactory results, the multi-layer Perceptron type (artificial) neural network model was used. The model includes 3 inputs and 2 outputs. The first, essential stage consists of finding the optimal number of neurons in the masked layer. It is important to mention that despite maximum errors of 40% and 20% on the prediction of time and peak flow rate, mean errors of only 3% and 4% are observed. Given this result, 4 neurons were chosen in the masked layer. This model therefore includes 3 inputs, 4 neurons in the masked layer, and 2 outputs. Following the learning phase with the results of the optimization phase, the so-called prediction phase was then performed. This consists of using the neural network with data with intermediary values with respect to those used in the learning phase. The neural network is used solely to predict values within the minimum and maximum limits of the learning phase. The prediction (or validation) phase revealed that the mean errors are in the order of 2.7% for the peak flow value and 5.5% for the instant of the same flow. The choice of 4 neurons in the masked layer during the prediction phase gives results with the same order of magnitude as in the learning phase, thus validating the structure of the neural network chosen. Subsequently, the proximity of the value and of the time position of the maximum flow rate for the propagation of rectangular hydrograms was studied. The performance of the model proposed is now verified by studying the propagation of a hydrogram of any given shape. Use of this model, validated on a hydrogram of any given shape and presenting several peaks of different intensities, yields a satisfactory reproduction of the output hydrogram and is a distinct improvement on the classic Muskingum model

Large K-exciton dynamics in GaN epilayers: the non-thermal and thermal regime

We present a detailed investigation concerning the exciton dynamics in GaN epilayers grown on c-plane sapphire substrates, focussing on the exciton formation and the transition from the nonthermal to the thermal regime. The time-resolved kinetics of LO-phonon replicas is used to address the energy relaxation in the excitonic band. From ps time-resolved spectra we bring evidence for a long lasting non-thermal excitonic distribution which accounts for the rst 50 ps. Such a behavior is con rmed in di erent experimental conditions, both when non-resonant and resonant excitation are used. At low excitation power density the exciton formation and their subsequent thermalization is dominated by impurity scattering rather than by acoustic phonon scattering. The estimate of the average energy of the excitons as a function of delay after the excitation pulse provides information on the relaxation time, which describes the evolution of the exciton population to the thermal regime.Comment: 9 pages,8 figure

A Second-Generation Janus Scorpionate Ligand: Controlling Coordination Modes in Iron(II) Complexes by Steric Modulation

The second-generation Janus scorpionate ligand [HB(mtdaMe)3−] containing methyl-mercaptothiadiazolyl (mtdaMe) heterocyclic rings and (N,N,N-) and (S,S,S-) binding pockets has been prepared. The effect of methyl substitution versus the unsubstituted first-generation Janus scorpionate [HB(mtda)3]− on the coordination chemistry with alkali metals and on the binding preferences and on the ground spin state of iron(II) complexes has been studied structurally and by 57Fe Mossbauer Spectroscopy

Bell inequalities for three systems and arbitrarily many measurement outcomes

We present a family of Bell inequalities for three parties and arbitrarily many outcomes, which can be seen as a natural generalization of the Mermin Bell inequality. For a small number of outcomes, we verify that our inequalities define facets of the polytope of local correlations. We investigate the quantum violations of these inequalities, in particular with respect to the Hilbert space dimension. We provide strong evidence that the maximal quantum violation can only be reached using systems with local Hilbert space dimension exceeding the number of measurement outcomes. This suggests that our inequalities can be used as multipartite dimension witnesses.Comment: v1 6 pages, 4 tables; v2 Published version with minor typos correcte

Theory of Adsorption and Surfactant Effect of Sb on Ag (111)

We present first-principles studies of the adsorption of Sb and Ag on clean and Sb-covered Ag (111). For Sb, the {\it substitutional} adsorption site is found to be greatly favored with respect to on-surface fcc sites and to subsurface sites, so that a segregating surface alloy layer is formed. Adsorbed silver adatoms are more strongly bound on clean Ag(111) than on Sb-covered Ag. We propose that the experimentally reported surfactant effect of Sb is due to Sb adsorbates reducing the Ag adatom mobility. This gives rise to a high density of Ag islands which coalesce into regular layers.Comment: RevTeX 3.0, 11 pages, 0 figures] 13 July 199

Blue lasing at room temperature in high quality factor GaN/AlInN microdisks with InGaN quantum wells

The authors report on the achievement of optically pumped III-V nitride blue microdisk lasers operating at room temperature. Controlled wet chemical etching of an AlInN interlayer lattice matched to GaN allows forming inverted cone pedestals. Whispering gallery modes are observed in the photoluminescence spectra of InGaN∕GaN quantum wells embedded in the GaN microdisks. Typical quality factors of several thousands are found (Q>4000). Laser action at ∼420nm is achieved under pulsed excitation at room temperature for a peak power density of 400kW/cm2. The lasing emission linewidth is down to 0.033nm

Radiation Tolerance of CMOS Monolithic Active Pixel Sensors with Self-Biased Pixels

CMOS Monolithic Active Pixel Sensors (MAPS) are proposed as a technology for various vertex detectors in nuclear and particle physics. We discuss the mechanisms of ionizing radiation damage on MAPS hosting the the dead time free, so-called self bias pixel. Moreover, we discuss radiation hardened sensor designs which allow operating detectors after exposing them to irradiation doses above 1 Mra

Synthesis and Characterization of Two Metallic Spin-Glass Phases of FeMo₄Ge₃

Polycrystalline samples of FeMo4Ge3 have been synthesized by the reduction of an oxide mixture at 1248 K and characterized by a combination of diffraction, muon spin relaxation (µ+SR), Mössbauer spectroscopy, magnetometry, transport, and heat-capacity measurements. The compound adopts a tetragonal W5Si3 structure (space group I4/mcm); the iron and molybdenum atoms are disordered over two crystallographic sites, 16k and either 4a or 4b. The synthesis conditions determine which fourfold site is selected; occupation of either leads to the presence of one-dimensional chains of transition metals in the structure. In both cases, the electrical resistivity below 200 K is ~175 µΩ cm. The dc magnetization rapidly rises below 35 K (Fe/Mo on 16k and 4b sites) or 16 K (16k and 4a sites), and a magnetization of 1µB or 0.8µB per Fe atom is observed in 4 T at 2 K. The ac susceptibility and the heat capacity both suggest that these are glasslike magnetic transitions, although the transition shows a more complex temperature dependence (with two maxima in χ ) when the 4b sites are partially occupied by iron. No long-range magnetic order is thought to be present at 5 K in either structural form; this has been proven by neutron diffraction and µ+SR for the case when Fe and Mo occupy the 16k and 4b sites