Continuum Singularities of a Mean Field Theory of Collisions

Consider a complex energy $z$ for a $N$-particle Hamiltonian $H$ and let $\chi$ be any wave packet accounting for any channel flux. The time independent mean field (TIMF) approximation of the inhomogeneous, linear equation $(z-H)|\Psi>=|\chi>$ consists in replacing $\Psi$ by a product or Slater determinant $\phi$ of single particle states $\phi_i.$ This results, under the Schwinger variational principle, into self consistent TIMF equations $(\eta_i-h_i)|\phi_i>=|\chi_i>$ in single particle space. The method is a generalization of the Hartree-Fock (HF) replacement of the $N$-body homogeneous linear equation $(E-H)|\Psi>=0$ by single particle HF diagonalizations $(e_i-h_i)|\phi_i>=0.$ We show how, despite strong nonlinearities in this mean field method, threshold singularities of the {\it inhomogeneous} TIMF equations are linked to solutions of the {\it homogeneous} HF equations.Comment: 21 pages, 14 figure

Antisymmetrization of a Mean Field Calculation of the T-Matrix

The usual definition of the prior(post) interaction $V(V^\prime )$ between projectile and target (resp. ejectile and residual target) being contradictory with full antisymmetrization between nucleons, an explicit antisymmetrization projector ${\cal A}$ must be included in the definition of the transition operator, $T\equiv V^\prime{\cal A}+V^\prime{\cal A}GV.$ We derive the suitably antisymmetrized mean field equations leading to a non perturbative estimate of $T$. The theory is illustrated by a calculation of forward $\alpha$-$\alpha$ scattering, making use of self consistent symmetries.Comment: 30 pages, no figures, plain TeX, SPHT/93/14

Entanglement and localization of wavefunctions

We review recent works that relate entanglement of random vectors to their localization properties. In particular, the linear entropy is related by a simple expression to the inverse participation ratio, while next orders of the entropy of entanglement contain information about e.g. the multifractal exponents. Numerical simulations show that these results can account for the entanglement present in wavefunctions of physical systems.Comment: 6 pages, 4 figures, to appear in the proceedings of the NATO Advanced Research Workshop 'Recent Advances in Nonlinear Dynamics and Complex System Physics', Tashkent, Uzbekistan, 200

Finite geometries and diffractive orbits in isospectral billiards

Several examples of pairs of isospectral planar domains have been produced in the two-dimensional Euclidean space by various methods. We show that all these examples rely on the symmetry between points and blocks in finite projective spaces; from the properties of these spaces, one can derive a relation between Green functions as well as a relation between diffractive orbits in isospectral billiards.Comment: 10 page

Bilan hydrologique d'un marais littoral à vocation agricole : Le marais de Moëze (Charente-Maritime, France)

