An iterative Multiscale Finite-Volume algorithm converging to the exact solution

The multiscale finite volume (MsFV) method has been developed to efficiently solve large heterogeneous problems (elliptic or parabolic); it is usually employed for pressure equations and delivers conservative flux fields to be used in transport problems. The method essentially relies on the hypothesis that the (fine-scale) problem can be reasonably described by a set of local solutions coupled by a conservative global (coarse-scale) problem. In most cases, the boundary conditions assigned for the local problems are satisfactory and the approximate conservative fluxes provided by the method are accurate. In numerically challenging cases, however, a more accurate localization is required to obtain a good approximation of the fine-scale solution. In this paper we develop a procedure to iteratively improve the boundary conditions of the local problems. The algorithm relies on the data structure of the MsFV method and employs a Krylov-subspace projection method to obtain an unconditionally stable scheme and accelerate convergence. Two variants are considered: in the first, only the MsFV operator is used; in the second, the MsFV operator is combined in a two-step method with an operator derived from the problem solved to construct the conservative flux field. The resulting iterative MsFV algorithms allow arbitrary reduction of the solution error without compromising the construction of a conservative flux field, which is guaranteed at any iteration. Since it converges to the exact solution, the method can be regarded as a linear solver. In this context, the schemes proposed here can be viewed as preconditioned versions of the Generalized Minimal Residual method (GMRES), with a very peculiar characteristic that the residual on the coarse grid is zero at any iteration (thus conservative fluxes can be obtained).

Indirect effects of peri-and postnatal choline treatment on place-learning abilities in rat.

This work was aimed at analyzing the effects of perinatal choline supplementation on the development of spatial abilities and upon adult performance. Choline supplementation (3.5 g/L in 0.02 M saccharin solution in tap water) was maintained for two weeks before birth and for up to four weeks postnatally. Additional supplementation was maintained from the fifth to the tenth week postnatally. Spatial-learning capacities were studied at the ages of 26, 65, or 80 days in a circular swimming pool (Morris place-navigation task) and at the age of 7 months in a homing arena. Treatment effects were found in both juvenile and adult rats, and thus persisted for several months after the cessation of the supplementation. The choline supplementation improved the performance in the water maze in a very selective manner. The most consistent effect was a reduction in the latency to reach a cued platform at a fixed position in space, whereas the improvement was limited when the platform was invisible and had to be located relative to distant cues only. However, after removal of the goal cue, the treated rats showed a better retention of the training position than did the control rats. A similar effect was observed in a dry-land task conducted in the homing arena. The choline supplementation thus induced a significant improvement of spatial memory. But since this effect was only evident following training with a salient cue, it might be regarded as an indirect effect promoted by an optimal combination of cue guidance with a place strategy.

Measures of fit in multiple correspondence analysis of crisp and fuzzy coded data

When continuous data are coded to categorical variables, two types of coding are possible: crisp coding in the form of indicator, or dummy, variables with values either 0 or 1; or fuzzy coding where each observation is transformed to a set of "degrees of membership" between 0 and 1, using co-called membership functions. It is well known that the correspondence analysis of crisp coded data, namely multiple correspondence analysis, yields principal inertias (eigenvalues) that considerably underestimate the quality of the solution in a low-dimensional space. Since the crisp data only code the categories to which each individual case belongs, an alternative measure of fit is simply to count how well these categories are predicted by the solution. Another approach is to consider multiple correspondence analysis equivalently as the analysis of the Burt matrix (i.e., the matrix of all two-way cross-tabulations of the categorical variables), and then perform a joint correspondence analysis to fit just the off-diagonal tables of the Burt matrix - the measure of fit is then computed as the quality of explaining these tables only. The correspondence analysis of fuzzy coded data, called "fuzzy multiple correspondence analysis", suffers from the same problem, albeit attenuated. Again, one can count how many correct predictions are made of the categories which have highest degree of membership. But here one can also defuzzify the results of the analysis to obtain estimated values of the original data, and then calculate a measure of fit in the familiar percentage form, thanks to the resultant orthogonal decomposition of variance. Furthermore, if one thinks of fuzzy multiple correspondence analysis as explaining the two-way associations between variables, a fuzzy Burt matrix can be computed and the same strategy as in the crisp case can be applied to analyse the off-diagonal part of this matrix. In this paper these alternative measures of fit are defined and applied to a data set of continuous meteorological variables, which are coded crisply and fuzzily into three categories. Measuring the fit is further discussed when the data set consists of a mixture of discrete and continuous variables.

