A theoretical model for double diffusive phenomena in cloudy convection

International audienceUsing classical rheological principles, a model is proposed to depict the molecular diffusion in a moist-saturated dissipative atmosphere: due to the saturation condition existing between water vapor and liquid water in the medium, the equations are those of a double diffusive phenomenon with Dufour effect. The double diffusivity is important because of the huge diffusivity difference between the liquid phase and the gaseous phase. Reduced equations are constructed and are then applied to describe the linear free convection of a thin cloudy layer bounded by two free surfaces. The problem is solved with respect to two destabilizing parameters, a Rayleigh number Ra and a moist Rayleigh number Rh . Two instabilities may occur: (i) oscillatory modes, which exist for sufficiently large values of the Rayleigh number: these modes generalize the static instability of the medium; (ii) stationary modes, which mainly occur when the moist Rayleigh number is negative. These modes are due to the molecular diffusion, and exist even when the medium is statically stable: the corresponding motions describe, in the moist-saturated air, configurations such as "fleecy clouds". Growth rates are determined at the instability threshold for the two modes of instability occurring in the process. The case of vanishing moisture concentration is considered: the oscillatory unstable case appears as a singular perturbation (due to the moisture) of the stationary unstable state of the Rayleigh-Bénard convection in pure fluid, and, more generally, as the dynamical perturbation of the static instability. The convective behaviour of a cloud in the air at rest is then examined: the instability of the cloud is mainly due to moisture, while the instability of the surrounding air is mainly due to heating

Variabilité des caractéristiques statistiques des pluies extrêmes dans les Alpes francaises

Le but de cet article est la recherche de liaisons entre les précipitations extrêmes de pas de temps de 1 à 24 heures dans les Alpes Françaises. En particulier, il semble important de pouvoir déduire les valeurs pour de faibles pas de temps (1h, 2h... ) de celles de forts pas de temps, 24h en particulier. En effet, nous disposons actuellement de peu d'enregistrements historiques à pas de temps fin. En fait, le réseau de pluviographes utilisé est constitué de seulement 65 stations. Par contre, l'existence d'un réseau très dense de pluviomètres permet de déterminer les caractéristiques de pas de temps 24h.Pour ce faire, nous définissons une variable traduisant l'évolution des précipitations en fonction du temps de retour pour chaque pas de temps et chaque station : le gradex. Nous avons testé plusieurs types de relations pour lier les gradex des différents pas de temps entre eux : relation linéaire, puissance, exponentielle, logarithmique ; c'est la relation linéaire qui est la meilleure dans les Alpes Françaises. L'étude des relations entre les gradex des différents pas de temps montre que les pas de temps voisins sont bien corrélés entre eux, ce qui n'est plus le cas lorsque les pas de temps deviennent très distincts. Ces résultats sont confirmés par la définition de 4 régions homogènes par rapport aux précipitations extrêmes sur lesquelles nous testons l'éventualité de relations linéaires entre les gradex des différents pas de temps.Finalement, nous avons mis en évidence l'absence de relations simples permettant de passer de pas de temps longs à des pas de temps faibles. Par contre, on peut passer sans trop d'erreur d'un pas de temps de 24 heures à celui de 12 heures ou 6 heures, résultat déjà fort intéressant.For many development projects, it is important to have some idea of the magnitude of extreme precipitation events that may occur for different probability levels and for time steps of less than 24 hours. Unfortunately, most existing rain gauge networks measure precipitation on only a daily basis. In the French Alps, 65 rain gauge stations provide precipitation data over short time steps (1 to 24 hours). This very diverse network, managed jointly by the French electrical utility (Electricité de France), the national weather office (Météorologie Nationale) and the regional water resources service (SRAE), provides a valuable basis for investigating