We present an explicit scheme for a two-dimensional multilayer shallow water model with density stratification, for general meshes and collocated variables. The proposed strategy is based on a ...regularized model where the transport velocity in the advective fluxes is shifted proportionally to the pressure potential gradient. Using a similar strategy for the potential forces, we show the stability of the method in the sense of a discrete dissipation of the mechanical energy, in general multilayer and non-linear frames. These results are obtained at first-order in space and time and extended using a second-order MUSCL extension in space and a Heun's method in time. With the objective of minimizing the diffusive losses in realistic contexts, sufficient conditions are exhibited on the regularizing terms to ensure the scheme's linear stability at first and second-order in time and space. The other main result stands in the consistency with respect to the asymptotics reached at small and large time scales in low Froude regimes, which governs large-scale oceanic circulation. Additionally, robustness and well-balanced results for motionless steady states are also ensured. These stability properties tend to provide a very robust and efficient approach, easy to implement and particularly well suited for large-scale simulations. Some numerical experiments are proposed to highlight the scheme efficiency: an experiment of fast gravitational modes, a smooth surface wave propagation, an initial propagating surface water elevation jump considering a non-trivial topography, and a last experiment of slow Rossby modes simulating the displacement of a baroclinic vortex subject to the Coriolis force.
•We took into account all the reviewer#4 remarks and requirements.•Also, we have corrected all the minor points mentioned.•You will find all details in the point-to-point answers document.
The 2D ...shallow water equations adequately model some geophysical flows with wet-dry fronts (e.g. flood plain or tidal flows); nevertheless deriving accurate, robust and conservative numerical schemes for dynamic wet-dry fronts over complex topographies remains a challenge. Furthermore for these flows, data are generally complex, multi-scale and uncertain. Robust variational inverse algorithms, providing sensitivity maps and data assimilation processes may contribute to breakthrough shallow wet-dry front dynamics modelling. The present study aims at deriving an accurate, positive and stable finite volume scheme in presence of dynamic wet-dry fronts, and some corresponding inverse computational algorithms (variational approach). The schemes and algorithms are assessed on classical and original benchmarks plus a real flood plain test case (Lèze river, France). Original sensitivity maps with respect to the (friction, topography) pair are performed and discussed. The identification of inflow discharges (time series) or friction coefficients (spatially distributed parameters) demonstrate the algorithms efficiency.
In this paper, we introduce a new extended version of the shallow-water equations with surface tension which may be decomposed into a hyperbolic part and a second order derivative part which is ...skew-symmetric with respect to the L2 scalar product. This reformulation allows for large gradients of fluid height simulations using a splitting method. This result is a generalization of the results published by Noble and Vila (2016) 24 and by Bresch et al. (2016) 3 which are restricted to quadratic forms of the capillary energy respectively in the one dimensional and two dimensional setting. This is also an improvement of the results by J. Lallement, P. Villedieu et al. published in Lallement et al. (2018) 22 where the augmented version is not skew-symmetric with respect to the L2 scalar product. Based on this new formulation, we propose a new numerical scheme and perform a nonlinear stability analysis. Various numerical simulations of the shallow water equations are presented to show differences between quadratic (w.r.t. the gradient of the height) and general surface tension energy when high gradients of the fluid height occur.
Non-steroidal anti-inflammatory drugs (NSAIDs) such as piroxicam and mefenamic acid are commonly prescribed to treat inflammation, pain and fever. Similarly acetylsalicylic acid is used to prevent ...strokes and heart attacks. A rapid and selective method was developed for the simultaneous assay of three NSAIDs and salicylic acid via HPLC with fluorescence detection. The separation was performed using a “dual-mode” gradient (acetonitrile–0.1% aqueous orthophosphoric acid) and the analysis was completed within 7
min using an ACE
® column C18, 5
μm, 150
mm
×
4.6
mm. Naproxen was used as internal standard. The proposed method is simple, selective as well as with a good sensitivity reaching LOD lower than 2
pmol (0.05
μM) and was applied for quantitative analysis in pharmaceuticals and in human serum samples. The mean recovery was more than 95% and the within-day and between-days precisions were found to be satisfactory having RSD within the acceptable limits (<10%).
High performance anion exchange chromatography (HPAEC)-pulsed amperometric detection (PAD) is a performing technique for carbohydrate analysis, due to the selectivity and sensitivity of the ...detection. The identification occurs through retention times. In absence of standards, structural characterization of complex polysaccharides requests the coupling of HPAEC-PAD with electrospray ionization (ESI)-MS. This is a technological challenge, due to the non-volatility and high conductance of the eluents. Therefore, a desalting device has been installed on-line between the PAD and the MS. On-line HPAEC–MS has only been rarely described. We report here successful analysis of biological acidic oligosaccharides, allowing for the first time to demonstrate that membrane anchored 3-deoxy-
d-manno-2 octulosonic acid (Kdo) homopolymers are consensus sinorhizobial capsular polysaccharide (KPS).
