Modélisation du comportement des biomasses bactériennes libres et fixées dans les réseaux de distribution d'eau potable

La prolifération bactérienne en réseaux de distribution d'eau potable est un souci majeur des distributeurs d'eau. La complexité des phénomènes impliqués dans la croissance bactérienne en réseaux nécessite une modélisation mathématique pour définir l'impact des différents paramètres de la qualité de l'eau et généraliser ces résultats à l'échelle du réseau de distribution. Une approche déterministe a été choisie pour développer cette modélisation prédictive de la croissance bactérienne dans les systèmes de distribution. Le modèle prend en compte : la croissance de fa biomasse libre et de la biomasse fixée, la consommation en nutriments exprimés par le CODB, l'action bactéricide du chlore sur la flore libre et la dore fixée, la déposition des bactéries en suspension et le détachement des bactéries fixées. Le modèle propose une approche originale pour la modélisation de l'action bactéricide du chlore. Par ailleurs, différentes formulations du détachement ont été testées algébriquement pour définir la modélisation la plus adaptée à notre système d'équations. Ce modèle a été couplé au logiciel de modélisation hydraulique IMCCOI.O développé par la SAFEGE. Utilisant les données hydrauliques et de géométrie générées par PICCOLO, le modèle prédit les numérations bactériennes en chaque noeud et sur chaque arc du réseau de distribution. Utilisant l'interface graphique de PICCOLO, le modèle permet une visualisation de l'évolution de la qualité bactérienne par cartographie. Des simulations ont été réalisées sur de nombreux réseaux présentant des tailles et des niveaux de complexité variables. Le modèle a été validé à partir de campagnes de prélèvements sur sites. Ce modèle permettant de simuler l'évolution de la qualité bactériologique à l'échelle du réseau est un outil unique pour le diagnostic et la gestion qualitative des systèmes de distribution d'eau potable.Of the many causes of distributed water quality deterioration, biological phenomena are undoubtedly the subject of the most study, and are also the most closely monitored because of short-term public health risks. Although high heterotrophic bacterial counts do not necessary constitute a health risk, they are the sign that a particular network is subject to biological disorders which can protect pathogenic species. What is more, the evolution of the bacterial biomass in the network also affects other aspects of distributed water quality, such as tastes and odours, the development macro-invertebrates, the appearance of colour and turbidity and the appearance of biocorrosion phenomena. Qualitative management of distribution networks is therefore to ensure that the quality of the product is kept as constant as possible up to the farthest points of the distribution. With this in mind, it is essential to understand, describe and model the various phenomena which lead to the evolution of water quality during distribution. Mathematical modelling is necessary in order to take ail parameters into account in view of the complexity of the different phenomena involved. A determinist type modelling was developed to predict bacterial variations (viable and total bacteria) during distribution. The model takes into account: - the fate of available nutrients consumed for the growth of suspended and fixed bacteria, - the influence of temperature on bacterial dynamics, - the natural mortality of bacteria by senescence and grazing, - the mortality resulting from the presence of chlorine disinfectant, with a differentiation between the action on free et fixed bacteria,- the impact of different forms of chlorine in water (HCIO/CIO-) dépending on pH on the mortality rate,- the deposition of suspended bacteria and the detachment of fixed bacteria,- the chlorine decay kinetics onder the influence of temperature, hydraulics and pipe materials.The modelling of the fixed biomass as a layer uniformly distributed over the pipe surface, expressed as an équivalent thickness of carbon, has been adopted. By this way, a differentiation between the mathematical expression of the free and that of the fixed biomass was made in the model. This mean it is possible to distinguish between phenomena depending on their locations: reactions in solution, réaction at the water/biofilm surface interface and within the biofiJm.This model proposes also an original approach for chlorine bactericidal action on suspended and fixed biomass. To model the action of chlorine on the fixed biomass and its stronger résistance compared with the free biomass, the diffusion of the chlorine through the boundary layer and the biofilm has been taken into account. This calculation of the average penetration depth of the chlorine front into the biofilm enables the identification of two layers: a chlorinated layer and a layer not attained by the chlorine which provides a material indication of the better resistance of the fixed biomass.As detachment is a key phenomenon in the modelling of bacterial dynamics in distribution Systems, the influence of different formulas of detachment kinetics on the mathematical expression of model variables were determined by soiving model equations.The model has been interfaced with PICCOLO software, the SAFEGE hydraulic calculation model. It is constructed by using hydraulic results previously generated by PICCOLO and a numerical scheme to predict bacterial count at each node and on each link of a network. Installed on a PC type computer, the model uses the graphic interface of PICCOLO and provides an effective and easy way to visualise on a computer screen water quality variations in the network, using a colour code for bacterial count, nutrient concentration and chlorine residual.The first model calibration was done using data from our pipe loop pilot under various operating conditions. The model has been also used to simulate a variety of distribution Systems of different sizes and levels of details and a validation of the model has been carried out by means of measurement campaigns on different distribution Systems.Animating and visualising variations of bacteria counts in distribution system is an unique approach to study the changes in water quality. This tool is helpful to propose strategies for the management of distribution Systems and treatment plants and define the different zones of bacterial regrowth in relation with hydraulic conditions

