Hard hexagon partition function for complex fugacity

We study the analyticity of the partition function of the hard hexagon model in the complex fugacity plane by computing zeros and transfer matrix eigenvalues for large finite size systems. We find that the partition function per site computed by Baxter in the thermodynamic limit for positive real values of the fugacity is not sufficient to describe the analyticity in the full complex fugacity plane. We also obtain a new algebraic equation for the low density partition function per site.Comment: 49 pages, IoP styles files, lots of figures (png mostly) so using PDFLaTeX. Some minor changes added to version 2 in response to referee report

Integrability vs non-integrability: Hard hexagons and hard squares compared

In this paper we compare the integrable hard hexagon model with the non-integrable hard squares model by means of partition function roots and transfer matrix eigenvalues. We consider partition functions for toroidal, cylindrical, and free-free boundary conditions up to sizes $40\times40$ and transfer matrices up to 30 sites. For all boundary conditions the hard squares roots are seen to lie in a bounded area of the complex fugacity plane along with the universal hard core line segment on the negative real fugacity axis. The density of roots on this line segment matches the derivative of the phase difference between the eigenvalues of largest (and equal) moduli and exhibits much greater structure than the corresponding density of hard hexagons. We also study the special point $z=-1$ of hard squares where all eigenvalues have unit modulus, and we give several conjectures for the value at $z=-1$ of the partition functions.Comment: 46 page

Deuterium on Venus: Observations from Earth

In view of the importance of the deuterium-to-hydrogen ratio in understanding the evolutionary scenario of planetary atmospheres and its relationship to understanding the evolution of our own Earth, we undertook a series of observations designed to resolve previous observational conflicts. We observed the dark side of Venus in the 2.3 micron spectral region in search of both H2O and HDO, which would provide us with the D/H ratio in Venus' atmosphere. We identified a large number of molecular lines in the region, belonging to both molecules, and, using synthetic spectral techniques, obtained mixing ratios of 34 plus or minus 10 ppm and 1.3 plus or minus 0.2 ppm for H2O and HDO, respectively. These mixing ratios yield a D/H ratio for Venus of D/H equals 1.9 plus or minus 0.6 times 10 (exp 12) and 120 plus or minus 40 times the telluric ratio. Although the detailed interpretation is difficult, our observations confirm that the Pioneer Venus Orbiter results and establish that indeed Venus had a period in its early history in which it was very wet, perhaps not unlike the early wet period that seems to have been present on Mars, and that, in contrast to Earth, lost much of its water over geologic time

Holonomic functions of several complex variables and singularities of anisotropic Ising n-fold integrals

Lattice statistical mechanics, often provides a natural (holonomic) framework to perform singularity analysis with several complex variables that would, in a general mathematical framework, be too complex, or could not be defined. Considering several Picard-Fuchs systems of two-variables "above" Calabi-Yau ODEs, associated with double hypergeometric series, we show that holonomic functions are actually a good framework for actually finding the singular manifolds. We, then, analyse the singular algebraic varieties of the n-fold integrals $\chi^{(n)}$, corresponding to the decomposition of the magnetic susceptibility of the anisotropic square Ising model. We revisit a set of Nickelian singularities that turns out to be a two-parameter family of elliptic curves. We then find a first set of non-Nickelian singularities for $\chi^{(3)}$ and $\chi^{(4)}$, that also turns out to be rational or ellipic curves. We underline the fact that these singular curves depend on the anisotropy of the Ising model. We address, from a birational viewpoint, the emergence of families of elliptic curves, and of Calabi-Yau manifolds on such problems. We discuss the accumulation of these singular curves for the non-holonomic anisotropic full susceptibility.Comment: 36 page

Paramètres gouvernant la prolifération bactérienne dans les réseaux de distribution