The three phases of the ensemble forecasting of niche models: geographic range and shifts in climatically suitable areas of Utetheisa ornatrix (Lepidoptera, Arctiidae)

Species' geographic ranges are usually considered as basic units in macroecology and biogeography, yet it is still difficult to measure them accurately for many reasons. About 20 years ago, researchers started using local data on species' occurrences to estimate broad scale ranges, thereby establishing the niche modeling approach. However, there are still many problems in model evaluation and application, and one of the solutions is to find a consensus solution among models derived from different mathematical and statistical models for niche modeling, climatic projections and variable combination, all of which are sources of uncertainty during niche modeling. In this paper, we discuss this approach of ensemble forecasting and propose that it can be divided into three phases with increasing levels of complexity. Phase I is the simple combination of maps to achieve a consensual and hopefully conservative solution. In Phase II, differences among the maps used are described by multivariate analyses, and Phase III consists of the quantitative evaluation of the relative magnitude of uncertainties from different sources and their mapping. To illustrate these developments, we analyzed the occurrence data of the tiger moth, Utetheisa ornatrix (Lepidoptera, Arctiidae), a Neotropical moth species, and modeled its geographic range in current and future climates.

A note on the coincidence between Stackelberg and Nash equilibria in a differential game between government and firms

[cat] A Navas i Marín Solano es va demostrar la coincidència entre els equilibris de Nash i de Stackelberg per a una versi´o modificada del joc diferencial proposat por Lancaster (1973). Amb l’objectiu d’obtenir una solució interior, es van imposar restriccions importants sobre el valors dels paràmetres del model. En aquest treball estenem aquest resultat, en el límit en que la taxa de descompte és igual a zero, eliminant les restriccions i considerant totes les solucions possibles.

Nutrient supply by mass flow and diffusion to maize plants in response to soil aggregate size and water potential

Nutrients are basically transported to the roots by mass flow and diffusion. The aim of this study was to quantify the contribution of these two mechanisms to the acquisition of macronutrients (N, P, K, Ca, Mg, and S) and cationic micronutrients (Fe, Mn, Zn, and Cu) by maize plants as well as xylem exudate volume and composition in response to soil aggregate size and water availability. The experiment was conducted in a greenhouse with samples of an Oxisol, from under two management systems: a region of natural savanna-like vegetation (Cerradão, CER) and continuous maize under conventional management for over 30 years (CCM). The treatments were arranged in a factorial [2 x (1 + 2) x 2] design, with two management systems (CER and CCM), (1 + 2) soil sifted through a 4 mm sieve and two aggregate classes (< 0.5 mm and 0.5 - 4.0 mm) and two soil matric potentials (-40 and -10 kPa). These were evaluated in a randomized block design with four replications. The experiment was conducted for 70 days after sowing. The influence of soil aggregate size and water potential on the nutrient transport mechanisms was highest in soil samples with higher nutrient concentrations in solution, in the CER system; diffusion became more relevant when water availability was higher and in aggregates < 0.5 mm. The volume of xylem exudate collected from maize plants increased with the decrease in aggregate size and the increased availability of soil water in the CER system. The highest Ca and Mg concentrations in the xylem exudate of plants grown on samples from the CER system were related to the high concentrations of these nutrients in the soil solution of this management system.

Accurate and efficient simulation of multiphase flow in a heterogeneous reservoir by using error estimate and control in the multiscale finite-volume framework

The multiscale finite-volume (MSFV) method is designed to reduce the computational cost of elliptic and parabolic problems with highly heterogeneous anisotropic coefficients. The reduction is achieved by splitting the original global problem into a set of local problems (with approximate local boundary conditions) coupled by a coarse global problem. It has been shown recently that the numerical errors in MSFV results can be reduced systematically with an iterative procedure that provides a conservative velocity field after any iteration step. The iterative MSFV (i-MSFV) method can be obtained with an improved (smoothed) multiscale solution to enhance the localization conditions, with a Krylov subspace method [e.g., the generalized-minimal-residual (GMRES) algorithm] preconditioned by the MSFV system, or with a combination of both. In a multiphase-flow system, a balance between accuracy and computational efficiency should be achieved by finding a minimum number of i-MSFV iterations (on pressure), which is necessary to achieve the desired accuracy in the saturation solution. In this work, we extend the i-MSFV method to sequential implicit simulation of time-dependent problems. To control the error of the coupled saturation/pressure system, we analyze the transport error caused by an approximate velocity field. We then propose an error-control strategy on the basis of the residual of the pressure equation. At the beginning of simulation, the pressure solution is iterated until a specified accuracy is achieved. To minimize the number of iterations in a multiphase-flow problem, the solution at the previous timestep is used to improve the localization assumption at the current timestep. Additional iterations are used only when the residual becomes larger than a specified threshold value. Numerical results show that only a few iterations on average are necessary to improve the MSFV results significantly, even for very challenging problems. Therefore, the proposed adaptive strategy yields efficient and accurate simulation of multiphase flow in heterogeneous porous media.

