A low complexity algorithm for non-monotonically evolving fronts

A new algorithm is proposed to describe the propagation of fronts advected in the normal direction with prescribed speed function F. The assumptions on F are that it does not depend on the front itself, but can depend on space and time. Moreover, it can vanish and change sign. To solve this problem the Level-Set Method [Osher, Sethian; 1988] is widely used, and the Generalized Fast Marching Method [Carlini et al.; 2008] has recently been introduced. The novelty of our method is that its overall computational complexity is predicted to be comparable to that of the Fast Marching Method [Sethian; 1996], [Vladimirsky; 2006] in most instances. This latter algorithm is O(N^n log N^n) if the computational domain comprises N^n points. Our strategy is to use it in regions where the speed is bounded away from zero -- and switch to a different formalism when F is approximately 0. To this end, a collection of so-called sideways partial differential equations is introduced. Their solutions locally describe the evolving front and depend on both space and time. The well-posedness of those equations, as well as their geometric properties are addressed. We then propose a convergent and stable discretization of those PDEs. Those alternative representations are used to augment the standard Fast Marching Method. The resulting algorithm is presented together with a thorough discussion of its features. The accuracy of the scheme is tested when F depends on both space and time. Each example yields an O(1/N) global truncation error. We conclude with a discussion of the advantages and limitations of our method.Comment: 30 pages, 12 figures, 1 tabl

Thermochemistry of yavapaiite KFe(SO4)2: Formation and decomposition

Yavapaiite, KFe(SO4)2, is a rare mineral in nature, but its structure is considered as a reference for many synthetic compounds in the alum supergroup. Several authors mention the formation of yavapaiite by heating potassium jarosite above ca. 400°C. To understand the thermal decomposition of jarosite, thermodynamic data for phases in the K-Fe-S-O-(H) system, including yavapaiite, are needed. A synthetic sample of yavapaiite was characterized in this work by X-ray diffraction (XRD), scanning electron microscopy (SEM), Fourier transform infrared spectroscopy (FTIR), and thermal analysis. Based on X-ray diffraction pattern refinement, the unit cell dimensions for this sample were found to be a = 8.152 ± 0.001 Å, b = 5.151 ± 0.001 Å, c = 7.875 ± 0.001 Å, and β = 94.80°. Thermal decomposition indicates that the final breakdown of the yavapaiite structure takes place at 700°C (first major endothermic peak), but the decomposition starts earlier, around 500°C. The enthalpy of formation from the elements of yavapaiite, KFe(SO4)2, ΔH°f = −2042.8 ± 6.2 kJ/mol, was determined by high-temperature oxide melt solution calorimetry. Using literature data for hematite, corundum, and Fe/Al sulfates, the standard entropy and Gibbs free energy of formation of yavapaiite at 25°C (298 K) were calculated as S°(yavapaiite) = 224.7 ± 2.0 J.mol−1.K−1 and ΔG°f = −1818.8 ± 6.4 kJ/mol. The equilibrium decomposition curve for the reaction jarosite = yavapaiite + Fe2O3 + H2O has been calculated, at pH2O = 1 atm, the phase boundary lies at 219 ± 2°C

Jarosite stability on Mars

Jarosite, a potassium (sodium) iron sulphate hydrated mineral, has recently been identified on the martian surface by the Opportunity rover. Using recent thermochemical data [Drouet and Navrotsky, 2003, Geochim. Cosmochim. Acta 67, 2063–2076; Forray et al., 2005, Geochim. Cosmochim. Acta, in press], we calculate the equilibrium decomposition curve of jarosite and show that it is thermodynamically stable under most present martian pressures and temperatures. Its stability makes jarosite potentially useful to retain textural, chemical, and isotopic evidence of past history, including possible biological activity, on Mars

Low iron availability in continuous in vitro colonic fermentations induces strong dysbiosis of the child gut microbial consortium and a decrease in main metabolites

Iron (Fe) deficiency affects an estimated 2 billion people worldwide, and Fe supplements are a common corrective strategy. The impact of Fe deficiency and Fe supplementation on the complex microbial community of the child gut was studied using in vitro colonic fermentation models inoculated with immobilized fecal microbiota. Chyme media (all Fe chelated by 2,2′-dipyridyl to 26.5 mg Fe L−1) mimicking Fe deficiency and supplementation were continuously fermented. Fermentation effluent samples were analyzed daily on the microbial composition and metabolites by quantitative PCR, 16S rRNA gene 454-pyrosequencing, and HPLC. Low Fe conditions (1.56 mg Fe L−1) significantly decreased acetate concentrations, and subsequent Fe supplementation (26.5 mg Fe L−1) restored acetate production. High Fe following normal Fe conditions had no impact on the gut microbiota composition and metabolic activity. During very low Fe conditions (0.9 mg Fe L−1 or Fe chelated by 2,2′-dipyridyl), a decrease in Roseburia spp./Eubacterium rectale, Clostridium Cluster IV members and Bacteroides spp. was observed, while Lactobacillus spp. and Enterobacteriaceae increased consistent with a decrease in butyrate (−84%) and propionate (−55%). The strong dysbiosis of the gut microbiota together with decrease in main gut microbiota metabolites observed with very low iron conditions could weaken the barrier effect of the microbiota and negatively impact gut healt

