Chaos enhancement in large-spin chains

We study the chaotic properties of a large-spin XXZ chain with onsite disorder and a small number of excitations above the fully polarized state. We show that while the classical limit, which is reached for large spins, is chaotic, enlarging the spin suppresses quantum chaos features. We attribute this suppression to the occurrence of large and slow clusters of onsite excitations, and propose a way to facilitate their fragmentation by introducing additional decay channels. We numerically verify that the introduction of such relaxation channels restores chaoticity for large spins, so that only three excitations are required to achieve strong level repulsion and ergodic eigenstates.Comment: 7 pages, 5 figure

Complémentarités et convergences de méthodes de régionalisation des précipitations : application à une région endoréique du Nord-Mexique

La connaissance des champs pluviométriques annuels est importante dans les zones arides et semi-arides où la gestion de l'eau est un exercice permanent d'aménagement de la pénurie, comme cela est le cas au Nord du Mexique.On se propose de montrer ici qu'une meilleure connaissance des disponibilités en eau peut s'appuyer sur la détermination de régions pluviométriquement homogènes à partir de diverses méthodes complémentaires ou convergentes.Pour définir des régions homogènes, on part de la répartition des stations par rapport à la régression pluviométrie/altitude. Des analyses factorielles en composantes principales et des correspondances permettent également de proposer des régions homogènes suivant des variables définies et disponibles pour toutes les stations. On s'appuie aussi sur les régimes pluviométriques pour déterminer d'autres régionalisations. Parallèlement on a pu utiliser la répartition des stations par rapport au gradient altitudinal pour créer des régions dont l'homogénéité vis-à-vis des précipitations a pu être vérifiée par la Méthode du Vecteur Régional (MVR), basée sur le principe de la pseudo-proportionnalité des données de postes proches.La comparaison des résultats obtenus par chacune des méthodes permet de constater que dans la région traitée, les limites entre régions " homogènes " sont souvent les mêmes, bien que les modes de détermination soient différents. Enfin, les différences apportent une information supplémentaire pour la compréhension des mécanismes locaux ou régionaux de la répartition des champs de pluie.Knowledge of annual rainfall is of great importance in arid and semi-arid areas, because water management is dominated by scarcity. The Nazas-Aguanaval river basin constitutes one of the main endoreic basins in Mexico (92 000 km2). It extends from the crests of the Western SierraMadre to as far as the Chihuahuan desert, in the states of Durango, Coahuila and Zacatecas. Spatial variability of rainfall is significant with annual rainfall amounts ranging from 900 mm in the higher areas of the Sierra Madre to 180 mm at the centre of the Laguna de Mayran. However, temporal variability of the precipitation amount is also appreciable, and it increases from the sub-humid areas of the mountains to the desert. The coefficient of variation for annual precipitation ranges from 0.2 in the mountains to 0.4 in Chihuahuan desert. Furthermore, in 1992, 1994, 1995, and from 1997 to 2000 severe rainfall deficits forced farmers to reduce strongly irrigated areas, thus leading to socio-economic development problems in this region. It is shown in this paper that an improvement in water availability knowledge is attainable by the determination of homogeneous rainfall regions, based on complementary or convergent methods.Rainfall distribution is a result of many factors, including the atmospheric circulation, the continental pattern, the coastal design, the location of major mountainous massifs, the distance from the ocean, and other site factors. The regionalisation of precipitation has been the subject of much research for almost all types of climates. The influence of zonal and regional factors is also determined in regional monographs where the role of local variables (relief, vegetation, general roughness of landscape, etc.) is described in relation to the large-scale circulation scheme. In most of the cases, the interpolation of values between two observations is necessary and quite difficult. Kriging is widely used for this purpose, as is co-kriging, which takes into account the topography or some other local factors and frequently gives better reconstitution of rainfall data. In order to determine the first set of homogeneous regions in northwestern Mexico, the elevation gradient of the rainfall amount was defined by a simple regression. All the stations were located with respect to the regression line and they can form apparent groups. The following relation was obtained :P=0.31 H - 133r2=0.73; n=84)(where P is annual rainfall in mm and H the altitude in m).In the same way, various statistical analysis were performed using all data available from the rainfall measurement stations, such as elevation, distance from the Pacific Ocean, exposure, annual rainfall amount, and the type of topography and vegetation cover surrounding the station. An Empirical Orthogonal Function Analysis (EOF) and a Factorial Analysis of Correspondences (FAC) revealed other kinds of regionalisation. The precipitation regime is tropical-like in spite of the latitude (25° N), but the percentage of annual precipitation in winter appeared as a segregating factor and thus was used to define the climatic geography. This was determined by a stepwise discriminant analysis, which allowed the segregation of the north-eastern area of the Nazas-Aguanaval basin. This is the dryer region of the basin because it is less exposed to monsoon fluxes and the proportion of winter rain is higher there than in the remaining basin.The main variables explaining the spatial distribution of precipitation are altitude and distance from the Pacific Ocean, as determined by both the EOF analysis and the analysis of correspondences. The grouping of stations segregated by the elevation gradient regression led to regions where the homogeneity in relation to the annual rainfall amount was tested and verified by the Regional Vector Method (RVM). This method is based on the principle of pseudo-proportionality between annual rainfall amounts at close stations.The Nazas-Aguanaval basin is divided into three climatic regions defined by precipitation: the Western Sierra Madre, the Chihuahuan desert, and a semi-arid area that is divided into two sub-regions (Middle Nazas basin and Aguanaval plateau) by the analysis of correspondences. As a result of the regional rainfall analysis, some variograms were performed to determine the length of the validity of the rainfall data. However, it appeared that a multidirectional variogram did not explain these data. The role that relief (mainly the Western Sierra Madre) plays in the spatial distribution of precipitation does not explain the length of rainfall data. Introducing the direction of mountain range into the variogram demonstrated that the relief played a significant role, and in this case the length of the rainfall variogram data was 180 km.A comparison of results obtained using each method led to the conclusion that the boundaries between homogeneous regions are often the same while the determination processes are different. Finally, all the proposed methods are complementary and the differences between all characterisations give additional information regarding the local and regional processes that explain the annual rainfall spatial distribution. Simple tools have been used to acquire a better knowledge of rainfall spatial distribution.In the case of Northern Mexico, the low density of a measurement network (rain gauges), particularly in mountainous or arid zones, is partially attenuated by the possibility of evaluating the main climatic characteristics for the different regions defined in terms of rainfall