Single-hole GPR reflection imaging of solute transport in a granitic aquifer

Identifying transport pathways in fractured rock is extremely challenging as flow is often organized in a few fractures that occupy a very small portion of the rock volume. We demonstrate that saline tracer experiments combined with single-hole ground penetrating radar (GPR) reflection imaging can be used to monitor saline tracer movement within mm-aperture fractures. A dipole tracer test was performed in a granitic aquifer by injecting a saline solution in a known fracture, while repeatedly acquiring single-hole GPR sections in the pumping borehole located 6 m away. The final depth-migrated difference sections make it possible to identify consistent temporal changes over a 30 m depth interval at locations corresponding to fractures previously imaged in GPR sections acquired under natural flow and tracer-free conditions. The experiment allows determining the dominant flow paths of the injected tracer and the velocity (0.4-0.7 m/min) of the tracer front. Citation: Dorn, C., N. Linde, T. Le Borgne, O. Bour, and L. Baron (2011), Single-hole GPR reflection imaging of solute transport in a granitic aquifer, Geophys. Res. Lett., 38, L08401, doi: 10.1029/2011GL047152.

Competitive sorption and desorption of phosphate and citrate in clayey and sandy loam soils

The increase of organic acids in soils can reduce phosphorus sorption. The objective of the study was to evaluate the competitive sorption of P and citrate in clayey and sandy loam soils, using a stirred-flow system. Three experiments were performed with soil samples (0-20 cm layer) of clayey (RYL-cl) and sandy loam (RYL-sl) Red Yellow Latosols (Oxisols). In the first study, the treatments were arranged in a 2 × 5 factorial design, with two soil types and five combinations of phosphorus and citrate application (only P; P + citrate; and citrate applied 7, 22, 52 min before P); in the second, the treatments were arranged in a 2 × 2 factorial design, corresponding to two soils and two forms of P and citrate application (only citrate and citrate + P); and in the third study, the treatments in a 2 × 2 × 6 factorial design consisted of two soils, two extractors (citrate and water) and six incubation times. In the RYL-cl and RYL-sl, P sorption was highest (44 and 25 % of P application, respectively), in the absence of citrate application. Under citrate application, P sorption was reduced in all treatments. The combined application of citrate and P reduced P sorption to 25.8 % of the initially applied P in RYL-cl and to 16.7 % in RYL-sl, in comparison to P without citrate. Citrate sorption in RYL-cl and RYL-sl was highest in the absence of P application, corresponding to 32.0 and 30.2 % of the citrate applied, respectively. With P application, citrate sorption was reduced to 26.4 and 19.7 % of the initially applied citrate in RYL-cl and RYL-sl, respectively. Phosphorus desorption was greater when citrate was used. Phosphorus desorption with citrate and water was higher in the beginning (until 24 h of incubation of P) in RYL-cl and RYL-sl, indicating a rapid initial phase, followed by a slow release phase. This suggests that according to the contact time of P with the soil colloids, the previously adsorbed P can be released to the soil solution in the presence of competing ligands such as citrate. In conclusion, a soil management with continuous input of organic acids is desirable, in view of their potential to compete for P sorption sites, especially in rather weathered soils.

Strong coupling solution to Schrödinger Equation: the mixing of states

In this paper we give some ideas that can be useful to solve Schrödinger equations in the case when the Hamiltonian contains a large term. We obtain an expansion of the solution in reciprocal powers of the large coupling constant. The procedure followed consists in considering that the small part of the Hamiltonian engenders a motion adiabatic to the motion generated by the large part of the same.

