Error estimate for time-explicit finite volume approximation of strong solutions to systems of conservation laws

International audienceWe study the finite volume approximation of strong solutions to nonlinear systems of conservation laws. We focus on time-explicit schemes on unstructured meshes, with entropy satisfying numerical fluxes. The numerical entropy dissipation is quantified at each interface of the mesh, which enables to prove a weak–BV estimate for the numerical approximation under a strengthen CFL condition. Then we derive error estimates in the multidimensional case, using the relative entropy between the strong solution and its finite volume approximation. The error terms are carefully studied, leading to a classical $h^1/4$ estimate in $L^2$ under this strengthen CFL condition

Error analysis of a dynamic model adaptation procedure for nonlinear hyperbolic equations

International audienceWe propose a dynamic model adaptation method for a nonlinear conservation law coupled with an ordinary differential equation. This model, called the ''fine model", involves a small time scale and setting this time scale to 0 leads to a classical conservation law, called the ''coarse model", with a flux which depends on the unknown and on space and time. The dynamic model adaptation consists in detecting the regions where the fine model can be replaced by the coarse one in an automatic way, without deteriorating the accuracy of the result. To do so, we provide an error estimate between the solution of the fine model and the solution of the adaptive method, enabling a sharp control of the different parameters. This estimate rests upon stability results for conservation laws with respect to the flux function. Numerical results are presented at the end and show that our estimate is optimal

OSAMOAL: optimized simulations by adapted models using asymptotic limits

We propose in this work to address the problem of model adaptation, dedicated to hyper- bolic models with relaxation and to their parabolic limit. The goal is to replace a hyperbolic system of balance laws (the so-called fine model) by its parabolic limit (the so-called coarse model), in delimited parts of the computational domain. Our method is based on the construction of asymptotic preserving schemes and on interfacial coupling methods between hyperbolic and parabolic models. We study in parallel the cases of the Goldstein-Taylor model and of the p-system with friction

Comparative kinetic analysis of two fungal β-glucosidases

<p>Abstract</p> <p>Background</p> <p>The enzymatic hydrolysis of cellulose is still considered as one of the main limiting steps of the biological production of biofuels from lignocellulosic biomass. It is a complex multistep process, and various kinetic models have been proposed. The cellulase enzymatic cocktail secreted by <it>Trichoderma reesei </it>has been intensively investigated. β-glucosidases are one of a number of cellulolytic enzymes, and catalyze the last step releasing glucose from the inhibitory cellobiose. β-glucosidase (BGL1) is very poorly secreted by <it>Trichoderma reesei </it>strains, and complete hydrolysis of cellulose often requires supplementation with a commercial β-glucosidase preparation such as that from <it>Aspergillus niger </it>(Novozymes SP188). Surprisingly, kinetic modeling of β-glucosidases lacks reliable data, and the possible differences between native <it>T. reesei </it>and supplemented β-glucosidases are not taken into consideration, possibly because of the difficulty of purifying BGL1.</p> <p>Results</p> <p>A comparative kinetic analysis of β-glucosidase from <it>Aspergillus niger </it>and BGL1 from <it>Trichoderma reesei</it>, purified using a new and efficient fast protein liquid chromatography protocol, was performed. This purification is characterized by two major steps, including the adsorption of the major cellulases onto crystalline cellulose, and a final purification factor of 53. Quantitative analysis of the resulting β-glucosidase fraction from <it>T. reesei </it>showed it to be 95% pure. Kinetic parameters were determined using cellobiose and a chromogenic artificial substrate. A new method allowing easy and rapid determination of the kinetic parameters was also developed. β-Glucosidase SP188 (K_m= 0.57 mM; K_p= 2.70 mM) has a lower specific activity than BGL1 (K_m= 0.38 mM; K_p= 3.25 mM) and is also more sensitive to glucose inhibition. A Michaelis-Menten model integrating competitive inhibition by the product (glucose) has been validated and is able to predict the β-glucosidase activity of both enzymes.</p> <p>Conclusions</p> <p>This article provides a useful comparison between the activity of β-glucosidases from two different fungi, and shows the importance of fully characterizing both enzymes. A Michaelis-Menten model was developed, including glucose inhibition and kinetic parameters, which were accurately determined and compared. This model can be further integrated into a cellulose hydrolysis model dissociating β-glucosidase activity from that of other cellulases. It can also help to define the optimal enzymatic cocktails for new β-glucosidase activities.</p