L'étude a permis de suivre l'évolution des caractéristiques physico-chimiques et microbiologiques des eaux dans un réseau de distribution expérimental de taille industrielle, afin de comparer d'une part l'effet du chlore et de la monochloramine sur la biomasse présente dans le système à l'équilibre et d'autre part d'établir des relations quantitatives entre prolifération bactérienne, oxydant et matière organique biodégradable.Dès les premières heures de transit dans le réseau, une consommation des oxydants est constatée, avec toutefois une plus grande stabilité de la monochloramine (vitesse de consommation de 0,05 mgCl2 l-1h-1 et 0,02 mgCl2 l-1h-1 respectivement pour le chlore et la monochloramine).Même en présence d'un désinfectant résiduel, il est possible de noter une accumulation de bactéries-à ta surface des tuyaux de distribution (105 à 106 cellules. cm-2, dont environ 1 % est cultivable sur gélose) qui augmente avec la diminution de concentration du désinfectant résiduel. Les relations logarithmiques entre densité cellulaire (phase eau ou biofilm) et oxydant résiduel montrent d'une part que pour inactiver totalement les bactéries en suspension dans l'eau il convient de maintenir une chloration en continu avec un résiduel constant supérieur ou égal à 0,5 mgCl2 l-1 et, d'autre part que les chloramines sont au moins 2,5 fois moins efficaces que le chlore, même vis-à-vis des bactéries fixées.La présence de matière organique biodégradable dans les eaux explique la prolifération des bactéries dans le système de distribution. Ainsi une concentration additionnelle de 100 µg.l-1 de carbone organique dissous biodégradable (CODB) dans l'eau entrant dans le réseau de distribution occasionne en 24 heures et à 20°C une augmentation du nombre de bactéries fixées (+7,5.105 cellules.cm-2) ou en suspension (+ 4.104 cellules.ml-1) dans le réseau de distribution, à l'équilibre, déjà largement colonisé par des micro-organismes.Ainsi le contrôle de la fraction biodégradable de la matière organique apparaît toujours comme un objectif primordial.This study was carried out in order to evaluate the variations in the physicochemical characteristics of the water in an experimental distribution system.The primary objectives of the study were :- to compare the disinfectant efficiency of chlorine and monochloramine- to establish quantitative correlations among bacterial density, concentration of residual disinfectant, and concentration of biodegradable organic matter.The finished waters were obtained from a water treatment pilot plant characterized by : prechlorination (average treatment rate : 1.4 mgCl2 l-1 and residual alter sand filtration : 0.08 mgCl2 l-1), coagulation-flocculation-sedimentation (FeCl3 treatment rate : 30 to 60 mg l-1 adjusted to the raw water turbidity below 0.3 NTU), sand filtration (filtration rate : 6 h-1) and post-disinfection with chloramine (average treatment rate : 1.8 mgCl2 l-1) or chloramine (average treatment rate : 1.66 mgCl2 l-1). The concentrations of post-disinfectant used were chosen in order to maintain chlorine at 0.2 to 0.5 mgCl2 l-1 and monochloramine at 1 mgC2 l-1 after the first 24 hours residence time in the experimental distribution system.The experimental distribution system is composed of three parallel loops connected in series (31 m length, 100 mm diameter, cement lined cast iron, water velocity : 1m s-1). The configuration and operation of the system permitted a residence time of 24 hours in each loop (that is 72 hours for the whole system). Appropriate sample tap locations facilitated removal of bulk water samples. Special sampling parts also permitted sampling of cement coupons for determination of attached biofilm.The measured parameters were : residual oxidant (DPD method), DOC, BDOC (28 days of incubation at 28 °C with a bacterial inoculum), cell density in the bulk water phase (CFU ml-1) and in the biofilm (CFU cm-2) after 15 days of incubation at 20-22 °C. Total cells were enumerated using the epifluorescence direct count technique.For each experiment, all the sampling sequences were carried out on each of three days, after quasi steady-state was achieved in the system (4 to 6 weeks after starting each experiment). The data were analysed in order to characterize the treated and distributed waters; the results discussed here are based on the averages of the measured parameters tram the water samples and biofilm samples taken after the system achieved quasi steady-state.Characteristics of the treated watersThe treated waters were characterized by important variations at the DOC, BDOC and cell density. For example, the concentrations of DOC showed a seasonal variation ranging from 0.8 to 1.3 mg Cl-1 in winter to 1.6 to 2.6 mg Cl-1 in summer.The