A Simple Model For the Intermolecular Interactions in Halogene Crystals

A simple effective atom-atom intermolecular potential for halogene solids (F2, Cl-, Br2 and 12) is proposed. The centers of inter action of the effective potential (6-exp type) are shifted from\u27 the atomic sites in order to reduce anisotropy of the intermolecular distances. The calculated results of the static properties for fluorine and chlorine are in good agreement with the experimental results. The calculated results for bromine and iodine crystals are less satisfactory. The limitations of the atom-atom model for description of the dynamical properties of halogene solids are also briefly discusse

A Simple Model For the Intermolecular Interactions in Halogene Crystals

A simple effective atom-atom intermolecular potential for halogene solids (F2, Cl-, Br2 and 12) is proposed. The centers of inter action of the effective potential (6-exp type) are shifted from\u27 the atomic sites in order to reduce anisotropy of the intermolecular distances. The calculated results of the static properties for fluorine and chlorine are in good agreement with the experimental results. The calculated results for bromine and iodine crystals are less satisfactory. The limitations of the atom-atom model for description of the dynamical properties of halogene solids are also briefly discusse

Low-Temperature Specific Heat of an Extreme-Type-II Superconductor at High Magnetic Fields

We present a detailed study of the quasiparticle contribution to the low-temperature specific heat of an extreme type-II superconductor at high magnetic fields. Within a T-matrix approximation for the self-energies in the mixed state of a homogeneous superconductor, the electronic specific heat is a linear function of temperature with a linear-$T$ coefficient $\gamma_s(H)$ being a nonlinear function of magnetic field $H$. In the range of magnetic fields H\agt (0.15-0.2)H_{c2} where our theory is applicable, the calculated $\gamma_s(H)$ closely resembles the experimental data for the borocarbide superconductor YNi$_2$B$_2$C.Comment: 7 pages, 2 figures, to appear in Physical Review

Quasiparticle spectrum of a type-II superconductor in a high magnetic field with randomly pinned vortices

We show that gapless superconductivity of a strongly type-II superconductor in a high magnetic field prevails in the presence of disorder, suggesting a topological nature. We calculate the density of states of the Bogoliubov-de Gennes quasiparticles for a two-dimensional inhomogeneous system in both cases of weak and strong disorder. In the limit of very weak disorder, the effect is very small and the density of states is not appreciably changed. As the disorder increases, the density of states at low energies increases and the ratio of the low-energy density of states to its maximum increases significantly

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

Absence of Persistent Magnetic Oscillations in Type-II Superconductors

We report on a numerical study intended to examine the possibility that magnetic oscillations persist in type II superconductors beyond the point where the pairing self-energy exceeds the normal state Landau level separation. Our work is based on the self-consistent numerical solution for model superconductors of the Bogoliubov-deGennes equations for the vortex lattice state. In the regime where the pairing self-energy is smaller than the cyclotron energy, magnetic oscillations resulting from Landau level quantization are suppressed by the broadening of quasiparticle Landau levels due to the non-uniform order parameter of the vortex lattice state, and by splittings of the quasiparticle bands. Plausible arguments that the latter effect can lead to a sign change of the fundamental harmonic of the magnetic oscillations when the pairing self-energy is comparable to the cyclotron energy are shown to be flawed. Our calculations indicate that magnetic oscillations are strongly suppressed once the pairing self-energy exceeds the Landau level separation.Comment: 7 pages, revtex, 7 postscript figure

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

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

Gap Anisotropy and de Haas-van Alphen Effect in Type-II Superconductors

We present a theoretical study on the de Haas-van Alphen (dHvA) oscillation in the vortex state of type-II superconductors, with a special focus on the connection between the gap anisotropy and the oscillation damping. Numerical calculations for three different gap structures clearly indicate that the average gap along extremal orbits is relevant for the magnitude of the extra damping, thereby providing a support for experimental efforts to probe gap anisotropy through the dHvA signal. We also derive an analytic formula for the extra damping which gives a good fit to the numerical results.Comment: 5 pages, 1 figure, changes in Introductio