A comparison between HPLC with conventional fluorescence detection and capillary-LC (μHPLC) with native laser-induced fluorescence (LIF) detection was done to determine chloroquine (CQ) and quinine ...(Q) in human serum. HPLC experiments were run with parameters of the conventional fluorimeter set at the highest level of sensitivity. Results were compared with those obtained on μHPLC coupled to a ZETALIF (He–Cd 325
nm) detector which provided a 50-fold increase in sensitivity. In μHPLC-LIF injection volumes were 200
nL instead of 10
μL in conventional HPLC. The separation was completed within 3
min (6
min on HPLC). The limit of detection on μHPLC-LIF was 1.9 and 1.3
fmol for CQ and Q, respectively. Both experiments were validated on serum samples. The mean recovery was more than 95% for CQ and Q. The intra- and inter-day precision and accuracy were found to be within the acceptable limits (<10%).
A two-dimensional depth-averaged model is derived for open-channel flows in the smooth turbulent case. The derivation is consistently obtained with a method of matched asymptotic expansions in the ...outer and inner layers using a mixing length model of turbulence including the free-surface reduction of the eddy viscosity. The shear effects are taken into account by an extra tensor variable of the model called the enstrophy tensor. The friction coefficient is an explicit expression of the water depth. The three-dimensional velocity field and the friction velocity can be reconstructed from the values of the depth-averaged quantities. Numerical simulations show that the enstrophy can be used to evaluate the development of the turbulent boundary layer. In the case of subcritical unsteady flows, the reconstructed velocity can be described with a logarithmic law modified by Coles’ wake function with apparent von Kármán constant, integration constant and wake-strength parameter, which differ from their values in steady flows. In the viscous sublayer the steady-state relation between the velocity and the vertical coordinate, in the inner scaling, is not valid for unsteady flows. Large errors on the calculation of the von Kármán constant can be made if the validity of the steady-state relation is assumed for unsteady flows. The comparisons of the reconstructed velocity profiles in the case of one-dimensional unsteady open-channel flows and two-dimensional wide trapezoidal channels show a good agreement with experiments.
Dendrimers are nanosized, nonlinear, hyperbranched polymers whose overall 3D shape is key for their biological activity. Poly(PhosphorHydrazone) (PPH) dendrimers capped with aza-bisphosphonate (ABP) ...end groups are known to have anti-inflammatory properties enabling the control of inflammatory diseases in different mouse models. Here we screen the anti-inflammatory activity of a series of PPH dendrimers bearing between 2 and 16 ABP end groups in a mouse model of arthritis and confront the biological results with atomistic simulations of the dendrimers. We show that only the PPH dendrimers capped with 10 and 12 ABP end groups can control the flare of the inflammatory disease. All-atom accelerated molecular dynamics simulations show that dendrimers with a low number of ABP end groups are directional but highly flexible/dynamic and have thereby limited efficiency in establishing multivalent interactions. The largest dendrimer appears as nondirectional, having 16 ABP end groups forming patches all over the dendrimer surface. Conversely, intermediate dendrimers having 10 or 12 ABP end groups reach the best compromise between the number of surface groups and their stable directional gathering, a real maximization of multivalency.
In recent papers, we presented a new analytical method for thiol quantification in serum. This method was developed with capillary electrophoresis (CE) and laser-induced fluorescence (LIF) to analyze ...thiol-iodoacetamidofluoresceine (IAF) derivatives. Quantitative results for homocysteine, glutathione, cysteinylglycine, and cysteine were presented (Caussé E., et al., Clin. Chem. 45 (1999) 412). An exhaustive comparison of the quantitation of homocysteine in plasma, using high-performance liquid chromatography with either conventional fluorescence detection or fluorescence polarization immunoassay was also reported (Caussé E., et al., Electrophoresis 21 (2000) 2074). Sample preparation prior to derivatization with IAF had never been investigated. Recently we studied protein precipitation in serum with different organic agents (Caussé E., et al., J. Chromatogr. A 895 (2000) 173). In this work, we evaluated the conditions of protein precipitation in function of the amounts of acetonitrile and their influence on quantitation and quality of the electropherograms. Then, we looked at the variation of thiol concentrations in the haemolysis states and studied the thiol stability of blood samples cooled on ice.
Structures of fatty acids present at very low quantities in mycobacteria are difficult to determine. A commonly used strategy is to introduce heteroatoms into functional groups by chemical means ...before subjecting them to gas chromatography/tandem mass spectrometry (GC/MS/MS) analysis. Routinely used methods give very low abundance diagnostic ions leading to ambiguities in structural conclusions. GC/MS/MS associated with electron capture ionization of pentafluorobenzyl esters was used to study very complex mixtures of fatty acids from Mycobacterium fallax and M. aurum. The charge-remote fragmentation of fatty acid carboxylate anions was used for structure determination at the nanogram level of a large number of unsaturated, branched, and cyclopropane-containing fatty acids. Some of them have not been observed previously in these Mycobacteria. On the basis of these studies, biosynthetic pathways of unsaturated, branched, and cyclopropane-containing fatty acid are proposed.
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