treated waters contained approximately the same concentrations of residual disinfectant, averaging 1.6 mgCl2 l-1 for chlorine and 1.5 mgCl2 l-1 for monochloramine.However, a significant difference cell density was found between the two post-disinfectants. Cell densities by the epifluorescence direct count technic were 1.6 x 103 ml-1 (0.3 % of CFU ml-1) with chlorine and 6.3 x 104 ml-1 (0.03 % of CFU ml-1) with monochloramine. The difference on cell density between the post-chlorination and the post-chloramination treatments has been observed systematically, and may be explained either as cellular lysis with chlorine or an interference when using epifluorescence counting for chlorinated waters.Characteristics of the distributed watersWhatever the season, depletion of oxidant (chlorine or monochloramine), and elimination of dissolved organic matter (DOC, BDOC) occured during the first hours of circulation of water in the distribution system. The net result was an increase in bacterial cell density.During the first hours of circulation of the waters in the distribution system, depletion of the disinfectant occured. Depletion was more rapid for chlorine (-0.05 mgCl2 l-1 h-1) titan for monochloramine (-0.02 mgCl2 l-1 h-1), winch is considered more stable titan chlorine.Even in the presence of a residual disinfectant in the distribution system, microorganisms are present in the water phase (104 to 106 cells ml-1 by epifluorescence direct count; 1 % CFU ml-1 after 15 days of incubation at 20-22 °C) and in the biofilm (105 to 106 cells cm-2 by epifluorescence direct count; 1 % CFU ml-1 after 15 days of incubation at 20-22 °C). The bacterial density increased white the disinfectant residual decreased. The apparent growth rate of the attached biomass (µfix) in loop 2 of the chlorinated distribution system (equivalent to 48 hours detention), was close to the µfix calculated for loop 2 of the chloraminated distribution system : the values were 0.0043 h-1 and 0.005 h-1 respectively.In addition, the change in the organic matter (expressed as DOC) occured in two steps :- a slight increase in DOC during the 24 first hours of residence time (loop 1), when increased residual disinfectant were present.- a bacterial consumption of DOC after 24 hours of residence time (loops 2 and 3), even in the presence of small concentrations of disinfectants.In loop 2 (48 hours residence time of the water in the system; chlorine : 0.01 mgCl2 l-1, chloramine : 0.3 mgCl2 l-1 h-1), the rates of DOC elimination averaged 13 mgCl2 l-1 h-1 and 0.42, mgCl2 l-1 h-1, respectively in the chlorinated and chloraminated distribution systems. This decrease in DOC concentrations was related to the increase in bacterial density.Relationships between cell density, oxidant and organic matterLinear relationships between the concentration of residual oxidant (chlorine or monochloramine) and the cell density in the water phase or in the biofilm show that :- whichever oxidant was used, the pipe loop sections without residual disinfectants were characterized by about 5 x 106 attached cells per cm2 (4 to 10% were able to grow on agar medium in 15 days at 20-22 °C) and by 4 x 105 planktonic cells per ml (1 % CFU ml-1);- consistently, in the sections of the system with a residual disinfectant, the bacteria (CFU and epilluorescence counting) in the water phase were more sensitive to the residual disinfectant (chlorine or monochloramine) than the bacteria attached to the pipe walls (biofilm).However, there was a difference in effectiveness between the two disinfectants; chlorine was more efficient in controlling planktonic bacteria and biofilm bacteria than was monochloramine.For example, to achieve complete inactivation of the planktonic bacteria (CFU ml-1) a constant chlorine residual of 0.5 mgCl2 l-1 was required throughout the whole distribution system, compared to 2.5 times more chloramine to achieve the same efficiency.Finally, with equivalent concentrations of residual disinfectant, the microbiological quality of the chlorinated distribution waters was better than that of the chloraminated distribution waters.From loop to loop, linear relationships between ∆DOC and cell density pointed out that the presence of biodegradable organic matter can explain the bacterial proliferation in the distribution system. For example, a concentration of BDOC as low as 0.1 mgC l-1 resulted in an increase in the cell density : an additional accumulation of 7.5 x 105 attached cells cm-2 and 4 x 104 planktonic cells ml-1 was observed in the experimental distribution system at quasi steady-state.Consequently, the control of the biodegradable organic carbon remains one of the prime objectives in order to achieve biologically stable distribution waters