possible relationships between the characteristics of extreme precipitation for 24-hour periods and those for shorter time periods. The results of such a study, although of course valid only for the investigated area, should provide an indication of whether or not it is possible to calculate the characteristics of rainfall over short time steps from much denser 24-hour rain gauge networks. A statistical analysis was carried out to estimate extreme rainfall values for return periods of 2, 5, 10, 20, 50 and 100 years and for time steps of 1, 2, 3, 6, 12 and 24 hours. Each station is therefore associated with 36 precipitation values as a function of return period and duration. A variable referred to as the gradex (gradient of the exponential) is defined, reflecting the change in precipitation values as a function of the return period for each time step and each station. The definition of this variable is based on the fact that Gumbel's law is used to represent the frequency distribution of extreme rainfalls over time intervals extending from 1 hour up to several days, which is equivalent to assuming an exponentially decreasing frequency distribution for extreme rainfalls for a given time step and a given location. When plotted on Gumbel paper, the right-hand part of this distribution has a slope equal to the parameter "a" of Gumbel's law: F(x)=exp{-exp{-(x-x>indice>0/a}}where F(x) is the probability of occurrence of a value less than x. The parameter "a" is the gradex, and has the same dimensions as x. It can be determined with the method of moments :a(t)=0.78xσxwhere σxis the standard deviation of the sample.This definition is equivalent to taking the slope of the line passing through the points corresponding to T=20 and 100 years on a Gumbel plot. For each of the stations, we can evaluate six gradex values, i.e. one for each time step. In this way, for each of the 65 stations and for each time step, we obtain the gradex values and estimated precipitation values for return periods from 2 to 100 years.Several types of curves were tested in order to determine possible relationships among the gradex values for different time steps, including linear, power law, exponential and logarithmic relationships. For the French Alps, the best fit was obtained with a linear relationship and we calculated the corresponding correlation coefficients. We found that the gradex values were well correlated for adjacent time steps, but not for those that were very different. In particular, it would appear to be impossible to deduce gradex values for very small time steps (1 to 6 hours) from the 24-hour gradex. The 24-hour gradex accounts for only 17% of the variance of the 1-hour gradex, while it accounts for 92% of the variance of the 12-hour gradex. Using a linear relationship, the only gradex values that can be estimated with any degree of accuracy from the 24-hour value are those corresponding to time steps greater than 6 hours.To check these results, we carried out a similar study after dividing the test area into four regions. The extreme precipitation values for these regions presented similar characteristics (same order of magnitude of precipitation and gradex values). For each region, we looked for significant linear relationships between the gradex values for the different time steps. The conclusions were the same as when we considered the entire area, i.e. the relationship between the gradex values of short time steps and the 24-hour values is very poor.We have shown that no simple relationship exists to deduce values for short time steps from those measured for long time steps. The problem we posed at the outset therefore appears to have no straight-forward solution. A network of rain gauges measuring daily precipitation values cannot be used to determine the statistical characteristics of the precipitation for much shorter time steps, i.e. less than 6 hours. The only solution would be to use devices capable of measuring the precipitation over short time intervals, for instance recording rain gauges or automatic stations linked to data acquisition systems. Unfortunately such devices have not been in use for a long time and provide records for periods rarely exceeding ten years.In conclusion, this study reveals the limits for the extrapolation of extreme daily rainfall characteristics to shorter time steps

