Application of numerical solutions to non-linear problems of fluid mechanics obtained by the method of least squares and the finite element method to unsteady Navier-Stokes equations

A method of calculating viscous fluid flows having an average Reynolds number is presented

The limits of precision monomer placement in chain growth polymerization

Precise control over the location of monomers in a polymer chain has been described as the ‘Holy Grail’ of polymer synthesis. Controlled chain growth polymerization techniques have brought this goal closer, allowing the preparation of multiblock copolymers with ordered sequences of functional monomers. Such structures have promising applications ranging from medicine to materials engineering. Here we show, however, that the statistical nature of chain growth polymerization places strong limits on the control that can be obtained. We demonstrate that monomer locations are distributed according to surprisingly simple laws related to the Poisson or beta distributions. The degree of control is quantified in terms of the yield of the desired structure and the standard deviation of the appropriate distribution, allowing comparison between different synthetic techniques. This analysis establishes experimental requirements for the design of polymeric chains with controlled sequence of functionalities, which balance precise control of structure with simplicity of synthesis

Hyperbranched polymers with high degrees of branching and low dispersity values : pushing the limits of thiol–yne chemistry

We propose a versatile approach to the production of hyperbranched polymers with high degrees of branching and low dispersity values (Đ), involving slow monomer addition of a thiol/yne monomer to multifunctional core molecules in the presence of photoinitiator and under UV irradiation. The small thiol/yne monomer was synthesized via 1-ethyl-3-(3-(dimethylamino)propyl)carbodiimide hydrochloride (EDC·HCl) esterification, and batch polymerizations were performed at varying concentrations. The batch thiol–yne polymerizations had fast reaction kinetics and large dispersity values that increased with increasing concentration. Introduction of monomer by slow addition to a multifunctional alkyne core (tri(prop-2-yn-1-yl) 1,3,5-benzenetricarboxylate) or alkene core (triallyl 1,3,5-benzenetricarboxylate) was found to lower dispersity at monomer concentrations of 0.5–2.0 M. Degrees of branching were determined by 1H NMR spectroscopy to be greater than 0.8 in most cases. Increasing the fraction of core molecule was found to decrease dispersity to values as low as 1.26 and 1.38 for the alkene core and alkyne core, respectively, for monomer concentrations of 0.5 M with 10 mol % core molecule. Molecular weights of the hyperbranched structures were also determined by light scattering size exclusion chromatography (SEC) detection, and intrinsic viscosities were determined by viscometry SEC detection. The Kuhn–Mark–Houwink–Sakurada α parameter decreased from 0.35 for the batch process to values as low as 0.21 (10 mol % alkene core) or 0.16 (10 mol % alkyne core), indicating that the thiol–yne structures became more globular and dense with the slow monomer addition strategy. This simple and versatile approach is a promising new development for the design of hyperbranched polymers of well-controlled molecular weight and molecular weight distributions, with very high degrees of branching

Percolation properties of 3-D multiscale pore networks: how connectivity controls soil filtration processes

Quantifying the connectivity of pore networks is a key issue not only for modelling fluid flow and solute transport in porous media but also for assessing the ability of soil ecosystems to filter bacteria, viruses and any type of living microorganisms as well inert particles which pose a contamination risk. Straining is the main mechanical component of filtration processes: it is due to size effects, when a given soil retains a conveyed entity larger than the pores through which it is attempting to pass. We postulate that the range of sizes of entities which can be trapped inside soils has to be associated with the large range of scales involved in natural soil structures and that information on the pore size distribution has to be complemented by information on a critical filtration size (CFS) delimiting the transition between percolating and non percolating regimes in multiscale pore networks. We show that the mass fractal dimensions which are classically used in soil science to quantify scaling laws in observed pore size distributions can also be used to build 3-D multiscale models of pore networks exhibiting such a critical transition. We extend to the 3-D case a new theoretical approach recently developed to address the connectivity of 2-D fractal networks (Bird and Perrier, 2009). Theoretical arguments based on renormalisation functions provide insight into multi-scale connectivity and a first estimation of CFS. Numerical experiments on 3-D prefractal media confirm the qualitative theory. These results open the way towards a new methodology to estimate soil filtration efficiency from the construction of soil structural models to be calibrated on available multiscale data

Polymerization induced self-assembly : tuning of morphology using ionic strength and pH

Investigations of RAFT dispersion polymerization-induced self-assembly (PISA) of 2-hydroxypropyl methacrylate (HPMA) in water/methanol at 60 °C using a cationically charged macroRAFT agent as the stabilizer block, namely P(N,N-diethylaminoethyl methacrylate)-stat-poly((ethylene glycol) methyl ether methacrylate) (PDEAEMA-stat-PEGMA), have been conducted with a view to tune particle morphologies by manipulation of the pH and the ionic strength. Above the LCST (45 °C) of (PDEAEMA-stat-PEGMA), the system can only be conducted as a dispersion polymerization at sufficiently low pH such that the stabilizer block is sufficiently protonated to ensure solubility in the continuous phase. It is demonstrated (reported in the form of an extensive morphology diagram) that a range of morphologies including spherical particles, rods and vesicles can be accessed by adjustment of the pH (via addition of HCl) and the ionic strength (via the concentration of NaCl). A decrease in the charge density of the coronal stabilizer layer via an increase in the pH (less protonation) shifts the system towards higher order morphologies. At a given pH, an increase in ionic strength leads to more extensive charge screening, thus allowing formation of higher order morphologies