Dynamic model adaptation for multiscale simulation of hyperbolic systems with relaxation

International audienceIn numerous industrial CFD applications, it is usual to use two (or more)different codes to solve a physical phenomenon: where the flow is a priori assumed to have a simple behavior, a code based on a coarse model is applied, while a code based on a fine model is used elsewhere. This leads to a complex coupling problem with fixed interfaces. The aim of the present work is to provide a numerical indicator to optimize to position of these coupling interfaces. In other words, thanks to this numerical indicator, one could verify if the use of the coarser model and of the resulting coupling does not introduce spurious effects. In order to validate this indicator, we use it in a dynamical multiscale method with moving coupling interfaces. The principle of this method is to use as much as possible a coarse model instead of the fine model in the computational domain, in order to obtain an accuracy which is comparable with the one provided by the fine model. We focus here on general hyperbolic systems with stiff relaxation source terms together with the corresponding hyperbolic equilibrium systems. Using a numerical Chapman-Enskog expansion and the distance to the equilibrium manifold, we construct the numerical indicator. Based on several works on the coupling of different hyperbolic models, an original numerical method of dynamic model adaptation is proposed. We prove that this multiscale method preserves invariant domains and that the entropy of the numerical solution decreases with respect to time. The reliability of the adaptation procedure is assessed on various 1D and 2D test cases coming from two-phase flow modeling

OSAMOAL: optimized simulations by adapted models using asymptotic limits

We propose in this work to address the problem of model adaptation, dedicated to hyper- bolic models with relaxation and to their parabolic limit. The goal is to replace a hyperbolic system of balance laws (the so-called fine model) by its parabolic limit (the so-called coarse model), in delimited parts of the computational domain. Our method is based on the construction of asymptotic preserving schemes and on interfacial coupling methods between hyperbolic and parabolic models. We study in parallel the cases of the Goldstein-Taylor model and of the p-system with friction

Influence of doping on charge carrier collection in normal and inverted geometry polymer: fullerene solar cells

While organic semiconductors used in polymer:fullerene photovoltaics are generally not intentionally doped, significant levels of unintentional doping have previously been reported in the literature. Here, we explain the differences in photocurrent collection between standard (transparent anode) and inverted (transparent cathode) low band-gap polymer:fullerene solar cells in terms of unintentional p-type doping. Using capacitance/voltage measurements, we find that the devices exhibit doping levels of order 1016 cm−3, resulting in space-charge regions ~100 nm thick at short circuit. As a result, low field regions form in devices thicker than 100 nm. Because more of the light is absorbed in the low field region in standard than in inverted architectures, the losses due to inefficient charge collection are greater in standard architectures. Using optical modelling, we show that the observed trends in photocurrent with device architecture and thickness can be explained if only charge carriers photogenerated in the depletion region contribute to the photocurrent

Monte Carlo Simulations for the Analysis of Non-linear Parameter Confidence Intervals in Optimal Experimental Design

Especially in biomanufacturing, methods to design optimal experiments are a valuable technique to fully exploit the potential of the emerging technical possibilities that are driving experimental miniaturization and parallelization. The general objective is to reduce the experimental effort while maximizing the information content of an experiment, speeding up knowledge gain in R&amp;D. The approach of model-based design of experiments (known as MBDoE) utilizes the information of an underlying mathematical model describing the system of interest. A common method to predict the accuracy of the parameter estimates uses the Fisher information matrix to approximate the 90% confidence intervals of the estimates. However, for highly non-linear models, this method might lead to wrong conclusions. In such cases, Monte Carlo sampling gives a more accurate insight into the parameter's estimate probability distribution and should be exploited to assess the reliability of the approximations made through the Fisher information matrix. We first introduce the model-based optimal experimental design for parameter estimation including parameter identification and validation by means of a simple non-linear Michaelis-Menten kinetic and show why Monte Carlo simulations give a more accurate depiction of the parameter uncertainty. Secondly, we propose a very robust and simple method to find optimal experimental designs using Monte Carlo simulations. Although computational expensive, the method is easy to implement and parallelize. This article focuses on practical examples of bioprocess engineering but is generally applicable in other fields

Characterization of two novel intronic OPA1 mutations resulting in aberrant pre-mRNA splicing.