Placement of metallic biliary endoprostheses in complex hilar tumours

AbstractPurposeTo assess the technical success, clinical success and complications after 1 month of percutaneous biliary drainage with the placement of several metallic endoprostheses in complex hilar liver tumours.Materials and methodsThis is a retrospective study, on a homogenous target population of 68 consecutive patients, who underwent multiple percutaneous biliary drainage for complex hilar tumour (Bismuth type II, III and IV) between August 1998 and August 2010. Patients benefiting from previous endoscopic drainage were excluded from the study. The clinical data, biological data, imaging and interventional radiology procedures were studied.ResultsThe rate of success of the technique was 98.5% and the clinical rate of success was 84% after 1 week and 93% after 1 month. The rate of minor and major complications was 25 and 13% respectively.ConclusionMultiple percutaneous biliary drainage in complex hilar tumour is a safe and effective first intention procedure

Modeling affirmative and negated action processing in the brain with lexical and compositional semantic models

Recent work shows that distributional semantic models can be used to decode patterns of brain activity associated with individual words and sentence meanings. However, it is yet unclear to what extent such models can be used to study and ecode fMRI patterns associated with specific aspects of semantic composition such as the negation function. In this paper, we apply lexical and compositional semantic models to decode fMRI patterns associated with negated and affirmative sentences containing hand-action verbs. Our results show reduced decoding (correlation) of sentences where the verb is in the negated context, as compared to the affirmative one, within brain regions implicated in action-semantic processing. This supports behavioral and brain imaging studies, suggesting that negation involves reduced access to aspects of the affirmative mental representation. The results pave the way for testing alternate semantic models of negation against human semantic processing in the brain

Random Matrix Theory and Classical Statistical Mechanics. I. Vertex Models

A connection between integrability properties and general statistical properties of the spectra of symmetric transfer matrices of the asymmetric eight-vertex model is studied using random matrix theory (eigenvalue spacing distribution and spectral rigidity). For Yang-Baxter integrable cases, including free-fermion solutions, we have found a Poissonian behavior, whereas level repulsion close to the Wigner distribution is found for non-integrable models. For the asymmetric eight-vertex model, however, the level repulsion can also disappearand the Poisson distribution be recovered on (non Yang--Baxter integrable) algebraic varieties, the so-called disorder varieties. We also present an infinite set of algebraic varieties which are stable under the action of an infinite discrete symmetry group of the parameter space. These varieties are possible loci for free parafermions. Using our numerical criterion we have tested the generic calculability of the model on these algebraic varieties.Comment: 25 pages, 7 PostScript Figure

On the Symmetries of Integrability

We show that the Yang-Baxter equations for two dimensional models admit as a group of symmetry the infinite discrete group $A_2^{(1)}$. The existence of this symmetry explains the presence of a spectral parameter in the solutions of the equations. We show that similarly, for three-dimensional vertex models and the associated tetrahedron equations, there also exists an infinite discrete group of symmetry. Although generalizing naturally the previous one, it is a much bigger hyperbolic Coxeter group. We indicate how this symmetry can help to resolve the Yang-Baxter equations and their higher-dimensional generalizations and initiate the study of three-dimensional vertex models. These symmetries are naturally represented as birational projective transformations. They may preserve non trivial algebraic varieties, and lead to proper parametrizations of the models, be they integrable or not. We mention the relation existing between spin models and the Bose-Messner algebras of algebraic combinatorics. Our results also yield the generalization of the condition $q^n=1$ so often mentioned in the theory of quantum groups, when no $q$ parameter is available.Comment: 23 page