Interspecific variation in the limb long bones among modern rhinoceroses—extent and drivers

International audienceAmong amniotes, numerous lineages are subject to an evolutionary trend toward body mass and size increases. Large terrestrial species may face important constraints linked to weight bearing, and the limb segments are particularly affected by such constraints due to their role in body support and locomotion. Such groups showing important limb modifications related to high body mass have been called "graviportal." Often considered graviportal, rhinoceroses are among the heaviest terrestrial mammals and are thus of particular interest to understand the limb modifications related to body mass and size increase. Here, we present a morphofunctional study of the shape variation of the limb long bones among the five living rhinos to understand how the shape may vary between these species in relation with body size, body mass and phylogeny. We used three dimensional geometric morphometrics and comparative analyses to quantify the shape variation. Our results indicate that the five species display important morphological differences depending on the considered bones. The humerus and the femur exhibit noticeable interspecific differences between African and Asiatic rhinos, associated with a significant effect of body mass. The radius and ulna are more strongly correlated with body mass. While the tibia exhibits shape variation both linked with phylogeny and body mass, the fibula displays the greatest intraspecific variation. We highlight three distinct morphotypes of bone shape, which appear in accordance with the phylogeny. The influence of body mass also appears unequally expressed on the different bones. Body mass increase among the five extant species is marked by an increase of the general robustness, more pronounced attachments for muscles and a development of medial parts of the bones. Our study underlines that the morphological features linked to body mass increase are not similar between rhinos and other heavy mammals such as elephants and hippos, suggesting that the weight bearing constraint can lead to different morphological responses

Energetics of lanthanide-doped calcium phosphate apatite

Lanthanides “Ln” (rare earths) are critical elements found in natural minerals such as calcium phosphate apatites, in sedimentary and igneous settings as well as in skeletal diagenesis. From a medical point of view, nanoparticles of lanthanide-doped apatites can be produced for conferring luminescence properties of interest in cancer cells detection. However, the impact of the substitution of Ln for Ca on the stability and solubility of related apatite phases is still essentially unknown. To investigate the thermochemical effects of such lanthanide substitution for calcium in apatite, we prepared and analyzed four series of apatites with up to 10% lanthanide substitution for calcium. After thorough physicochemical characterization via complementary techniques (XRD, FTIR, TG/DSC, and IPC-AES), high-temperature oxide melt solution calorimetry in molten sodium molybdate at 973 K was performed to determine their enthalpies of formation from constituent oxides and from the elements, at 298 K. Our results indicate that although enthalpies of formation are strongly exothermic in all cases, Ln-doping has a destabilizing effect, which increases with dopant concentration and with the size of the incorporated Ln3+ ion. After estimating standard entropies, Gibbs free energies of formation and equilibrium constants for Ca2+/Ln3+ exchange reactions in apatite were then evaluated, for the first time allowing access to quantitative thermodynamic data that may be used in various fields for stability calculations or partitioning estimates between fluids and solids

Numerical Simulation of Spouted Bed Reactors using Process Engineering Models: Application to Coal Gasification

A spouted bed reactor operating at high temperature has been modelled using one dimensional models based on process engineering concepts. The process of coal gasification has been selected to demonstrate the models achievements and predictions have been compared to previous spouted bed reactor experimental results

Outcome of CO2 laser vaporization for oral potentially malignant disorders treatment

Oral cancer is a public health issue worldwide. Oral potentially malignant disorders (OMPDs) are lesions of the oral mucosa that are predisposed to malignant transformation. The mainstay of OMPDs treatment around the world is now the carbon dioxide (CO2) laser but the reported recurrence and malignant transformation rates vary widely in the literature. We aimed to estimate the recurrence and the malignant transformation rates of OPMDs treated with CO2 laser at the University Hospital of Bordeaux, in France, from 2010 to 2014, and to identify associated factors with recurrence or malignant transformation. We conducted a retrospective study in patients with a minimum follow-up of 12 months. Collected variables included characteristics of the patients (gender, age, alcohol and tobacco consumption, previous diagnosis of graft-versus-host disease, previous treatments for OPMD or for upper aerodigestive tract cancers and human immunodeficiency virus infection), characteristics of the lesions (form, colour, size, location, degree of dysplasia), laser treatment outcome (complications, recurrence, malignant transformation). Twenty-five patients were included. Mean follow-up was 28.9 months. Recurrence was observed in 11 patients (44%). Annual recurrence rate was 18.3% and annual malignant transformation rate was 1.7%. Hyperplasia without dysplasia was the only factor found to be statistically associated with recurrence. Our results suggest that OMPDs treated by CO2 laser vaporization have high recurrence rates, particularly those presenting hyperplasia. A standardized definition of recurrence would be necessary for inter-study comparisons. Long-term follow-up is recommended in order to detect and treat squamous cell carcinoma in its early stages