En France, les sécheresses consécutives des années 1985, 1986, 1989 et 1990 ont mis en lumière les problèmes relatifs à l'alimentation en eau potable, l'irrigation des terres agricoles et la préservation des écosystèmes aquatiques. Dans le cas des zones humides, continentales et littorales, caractérisées par une compartimentation hydraulique souvent complexe, le manque de connaissance se fait particulièrement sentir. Bien que de nombreux travaux aient permis d'évaluer l'évaporation des masses d'eau et l'évapotranspiration de certaines espèces d'hydrophytes et d'hélophytes, les études débouchant sur des bilans quantitatifs restent peu fréquentes. Le bilan hydrologique du marais de Moëze (2250 ha) a été calculé par décade entre le 11/06/89 et le 31/08/89. Il prend en compte le débit au droit de l'ouvrage d'alimentation, les volumes prélevés pour l'irrigation hors marais, les infiltrations et l'évapotransplration sur les 318 km de canaux. L'estimation de la consommation d'eau des parcelles est globalisée au niveau des mesures d'infiltration.Les pertes par infiltration sont secondaires (9,4 %) au regard des volumes prélevés pour l'irrigation (38,0 %) et évapotransplrés par les canaux (43,7 %) dont 51,1 % uniquement par les 28,6 % des plans d'eau colonisés par Typha latifolia.L'optimisation de la gestion estivale de l'eau d'un marais littoral agricole nécessite dans un premier temps de minimiser les pertes. C'est essentiellement sur la consommation d'eau des canaux colonisés par les hélophytes que l'on peut intervenir. Nous proposons un abaque qui permet d'évaluer l'importance des économies d'eau réalisées en fonction de plusieurs scénarios d'aménagement du réseau hydraulique.In France, the drought that occurred during the years 1985, 1986, 1989 and 1990 have emphazised the problems of freshwater supplies for human consumption, for irrigation and for the conservation of aquatic systems. Today the water has to be economized through a rationalized management. Water balance must be evaluated in order to compare supply an demand. Hydrological functioning is particularly badly known as far as continental and coastal wetlands are concerned, probably because of a generally very complex hydrological partition. Many papers deal with the evaporation rate from a clear water surface or the evapotranspiration rate from several species of hydrophytes and halophytes. However studies of quantitative water budgets of wetlands remain few in number.This paper reports an analysis of the budget summer water in that was a salt marsh now containing freshwater. The 25 km2 marsh of Moëze is located on the French Atlantic coast; it has been progressively constituted by filling up a tidal bay since the flandrien period. The soils correspond to fluvio-marine silts, locally called « bri » accumulated over several tens of meters thick. The marsh is bounded on the North by the ancient limestone coast, on the South by the Arnoult River, and on the West by the coastline. Its drainage network includes permanently flowing main canals and also small silted-up ditches which sometimes dry up in summer and are largely colonized by aquatic plants, particularly Typha latifolia. The channels network is very dense (144 meters of ditches per hectare) and complex because of a close connection between all the canals and ditches. The regional oceanic climate is characterized by a surplus water balance from October to April (+ 315 mm) and quite a short one tram May to September (-338 mm).The important terms of the water budget equation in this study were : the quantity of water pumped from the Arnoult River through the inflow sluicegate (Qa), the precipitations (P), the irrigation out of the marsh (lr), the evapotranspiration of water bodies (Epo), the seepage through canals and ditches (ls), and the change in water soil strorage (Vs). These terms are not equally susceptible to be measured. Groundwater seepage and evapotranspiration are difficult to measure and they are often determined by difference, but, they contain the residual error of ail the terms. The methods to evaluate each term of water budget were carried as follows :1. As the inflow gate functions as a siphon, the flow rate (Qa) was calculated with the drowned orifice formula (LENCASTRE, 1984). The upstream and downstream water levels were permanently recorded by 2 limnigraphs. The upstream and downstream water velocities were measured every 2 days with a micro-currentmeter.2. The precipitation values (P) used in the water budget equation correspond to the average of 4 rain gauges placed around the marsh.3. The evapotranspiration of the channel network (Epo) was directly estimated through 4 experimental floating tanks (0.50 x 0.55 x 1.05 m size) previously used by GIRAUD (1985). One of the tanks was placed in clear water, the others was planted the typical aquatic vegetation of the marsh (Lemna sp., Ceratophyllum sp., and Typhia latifolia). The drop the water levels in the tanks corresponded to the loss of water due tou evapotranspiration. All the tanks were filled up to a fixed level, and the amount of water added, measured every 2 days.4. The outputs for irrigation (Ir) concern 298 ha of maïze out of the marsh, and 23 farmers. The water amounts taken off were estimated form an inquiry of irrigation practices associated to a field control.5. The water losses by seepage (ls) through canals and ditches were directly measured on the field by using the closed basin method. A length of canal was closed by 2 watertight bulkheads. The fall of water level was recorded and the amount of water added to maintain a fixed level was measured. This method is considered by KRAATZ (1977) as being the most accurate specially for low seepage. The fall of water level never exceeds 10 % of the water depth in the basin. 34 canals and ditches in the marsh were sampled. According to CHEVALLIER et al. (1984), 3 parameters influencing the soil permeability were measured : granulometry, CaC03 content and sodicity. After the sampling plan we have retained 4 experimental canals (average length =47 m, average water surface = 135 m2, average depth = 0.44 m).6. The water strorage in the soil (Vs) was evaluated by analyzing the groundwater table fluctuations and moisture changes.The water budget calculated for 10-day periods depending on the climatology calculations, from 10th June 1989 to 31st August 1989. The water losses due to seepage were secondary (9.4 %) compared to the amounts of water taken off by irrigation (38.0 %) and channel network evapotranspiration (43.7 %). The water consumption of helophytes such as Typhia latifolia was 2 to 3 times higher than the evaporation of a clear surface water body as shown in figure 3. In the marsh of Moëze, 51.1 % of channel evapotranspiration was due to the colonization by Typhia latifolia of the canals and ditches although they represent only 28.6 % of the channel network surface.This study shows that is possible to quantify a water budget for a large scale wetland from field measurements associated to experimental approaches, with a satisfactory accuracy : less than 10 %. To reduce the water consumption of the marsh of Moëze, three essential recommendations may be given : the reduction of the global channel network surface, the cleaning of a part of ditches colonized by Typhia latifolia, or the combination of both techniques. According to the different management schemes, it is possible to predict the amounts of freshwater saved (fig. 5)