Maximum-likelihood models for mapping genetic markers showing segregation distortion : 1. Backcross populations

Une approche du maximum de vraisemblance est utilisée pour estimer les fréquences de recombinaison entre des marqueurs présentant des distorsions de ségrégation dans des populations backcross. L'hypothèse faite ici est que les distorsions sont induites par des différences de viabilité entre gamètes ou zygotes dues à la présence d'un ou plusieurs allèles contre-sélectionnés. Nous montrons que l'estimateur de Bailey (1949) reste convergent donc efficace sous des conditions plus générales que celles définies par son auteur. Cet estimateur devrait donc être utilisé à la place de l'estimateur classique du maximum de vraisemblance. La question de la détection d'une liaison peut être affectée par les distorsions de ségrégation. (Résumé d'auteur

Dehydration mechanism of a small molecular solid: 5-nitrouracil hydrate

Previous studies of the dehydration of 5-nitrouracil (5NU) have resulted in it being classified as a ‘‘channel hydrate’’ in which dehydration proceeds principally by the exit of the water molecules along channels in the structure. We have re-examined this proposal and found that in fact there are no continuous channels in the 5NU structure that would contribute to such a mechanism. Product water molecules would be immediately trapped in unlinked voids in the crystal structure and would require some additional mechanism to break loose from the crystal. Through a detailed structural analysis of the macro and micro structure of the 5NU as it dehydrates, we have developed a model for the dehydration process based on the observed development of structural defects in the 5NU crystal and the basic crystallography of the material. The model was tested against standard kinetic measurements and found to present a satisfactory account of kinetic observations, thus defining the mechanism. Overall, the study shows the necessity of complementing standard kinetic studies with a parallel macro and micro examination of the dehydrating material when evaluating the mechanisms of dehydration and decomposition processes

Influence of the calcaneus shape on the risk of posterior heel ulcer using 3D patient-specific biomechanical modeling.

International audienceMost posterior heel ulcers are the consequence of inactivity and prolonged time lying down on the back. They appear when pressures applied on the heel create high internal strains and the soft tissues are compressed by the calcaneus. It is therefore important to monitor those strains to prevent heel pressure ulcers. Using a biomechanical lower leg model, we propose to estimate the influence of the patient-specific calcaneus shape on the strains within the foot and to determine if the risk of pressure ulceration is related to the variability of this shape. The biomechanical model is discretized using a 3D Finite Element mesh representing the soft tissues, separated into four domains implementing Neo Hookean materials with different elasticities: skin, fat, Achilles' tendon, and muscles. Bones are modelled as rigid bodies attached to the tissues. Simulations show that the shape of the calcaneus has an influence on the formation of pressure ulcers with a mean variation of the maximum strain over 6.0 percentage points over 18 distinct morphologies. Furthermore, the models confirm the influence of the cushion on which the leg is resting: a softer cushion leading to lower strains, it has less chances of creating a pressure ulcer. The methodology used for patient-specific strain estimation could be used for the prevention of heel ulcer when coupled with a pressure sensor

RAD-sequencing for estimating GRM-based heritability in the wild:a case study in roe deer

International audienceEstimating the evolutionary potential of quantitative traits and reliably predicting responses to selection in wild populations are important challenges in evolutionary biology. The genomic revolution has opened up opportunities for measuring relatedness among individuals with precision, enabling pedigree‐free estimation of trait heritabilities in wild populations. However, until now, most quantitative genetic studies based on a genomic relatedness matrix (GRM) have focused on long‐term monitored populations for which traditional pedigrees were also available, and have often had access to knowledge of genome sequence and variability. Here, we investigated the potential of RAD‐sequencing for estimating heritability in a free‐ranging roe deer (Capreolous capreolus) population for which no prior genomic resources were available. We propose a step‐by‐step analytical framework to optimize the quality and quantity of the genomic data and explore the impact of the single nucleotide polymorphism (SNP) calling and filtering processes on the GRM structure and GRMbased heritability estimates. As expected, our results show that sequence coverage strongly affects the number of recovered loci, the genotyping error rate and the amount of missing data. Ultimately, this had little effect on heritability estimates and their standard errors, provided that the GRM was built from a minimum number of loci (above 7,000). Genomic relatedness matrix‐based heritability estimates thus appear robust to a moderate level of genotyping errors in the SNP data set. We also showed that quality filters, such as the removal of low‐frequency variants, affect the relatedness structure of the GRM, generating lower h2 estimates. Our work illustrates the huge potential of RAD‐sequencing for estimating GRM‐based heritability in virtually any natural population