Thermodynamic Analysis of Interacting Nucleic Acid Strands

Motivated by the analysis of natural and engineered DNA and RNA systems, we present the first algorithm for calculating the partition function of an unpseudoknotted complex of multiple interacting nucleic acid strands. This dynamic program is based on a rigorous extension of secondary structure models to the multistranded case, addressing representation and distinguishability issues that do not arise for single-stranded structures. We then derive the form of the partition function for a fixed volume containing a dilute solution of nucleic acid complexes. This expression can be evaluated explicitly for small numbers of strands, allowing the calculation of the equilibrium population distribution for each species of complex. Alternatively, for large systems (e.g., a test tube), we show that the unique complex concentrations corresponding to thermodynamic equilibrium can be obtained by solving a convex programming problem. Partition function and concentration information can then be used to calculate equilibrium base-pairing observables. The underlying physics and mathematical formulation of these problems lead to an interesting blend of approaches, including ideas from graph theory, group theory, dynamic programming, combinatorics, convex optimization, and Lagrange duality

On the effect of buoyancy on lateral migration of bubbles in turbulent flows insights from Direct Numerical Simulations

International audienceBubble migration is a key concern in turbulent bubbly flows as it dramatically affects momentum and mass transfers between phases. Its prediction in steam-water conditions relevant to PWR applications is difficult to assess because experiments are often conducted with air/water flows that present substantially different properties. The effect of the deformability of bubbles on the lift force has been extensively studied experimentally, or numerically, and characterized based on the Eotvos and Reynolds numbers. Nonetheless, the effect of buoyancy is not well understood. The strength of gravity and the resultant enhancement of turbulence can have a significant impact on bubble migration in the cross-flow direction.In this work, we propose to use Direct Numerical Simulations (DNS) of turbulent bubbly flows to better understand the dominant physical mechanisms at play and cover ranges of conditions difficult to access experimentally. DNS offers a rich insight into the underlying physical phenomena and allows us to control the relative importance of different sub-physics. Starting from the flow conditions studied by Lu and Tryggvason [1], we perform four DNS of bubbly flows at a slightly higher Reynolds friction number, covering deformable and almost-spherical bubbles in weakly-buoyant or buoyant conditions. Separate effects of the Eotvos number and of an increasing gravitational force are assessed. Mean quantities, Reynolds stresses and higher-order statistics are computed to analyze the effect of bubbles on liquid turbulence levels, which influences the wall-normal void fraction profile. New insights on the way bubbles alters liquid turbulence levels and influence the lateral migration of bubbles are presented. Further experimental and numerical studies are required to support and extend this analysis

Statistical analysis of Fisher et al. PBPK model of trichloroethylene kinetics.

Two physiologically based pharmacokinetic models for trichloroethylene (TCE) in mice and humans were calibrated with new toxicokinetic data sets. Calibration is an important step in model development, essential to a legitimate use of models for research or regulatory purposes. A Bayesian statistical framework was used to combine prior information about the model parameters with the data likelihood to yield posterior parameter distributions. For mice, these distributions represent uncertainty. For humans, the use of a population statistical model yielded estimates of both variability and uncertainty in human toxicokinetics of TCE. After adjustment of the models by Markov chain Monte Carlo sampling, the mouse model agreed with a large part of the data. Yet, some data on secondary metabolites were not fit well. The posterior parameter distributions obtained for mice were quite narrow (coefficient of variation [CV] of about 10 or 20%), but these CVs might be underestimated because of the incomplete fit of the model. The data fit, for humans, was better than for mice. Yet, some improvement of the model is needed to correctly describe trichloroethanol concentrations over long time periods. Posterior uncertainties about the population means corresponded to 10-20% CV. In terms of human population variability, volumes and flows varied across subject by approximately 20% CV. The variability was somewhat higher for partition coefficients (between 30 and 40%) and much higher for the metabolic parameters (standard deviations representing about a factor of 2). Finally, the analysis points to differences between human males and females in the toxicokinetics of TCE. The significance of these differences in terms of risk remains to be investigated

Global dynamics and stability limits for planetary systems around HD 12661, HD 38529, HD 37124 and HD 160691

In order to distinguish between regular and chaotic planetary orbits we apply a new technique called MEGNO in a wide neighbourhood of orbital parameters determined using standard two-body Keplerian fits for HD 12661, HD 38529, HD 37124 and HD 160691 planetary systems. We show that the currently announced orbital parameters place these systems in very different situations from the point of view of dynamical stability. While HD 38529 and HD 37124 are located within large stability zones in the phase space around their determined orbits, the preliminary orbits in HD 160691 are highly unstable. The orbital parameters of the HD 12661 planets are located in a border region between stable and unstable dynamical regimes, so while its currently determined orbital parameters produce stable regular orbits, a minor change within the margin of error of just one parameter may result in a chaotic dynamical system.Comment: 12 pages, 3 figures, accepted ApJ, revised version following the referee's repor

Model Fusion to Enhance the Clinical Acceptability of Long-Term Glucose Predictions

This paper presents the Derivatives Combination Predictor (DCP), a novel model fusion algorithm for making long-term glucose predictions for diabetic people. First, using the history of glucose predictions made by several models, the future glucose variation at a given horizon is predicted. Then, by accumulating the past predicted variations starting from a known glucose value, the fused glucose prediction is computed. A new loss function is introduced to make the DCP model learn to react faster to changes in glucose variations. The algorithm has been tested on 10 \textit{in-silico} type-1 diabetic children from the T1DMS software. Three initial predictors have been used: a Gaussian process regressor, a feed-forward neural network and an extreme learning machine model. The DCP and two other fusion algorithms have been evaluated at a prediction horizon of 120 minutes with the root-mean-squared error of the prediction, the root-mean-squared error of the predicted variation, and the continuous glucose-error grid analysis. By making a successful trade-off between prediction accuracy and predicted-variation accuracy, the DCP, alongside with its specifically designed loss function, improves the clinical acceptability of the predictions, and therefore the safety of the model for diabetic people