Density of states of a type-II superconductor in a high magnetic field: Impurity effects

We have calculated the density of states $N(\omega)$ of a dirty but homogeneous superconductor in a high magnetic field. We assume a dilute concentration of scalar impurities and find how $N(\omega)$ behaves as one crosses from the weak scattering to the strong scattering limit. At low energies, $N(\omega)\sim \omega ^2$ for small values of the impurity concentration and scattering strength. When the disorder becomes stronger than some critical value, a finite density of states is created at the Fermi surface. These results are a consequence of the gapless nature of the quasiparticle excitation spectrum in a high magnetic field.Comment: 20 pages in RevTeX, 4 figures, to appear in Phys. Rev. B (July 1, 1997

Coherence in the Quasi-Particle 'Scattering' by the Vortex Lattice in Pure Type-II Superconductors

The effect of quasi-particle (QP) 'scattering' by the vortex lattice on the de-Haas van-Alphen oscillations in a pure type-II superconductor is investigated within mean field,asymptotic perturbation theory. Using a 2D electron gas model it is shown that, due to a strict phase coherence in the many-particle correlation functions, the 'scattering' effect in the asymptotic limit ($\sqrt{E_F/\hbar\omega_c}\gg 1$) is much weaker than what is predicted by the random vortex lattice model proposed by Maki and Stephen, which destroys this coherence . The coherent many particle configuration is a collinear array of many particle coordinates, localized within a spatial region with size of the order of the magnetic length. The amplitude of the magnetization oscillations is sharply damped just below $$ because of strong $180^{\circ}$ out of phase magnetic oscillations in the superconducting condensation energy ,which tend to cancel the normal electron oscillations. Within the ideal 2D model used it is found, however, that because of the relative smallness of the quartic and higher order terms in the expansion, the oscillations amplitude at lower fields does not really damp to zero, but only reverses sign and remains virtually undamped well below $H_{c2}$. This conclusion may be changed if disorder in the vortex lattice, or vortex lines motion will be taken into account. The reduced QP 'scattering' effect may be responsible for the apparent crossover from a strong damping of the dHvA oscillations just below $H_{c2}$ to a weaker damping at lower fields observed experimentally in several 3D superconductors.Comment: 26 pages, Revtex no Figure

Single-electron transport through the vortex core levels in clean superconductors

We develop a microscopic theory of single-electron transport in N-S-N hybrid structures in the presence of applied magnetic field introducing vortex lines in a superconductor layer. We show that vortex cores in a thick and clean superconducting layer are similar to mesoscopic conducting channels where the bound core states play the role of transverse modes. The transport through not very thick layers is governed by another mechanism, namely by resonance tunneling via vortex core levels. We apply our method to calculation of the thermal conductance along the magnetic field.Comment: 4 pages, 1 figur

Resuscitation and quantification of stressed Escherichia coli K12 NCTC8797 in water samples

The aim of this study was to investigate the impact on numbers of using different media for the enumeration of Escherichia coli subjected to stress, and to evaluate the use of different resuscitation methods on bacterial numbers. E. coli was subjected to heat stress by exposure to 55 °C for 1 h or to light-induced oxidative stress by exposure to artificial light for up to 8 h in the presence of methylene blue. In both cases, the bacterial counts on selective media were below the limits of detection whereas on non-selective media colonies were still produced. After resuscitation in non-selective media, using a multi-well MPN resuscitation method or resuscitation on membrane filters, the bacterial counts on selective media matched those on non-selective media. Heat and light stress can affect the ability of E. coli to grow on selective media essential for the enumeration as indicator bacteria. A resuscitation method is essential for the recovery of these stressed bacteria in order to avoid underestimation of indicator bacteria numbers in water. There was no difference in resuscitation efficiency using the membrane filter and multi-well MPN methods. This study emphasises the need to use a resuscitation method if the numbers of indicator bacteria in water samples are not to be underestimated. False-negative results in the analysis of drinking water or natural bathing waters could have profound health effects

Ginzburg-Landau-Gor'kov Theory of Magnetic oscillations in a type-II 2-dimensional Superconductor