Numerical prediction of saturation in dual scale fibrous reinforcements during Liquid Composite Molding

This paper presents a fractional flow model based on two-phase flow, resin and air, through a porous medium to simulate numerically Liquid Composites Molding (LCM) processes. It allows predicting the formation, transport and compression of voids in the modeling of LCM. The equations are derived by combining Darcy’s law and mass conservation for each phase (resin/air). In the model, the relative permeability and capillary pressure depend on saturation. The resin is incompressible and the air slightly compressible. Introducing some simplifications, the fractional flow model consists of a saturation equation coupled with a pressure/velocity equation including the effects of air solubility and compressibility. The introduction of air compressibility in the pressure equation allows for the numerical prediction of the experimental behavior at low constant resin injection flow rate. A good agreement was obtained between the numerical prediction of saturation in a glass fiber reinforcement and the experimental observations during the filling of a test mold by Resin Transfer Molding (RTM). 2015 Elsevier Ltd. All rights reserved.The authors acknowledge financial support of the Spanish Government (Project DPI2013-44903-R-AR).Gascón Martínez, ML.; García Manrique, JA.; Lebel, F.; Ruiz, E.; Trochu, F. (2015). Numerical prediction of saturation in dual scale fibrous reinforcements during Liquid Composite Molding. Composites Part A: Applied Science and Manufacturing. 77:275-284. https://doi.org/10.1016/j.compositesa.2015.05.019S2752847

A two-phase flow model to simulate mold filling and saturation in Resin Transfer Molding