Renal tumor ablation using radiofrequency: results in 28 patient. Exposition scientifique: Radiologie interventionnelle

Objectifs: To describe the technique and results of radiofrequency ablation (RFA) of small renal tumors.Matériels et méthodes: 28 patients with median age 79 years were treated with RFA for small renal exophytic tumor (median size 20 mm). Most patients were poor operative candidatesbecause of associated morbidity. Four patients were treated for biopsy proven papillary tumor, 7 for clear cell carcinoma, 2 for oncocytoma and one for renalhepatocellular metastasis. No biopsy sample was obtained for the others because of a typical radiological aspect of RCC.Résultats: All patients but one were treated successfully in one session under combined ultrasound and CT guidance using either Radionics 2000 cool-tip or Bostonscientific expandable needles, one was treated in two sessions. One Splenic, 3 colic and 1 pancreatic displacement with CO2 injection and one injection of G5%solution in the costo-phrenic recessus were done in order to protect adjacent organs. Two complications were observed, one splenic iatrogenic lesion treated byembolization and one renal pelvis stenosis treated with JJ stent. After a mean follow-up of 20 months, no patient developped local recurrence on MRI follow-up.Conclusion: RFA is a simple and efficient technique pending on strict selected criteria (small size < 3 cm and exophytic lesion). Long local control is obtained with minimalmorbidity.

A note on the coincidence between Stackelberg and Nash equilibria in a differential game between government and firms

[cat] A Navas i Marín Solano es va demostrar la coincidència entre els equilibris de Nash i de Stackelberg per a una versi´o modificada del joc diferencial proposat por Lancaster (1973). Amb l’objectiu d’obtenir una solució interior, es van imposar restriccions importants sobre el valors dels paràmetres del model. En aquest treball estenem aquest resultat, en el límit en que la taxa de descompte és igual a zero, eliminant les restriccions i considerant totes les solucions possibles.

Absence of collective effects in Heisenberg systems with localized magnetic moments

Existence of collective effects in magnetic coupling in ionic solids is studied by mapping spin eigenstates of the Heisenberg and exact nonrelativistic Hamiltonians on cluster models representing KNiF3, K2NiF4, NiO, and La2CuO4. Ab initio techniques are used to estimate the Heisenberg constant J. For clusters with two magnetic centers, the values obtained are about the same for models having more magnetic centers. The absence of collective effects in J strongly suggests that magnetic interactions in this kind of ionic solids are genuinely local and entangle only the two magnetic centers involved.

Ground- and excited-state properties of M-center oxygen vacancy aggregates in the bulk and the surface of MgO

Aggregates of oxygen vacancies (F centers) represent a particular form of point defects in ionic crystals. In this study we have considered the combination of two oxygen vacancies, the M center, in the bulk and on the surface of MgO by means of cluster model calculations. Both neutral and charged forms of the defect M and M+ have been taken into account. The ground state of the M center is characterized by the presence of two doubly occupied impurity levels in the gap of the material; in M+ centers the highest level is singly occupied. For the ground-state properties we used a gradient corrected density functional theory approach. The dipole-allowed singlet-to-singlet and doublet-to-doublet electronic transitions have been determined by means of explicitly correlated multireference second-order perturbation theory calculations. These have been compared with optical transitions determined with the time-dependent density functional theory formalism. The results show that bulk M and M+ centers give rise to intense absorptions at about 4.4 and 4.0 eV, respectively. Another less intense transition at 1.3 eV has also been found for the M+ center. On the surface the transitions occur at 1.6 eV (M+) and 2 eV (M). The results are compared with recently reported electron energy loss spectroscopy spectra on MgO thin films.

Detection of smuggled cocaine in cargo using MDCT.

OBJECTIVE: Smuggling dissolved drugs, especially cocaine, in bottled liquids is an ongoing problem at borders. Common fluoroscopy of packages at the border cannot detect contaminated liquids. The objective of our study was to develop an MDCT screening method to detect cocaine-containing vessels that are hidden between uncontaminated ones in a shipment. MATERIALS AND METHODS: Studies were performed on three wine bottles containing cocaine solutions that were confiscated at the Swiss border. Reference values were obtained by scans of different sorts of commercially available wine and aqueous solutions of dissolved sugar. All bottles were scanned using MDCT, and data evaluation was performed by measuring the mean peak of Hounsfield units. To verify the method, simulated testing was performed. RESULTS: Using measurements of the mean peak of Hounsfield units enables the detection of dissolved cocaine in wine bottles in a noninvasive and rapid fashion. Increasing opacity corresponds well with the concentration of dissolved cocaine. Simulated testing showed that it is possible to distinguish between cocaine-contaminated and uncontaminated wine bottles. CONCLUSION: The described method is an efficacious screening method to detect cocaine-contaminated bottles that are hidden between untreated bottles in cargo. The noninvasive examination of cargo allows a questionable delivery to be tracked without arousing the suspicion of the smugglers.