We investigate de Haas-van Alphen (dHvA) oscillations in the mixed state of a type-II two-dimensional superconductor within a self-consistent Gor'kov perturbation scheme. Assuming that the order parameter forms a vortex lattice we can calculate the expansion coefficients exactly to any order. We have tested the results of the perturbation theory to fourth and eight order against an exact numerical solution of the corresponding Bogoliubov-de Gennes equations. The perturbation theory is found to describe the onset of superconductivity well close to the transition point $H_{c2}$. Contrary to earlier calculations by other authors we do not find that the perturbative scheme predicts any maximum of the dHvA-oscillations below $H_{c2}$. Instead we obtain a substantial damping of the magnetic oscillations in the mixed state as compared to the normal state. We have examined the effect of an oscillatory chemical potential due to particle conservation and the effect of a finite Zeeman splitting. Furthermore we have investigated the recently debated issue of a possibility of a sign change of the fundamental harmonic of the magnetic oscillations. Our theory is compared with experiment and we have found good agreement.Comment: 39 pages, 8 figures. This is a replacement of supr-con/9608004. Several sections changed or added, including a section on the effect of spin and the effect of a conserved number of particles. To be published in Phys. Rev.

Superconducting fluctuations at low temperature

The effect of fluctuations on the transport and thermodynamic properties of two-dimensional superconductors in a magnetic field is studied at low temperature. The fluctuation conductivity is calculated in the framework of the perturbation theory with the help of usual diagram technique. It is shown that in the dirty case the Aslamazov-Larkin, Maki-Thomson and Density of States contributions are of the same order. At extremely low temperature, the total fluctuation correction to the normal conductivity is negative in the dirty limit and depends on the external magnetic field logarithmically. In the non-local clean limit, the Aslamazov-Larkin contribution to conductivity is evaluated with the aid of the Helfand-Werthamer theory. The longitudinal and Hall conductivities are found. The fluctuating magnetization is calculated in the one-loop and two-loop approximations.Comment: 12 pages, 4 figures, submitted to Phys. Rev.

Quasiparticles of d-wave superconductors in finite magnetic fields

We study quasiparticles of d-wave superconductors in the vortex lattice by self-consistently solving the Bogoliubov-de Gennes equations. It is found for a pure $d_{x^2-y^2}$ state that: (i) low-energy quasiparticle bands in the magnetic Brillouin zone have rather large dispersion even in low magnetic fields, indicating absense of bound states for an isolated vortex; (ii) in finite fields with $k_F \xi_0$ small, the calculated tunneling conductance at the vortex core shows a double-peak structure near zero bias, as qualitatively consistent with the STM experiment by Maggio-Aprile et al. [Phys. Rev. Lett. {\bf 75} (1995) 2754]. We also find that mixing of a $d_{xy}$- or an s-wave component, if any, develops gradually without transitions as the field is increased, having little effect on the tunneling spectra.Comment: 4 pages, 4 figures, LaTe

Rules Governing Selective Protein Carbonylation

BACKGROUND:Carbonyl derivatives are mainly formed by direct metal-catalysed oxidation (MCO) attacks on the amino-acid side chains of proline, arginine, lysine and threonine residues. For reasons unknown, only some proteins are prone to carbonylation. METHODOLOGY/PRINCIPAL FINDINGS:we used mass spectrometry analysis to identify carbonylated sites in: BSA that had undergone in vitro MCO, and 23 carbonylated proteins in Escherichia coli. The presence of a carbonylated site rendered the neighbouring carbonylatable site more prone to carbonylation. Most carbonylated sites were present within hot spots of carbonylation. These observations led us to suggest rules for identifying sites more prone to carbonylation. We used these rules to design an in silico model (available at http://www.lcb.cnrs-mrs.fr/CSPD/), allowing an effective and accurate prediction of sites and of proteins more prone to carbonylation in the E. coli proteome. CONCLUSIONS/SIGNIFICANCE:We observed that proteins evolve to either selectively maintain or lose predicted hot spots of carbonylation depending on their biological function. As our predictive model also allows efficient detection of carbonylated proteins in Bacillus subtilis, we believe that our model may be extended to direct MCO attacks in all organisms

Quasi-Classical Calculation of the Mixed-State Thermal Conductivity in s-Wave and d-Wave Superconductors

To see how superconducting gap structures affect the longitudinal component of mixed-state thermal conductivity kappa_{xx}(B), the magnetic-field dependences of kappa_{xx}(B) in s-wave and d-wave superconductors are investigated. Calculations are performed on the basis of the quasi-classical theory of superconductivity by fully taking account of the spatial variation of the normal Green's function, neglected in previous works, by the Brandt-Pesch-Tewordt approximation. On the basis of our result, we discuss the possibility of kappa_{xx}(B) measurement as a method of probing the gap structure.Comment: To appear in J. Phys. Soc. Jp