BACKGROUND We report two novel splice region mutations in OPA1 in two unrelated families presenting with autosomal-dominant optic atrophy type 1 (ADOA1) (ADOA or Kjer type optic atrophy). Mutations in OPA1 encoding a mitochondrial inner membrane protein are a major cause of ADOA. METHODS We analyzed two unrelated families including four affected individuals clinically suspicious of ADOA. Standard ocular examinations were performed in affected individuals of both families. All coding exons, as well as exon-intron boundaries of the OPA1 gene were sequenced. In addition, multiplex ligation-dependent probe amplification (MLPA) was performed to uncover copy number variations in OPA1. mRNA processing was monitored using RT-PCR and subsequent cDNA analysis. RESULTS We report two novel splice region mutations in OPA1 in two unrelated individuals and their affected relatives, which were previously not described in the literature. In one family the heterozygous insertion and deletion c.[611-37_611-38insACTGGAGAATGTAAAGGGCTTT;611-6_611-16delCATATTTATCT] was found in all investigated family members leading to the activation of an intronic cryptic splice site. In the second family sequencing of OPA1 disclosed a de novo heterozygous deletion c.2012+4_2012+7delAGTA resulting in exon 18 and 19 skipping, which was not detected in healthy family members. CONCLUSION We identified two novel intronic mutations in OPA1 affecting the correct OPA1 pre-mRNA splicing, which was confirmed by OPA1 cDNA analysis. This study shows the importance of transcript analysis to determine the consequences of unclear intronic mutations in OPA1 in proximity to the intron-exon boundaries

An assessment of the Atlantic and Arctic sea–air CO2 fluxes, 1990–2009

© The Author(s), 2013. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Biogeosciences 10 (2013): 607-627, doi:10.5194/bg-10-607-2013.The Atlantic and Arctic Oceans are critical components of the global carbon cycle. Here we quantify the net sea–air CO2 flux, for the first time, across different methodologies for consistent time and space scales for the Atlantic and Arctic basins. We present the long-term mean, seasonal cycle, interannual variability and trends in sea–air CO2 flux for the period 1990 to 2009, and assign an uncertainty to each. We use regional cuts from global observations and modeling products, specifically a pCO2-based CO2 flux climatology, flux estimates from the inversion of oceanic and atmospheric data, and results from six ocean biogeochemical models. Additionally, we use basin-wide flux estimates from surface ocean pCO2 observations based on two distinct methodologies. Our estimate of the contemporary sea–air flux of CO2 (sum of anthropogenic and natural components) by the Atlantic between 40° S and 79° N is −0.49 ± 0.05 Pg C yr−1, and by the Arctic it is −0.12 ± 0.06 Pg C yr−1, leading to a combined sea–air flux of −0.61 ± 0.06 Pg C yr−1 for the two decades (negative reflects ocean uptake). We do find broad agreement amongst methodologies with respect to the seasonal cycle in the subtropics of both hemispheres, but not elsewhere. Agreement with respect to detailed signals of interannual variability is poor, and correlations to the North Atlantic Oscillation are weaker in the North Atlantic and Arctic than in the equatorial region and southern subtropics. Linear trends for 1995 to 2009 indicate increased uptake and generally correspond between methodologies in the North Atlantic, but there is disagreement amongst methodologies in the equatorial region and southern subtropics.U. Schuster has been supported by EU grants IP 511176-2 (CARBOOCEAN), 212196 (COCOS), and 264879 (CARBOCHANGE), and UK NERC grant NE/H017046/1 (UKOARP). G. A. McKinley and A. Fay thank NASA for support (NNX08AR68G, NNX11AF53G). P. Landsch¨utzer has been supported by EU grant 238366 (GREENCYCLESII). N. Metzl acknowledges the French national funding program LEFE/INSU. Support for N. Gruber has been provided by EU grants 264879 (CARBOCHANGE) and 283080 (GEO-CARBON) S. Doney acknowledges support from NOAA (NOAA-NA07OAR4310098). T. Takahashi is supported by NOAA (NAO80AR4320754)