Bilan hydrologique d'un marais littoral à vocation agricole : Le marais de Moëze (Charente-Maritime, France)

En France, les sécheresses consécutives des années 1985, 1986, 1989 et 1990 ont mis en lumière les problèmes relatifs à l'alimentation en eau potable, l'irrigation des terres agricoles et la préservation des écosystèmes aquatiques. Dans le cas des zones humides, continentales et littorales, caractérisées par une compartimentation hydraulique souvent complexe, le manque de connaissance se fait particulièrement sentir. Bien que de nombreux travaux aient permis d'évaluer l'évaporation des masses d'eau et l'évapotranspiration de certaines espèces d'hydrophytes et d'hélophytes, les études débouchant sur des bilans quantitatifs restent peu fréquentes. Le bilan hydrologique du marais de Moëze (2250 ha) a été calculé par décade entre le 11/06/89 et le 31/08/89. Il prend en compte le débit au droit de l'ouvrage d'alimentation, les volumes prélevés pour l'irrigation hors marais, les infiltrations et l'évapotransplration sur les 318 km de canaux. L'estimation de la consommation d'eau des parcelles est globalisée au niveau des mesures d'infiltration.Les pertes par infiltration sont secondaires (9,4 %) au regard des volumes prélevés pour l'irrigation (38,0 %) et évapotransplrés par les canaux (43,7 %) dont 51,1 % uniquement par les 28,6 % des plans d'eau colonisés par Typha latifolia.L'optimisation de la gestion estivale de l'eau d'un marais littoral agricole nécessite dans un premier temps de minimiser les pertes. C'est essentiellement sur la consommation d'eau des canaux colonisés par les hélophytes que l'on peut intervenir. Nous proposons un abaque qui permet d'évaluer l'importance des économies d'eau réalisées en fonction de plusieurs scénarios d'aménagement du réseau hydraulique.In France, the drought that occurred during the years 1985, 1986, 1989 and 1990 have emphazised the problems of freshwater supplies for human consumption, for irrigation and for the conservation of aquatic systems. Today the water has to be economized through a rationalized management. Water balance must be evaluated in order to compare supply an demand. Hydrological functioning is particularly badly known as far as continental and coastal wetlands are concerned, probably because of a generally very complex hydrological partition. Many papers deal with the evaporation rate from a clear water surface or the evapotranspiration rate from several species of hydrophytes and halophytes. However studies of quantitative water budgets of wetlands remain few in number.This paper reports an analysis of the budget summer water in that was a salt marsh now containing freshwater. The 25 km2 marsh of Moëze is located on the French Atlantic coast; it has been progressively constituted by filling up a tidal bay since the flandrien period. The soils correspond to fluvio-marine silts, locally called « bri » accumulated over several tens of meters thick. The marsh is bounded on the North by the ancient limestone coast, on the South by the Arnoult River, and on the West by the coastline. Its drainage network includes permanently flowing main canals and also small silted-up ditches which sometimes dry up in summer and are largely colonized by aquatic plants, particularly Typha latifolia. The channels network is very dense (144 meters of ditches per hectare) and complex because of a close connection between all the canals and ditches. The regional oceanic climate is characterized by a surplus water balance from October to April (+ 315 mm) and quite a short one tram May to September (-338 mm).The important terms of the water budget equation in this study were : the quantity of water pumped from the Arnoult River through the inflow sluicegate (Qa), the precipitations (P), the irrigation out of the marsh (lr), the evapotranspiration of water bodies (Epo), the seepage through canals and ditches (ls), and the change in water soil strorage (Vs). These terms are not equally susceptible to be measured. Groundwater seepage and evapotranspiration are difficult to measure and they are often determined by difference, but, they contain the residual error of ail the terms. The methods to evaluate each term of water budget were carried as follows :1. As the inflow gate functions as a siphon, the flow rate (Qa) was calculated with the drowned orifice formula (LENCASTRE, 1984). The upstream and downstream