The final publication is available at Springer via http://dx.doi.org/10.1007/s12289-015-1225-zThis paper addresses the numerical simulation of void formation and transport during mold filling in Resin Transfer Molding (RTM). The saturation equation, based on a two-phase flow model resin/air, is coupled with Darcy s law and mass conservation to simulate the unsaturated filling flow that takes place in a RTM mold when resin is injected through the fiber bed. These equations lead to a system composed of an advection diffusion equation for saturation including capillary effects and an elliptic equation for pressure taking into account the effect of air residual saturation. The model introduces the relative permeability as a function of resin saturation. When capillary effects are omitted, the hyperbolic nature of the saturation equation and its strong coupling with Darcy equation through relative permeability represent a challenging numerical issue. The combination of the constitutive physical laws relating permeability to saturation with the coupled system of the pressure and saturation equations allows predicting the saturation profiles. The model was validated by comparison with experimental data obtained for a fiberglass reinforcement injected in a RTM mold at constant flow rate. The saturation measured as a function of time during the resin impregnation of the fiber bed compared very well with numerical predictions.The authors acknowledge financial support of the Spanish Government (Projects DPI2010-20333 and DPI2013-44903-R-AR), of the National Science and Research Council of Canada (NSERC) and of the Canada Reseach Chair (CRC) program.Gascón Martínez, ML.; García Manrique, JA.; Lebel, F.; Ruiz, E.; Trochu, F. (2016). A two-phase flow model to simulate mold filling and saturation in Resin Transfer Molding. International Journal of Material Forming. 9(2):229-239. doi:10.1007/s12289-015-1225-zS22923992Patel N, Lee LJ (1996) Modeling of void formation and removal in liquid composite molding. Part I: wettability analysis. Polym Compos 17(1):96–103Ruiz E, Achim V, Soukane S, Trochu F, Bréard J (2006) Optimization of injection flow rate to minimize micro/macro-voids formation in resin transfer molded composites. Compos Sci Technol 66(3–4):475–486Trochu F, Ruiz E, Achim V, Soukane S (2006) Advanced numerical simulation of liquid composite molding for process analysis and optimization. Compos A: Appl Sci Manuf 37(6):890–902Park CH, Lee W (2011) Modeling void formation and unsaturated flow in liquid composite molding processes: a survey and review. J Reinf Plast Compos 30(11):957–977Pillai KM (2004) Modeling the unsaturated flow in liquid composite molding processes: a review and some thoughts. J Compos Mater 38(23):2097–2118Breard J, Saouab A, Bouquet G (2003) Numerical simulation of void formation in LCM. Compos A: Appl Sci Manuf 34:517–523Breard J, Henzel Y, Trochu F, Gauvin R (2003) Analysis of dynamic flows through porous media. Part I: comparison between saturated and unsaturated flows in fibrous reinforcements. Polym Compos 24(3):391–408Parnas RS, Phelan FR Jr (1991) The effect of heterogeneous porous media on mold filling in Resin Transfer Molding. SAMPE Q 22(2):53–60Parseval DY, Pillai KM, Advani SG (1997) A simple model for the variation of permeability due to partial saturation in dual scale porous media. Transp Porous Media 27(3):243–264Pillai KM (2002) Governing equations for unsaturated flow through woven fiber mats. Part 1. Isothermal flows. Compos A: Appl Sci Manuf 33(7):1007–1019Simacek P, Advani SG (2003) A numerical model to predict fiber tow saturation during Liquid Composite Molding. Compos Sci Technol 63:1725–1736García JA, Gascón L, Chinesta F (2010) A flux limiter strategy for solving the saturation equation in RTM process simulation. Compos A: Appl Sci Manuf 41:78–82Chui WK, Glimm J, Tangerman FM, Jardine AP, Madsen JS, Donnellan TM, Leek R (1997) Process modeling in Resin Transfer Molding as a method to enhance product quality. SIAM Rev 39(4):714–727Nordlund M, Michaud V (2012) Dynamic saturation curve measurement for resin flow in glass fibre reinforcement. Compos A: Appl Sci Manuf 43:333–343García JA, Ll G, Chinesta F (2003) A fixed mesh numerical method for modelling the flow in liquid composites moulding processes using a volume of fluid technique. Comput Methods Appl Mech Eng 192(7–8):877–893García JA, Ll G, Chinesta F, Trochu F, Ruiz E (2010) An efficient solver of the saturation equation in liquid composite molding processes. Int J Mater Form 3(2):1295–1302Lebel F (2012) Contrôle de la fabrication des composites par injection sur renforts. École Polytechnique de Montréal, CanadaVan Genuchten MT (1980) Closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci Soc Am J 44(5):892–898Buckley SE, Leverett MC (1942) Mechanism of fluid displacement in sands. Pet Trans AWME 146:107–116Lundstrom TS, Gebart BR (1994) Influence from process parameters on void formation in Resin Transfer Molding. Polym Compos 15(1):25–33Lundstrom TS (1997) Measurement of void collapse during Resin Transfer Molding. Compos A: Appl Sci Manuf 28(3):201–214Lundstrom TS, Frishfelds V, Jakovics A (2010) Bubble formation and motion in non-crimp fabrics with perturbed bundle geometry. Compos A: Appl Sci Manuf 41:83–92Lebel F, Fanaei A, Ruiz E, Trochu F (2012) Experimental characterization by fluorescence of capillary flows in the fiber tows of engineering fabrics. Open J Inorg Non-Metallic Mater 2(3):25–45Brooks RH, Corey AT (1964) Hydraulic properties of porous media. Colorado State University. Hydrology Papers 1–37Corey AT (1954) The interrelation between gas and oil relative permeabilities. Prod Monthly 19(1):38–4

HAPEX-Sahel : a large-scale study of land-atmosphere interactions in the semi-arid tropics

The Hydrologic Atmospheric Pilot EXperiment in the Sahel (HAPEX-Sahel) was carried out in Niger, West Africa, during 1991 - 1992, with an intensive observation period (IOP) in August - October 1992. It aims at improving the parameterization of land surface atmosphere interactions at the Global Circulation Model (GCM) gridbox scale. The experiment combines remote sensing and ground based measurements with hydrological and meteorological modelling to develop aggregation techniques for use in large scale estimates of the hydrological and meteorological behaviour of large areas in the Sahel. The experimental strategy consisted of a period of intensive measurements during the transition period of the rainy to the dry season, backed up by a series of long term measurements in a 1° by 1° square in Niger. Three "supersites" were instrumented with a variety of hydrological and (micro) meteorological equipment to provide detailed information on the surface energy exchange at the local scale. Boundary layer measurements and aircraft measurements were used to provide information at scales of 100 - 500 km2. All relevant remote sensing images were obtained for this period. This programme of measurements is now being analyzed and an extensive modelling programme is under way to aggregate the information at all scales up to the GCM grid box scale. The experimental strategy and some preliminary results of the IOP are described