water levels were permanently recorded by 2 limnigraphs. The upstream and downstream water velocities were measured every 2 days with a micro-currentmeter.2. The precipitation values (P) used in the water budget equation correspond to the average of 4 rain gauges placed around the marsh.3. The evapotranspiration of the channel network (Epo) was directly estimated through 4 experimental floating tanks (0.50 x 0.55 x 1.05 m size) previously used by GIRAUD (1985). One of the tanks was placed in clear water, the others was planted the typical aquatic vegetation of the marsh (Lemna sp., Ceratophyllum sp., and Typhia latifolia). The drop the water levels in the tanks corresponded to the loss of water due tou evapotranspiration. All the tanks were filled up to a fixed level, and the amount of water added, measured every 2 days.4. The outputs for irrigation (Ir) concern 298 ha of maïze out of the marsh, and 23 farmers. The water amounts taken off were estimated form an inquiry of irrigation practices associated to a field control.5. The water losses by seepage (ls) through canals and ditches were directly measured on the field by using the closed basin method. A length of canal was closed by 2 watertight bulkheads. The fall of water level was recorded and the amount of water added to maintain a fixed level was measured. This method is considered by KRAATZ (1977) as being the most accurate specially for low seepage. The fall of water level never exceeds 10 % of the water depth in the basin. 34 canals and ditches in the marsh were sampled. According to CHEVALLIER et al. (1984), 3 parameters influencing the soil permeability were measured : granulometry, CaC03 content and sodicity. After the sampling plan we have retained 4 experimental canals (average length =47 m, average water surface = 135 m2, average depth = 0.44 m).6. The water strorage in the soil (Vs) was evaluated by analyzing the groundwater table fluctuations and moisture changes.The water budget calculated for 10-day periods depending on the climatology calculations, from 10th June 1989 to 31st August 1989. The water losses due to seepage were secondary (9.4 %) compared to the amounts of water taken off by irrigation (38.0 %) and channel network evapotranspiration (43.7 %). The water consumption of helophytes such as Typhia latifolia was 2 to 3 times higher than the evaporation of a clear surface water body as shown in figure 3. In the marsh of Moëze, 51.1 % of channel evapotranspiration was due to the colonization by Typhia latifolia of the canals and ditches although they represent only 28.6 % of the channel network surface.This study shows that is possible to quantify a water budget for a large scale wetland from field measurements associated to experimental approaches, with a satisfactory accuracy : less than 10 %. To reduce the water consumption of the marsh of Moëze, three essential recommendations may be given : the reduction of the global channel network surface, the cleaning of a part of ditches colonized by Typhia latifolia, or the combination of both techniques. According to the different management schemes, it is possible to predict the amounts of freshwater saved (fig. 5)

Choice drivers for quality-labelled food: A cross-cultural comparison on pdo cheese

This study aims at examining the consumers’ preferences and drivers affecting the choice of quality-labelled food products, i.e., protected designation of origin (PDO) labelled cheese. We applied the theory of planned behaviour (TPB) to analyse the purchase of Parmigiano Reggiano PDO and Comté PDO hard cheeses in Italy and France, respectively. A cross-sectional sample of 808 consumers (400 French and 408 Italian) completed a questionnaire. Structural equation modelling (SEM) indicated perceived behavioural control (PBC) and attitude to be significant predictors of intention to purchase PDO-labelled cheese in France and Italy. Subjective and moral norms affected intention in France. Intention significantly influenced the hard cheese purchase behaviour. The results confirm that the TPB model predicted the self-reported measure of behaviour more than the observed one, measured with a discrete choice experiment, in both countries. The TPB interrelationships varied between countries, suggesting that food systems operators and public authorities should carefully target their intervention to stimulate the demand of PDO-labelled products