473 research outputs found

    A posteriori error control for discontinuous Galerkin methods for parabolic problems

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    We derive energy-norm a posteriori error bounds for an Euler time-stepping method combined with various spatial discontinuous Galerkin schemes for linear parabolic problems. For accessibility, we address first the spatially semidiscrete case, and then move to the fully discrete scheme by introducing the implicit Euler time-stepping. All results are presented in an abstract setting and then illustrated with particular applications. This enables the error bounds to hold for a variety of discontinuous Galerkin methods, provided that energy-norm a posteriori error bounds for the corresponding elliptic problem are available. To illustrate the method, we apply it to the interior penalty discontinuous Galerkin method, which requires the derivation of novel a posteriori error bounds. For the analysis of the time-dependent problems we use the elliptic reconstruction technique and we deal with the nonconforming part of the error by deriving appropriate computable a posteriori bounds for it.Comment: 6 figure

    Combined battery SOC/SOH estimation using a nonlinear adaptive observer

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    International audience— This work presents a modeling and estimation techniques for State of Charge and State of Health estimation for Li-ion batteries. The analysis is done using an adaptive estimation approach for joint state and parameter estimation and by simplifying an existing nonlinear model previously obtained from experiments tests. A switching mechanism between two observers, one for the charging phase and one for the discharging phase, is done to avoid transients due to the discontinuity of model's parameters. Simulations on experimental data show that the approach is feasible and enhance the interest of the proposed estimation technique

    A posteriori error estimates for leap-frog and cosine methods for second order evolution problems

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    We consider second order explicit and implicit two-step time-discrete schemes for wave-type equations. We derive optimal order aposteriori estimates controlling the time discretization error. Our analysis, has been motivated by the need to provide aposteriori estimates for the popular leap-frog method (also known as Verlet's method in molecular dynamics literature); it is extended, however, to general cosine-type second order methods. The estimators are based on a novel reconstruction of the time-dependent component of the approximation. Numerical experiments confirm similarity of convergence rates of the proposed estimators and of the theoretical convergence rate of the true error

    Implicit-explicit timestepping with finite element approximation of reaction-diffusion systems on evolving domains

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    We present and analyse an implicit-explicit timestepping procedure with finite element spatial approximation for a semilinear reaction-diffusion systems on evolving domains arising from biological models, such as Schnakenberg's (1979). We employ a Lagrangian formulation of the model equations which permits the error analysis for parabolic equations on a fixed domain but introduces technical difficulties, foremost the space-time dependent conductivity and diffusion. We prove optimal-order error estimates in the \Lp{\infty}(0,T;\Lp{2}(\W)) and \Lp{2}(0,T;\Hil{1}(\W)) norms, and a pointwise stability result. We remark that these apply to Eulerian solutions. Details on the implementation of the Lagrangian and the Eulerian scheme are provided. We also report on a numerical experiment for an application to pattern formation on an evolving domain

    Trichloroethylene Exposure during Cardiac Valvuloseptal Morphogenesis Alters Cushion Formation and Cardiac Hemodynamics in the Avian Embryo

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    It is controversial whether trichloroethylene (TCE) is a cardiac teratogen. We exposed chick embryos to 0, 0.4, 8, or 400 ppb TCE/egg during the period of cardiac valvuloseptal morphogenesis (2–3.3 days’ incubation). Embryo survival, valvuloseptal cellularity, and cardiac hemodynamics were evaluated at times thereafter. TCE at 8 and 400 ppb/egg reduced embryo survival to day 6.25 incubation by 40–50%. At day 4.25, increased proliferation and hypercellularity were observed within the atrioventricular and outflow tract primordia after 8 and 400 ppb TCE. Doppler ultrasound revealed that the dorsal aortic and atrioventricular blood flows were reduced by 23% and 30%, respectively, after exposure to 8 ppb TCE. Equimolar trichloroacetic acid (TCA) was more potent than TCE with respect to increasing mortality and causing valvuloseptal hypercellularity. These results independently confirm that TCE disrupts cardiac development of the chick embryo and identifies valvuloseptal development as a period of sensitivity. The hypercellular valvuloseptal profile is consistent with valvuloseptal heart defects associated with TCE exposure. This is the first report that TCA is a cardioteratogen for the chick and the first report that TCE exposure depresses cardiac function. Valvuloseptal hypercellularity may narrow the cardiac orifices, which reduces blood flow through the heart, thereby compromising cardiac output and contributing to increased mortality. The altered valvuloseptal formation and reduced hemodynamics seen here are consistent with such an outcome. Notably, these effects were observed at a TCE exposure (8 ppb) that is only slightly higher than the U.S. Environmental Protection Agency maximum containment level for drinking water (5 ppb)

    Aroma-loaded microcapsules with antibacterial activity for eco-friendly textile application: synthesis, characterization, release, and green grafting

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    Fragrant and antimicrobial properties were conferred to cotton fabrics following microencapsulation using green materials. Limonene and vanillin microcapsules were produced by complex coacervation using chitosan/gum Arabic as shell materials and tannic acid as hardening agent. The effect of two emulsifiers; Span 85 and polyglycerol polyricinoleate (PGPR), on the encapsulation efficiency (EE%), microcapsule’s size and morphology, and cumulative release profiles was studied. The mean diameter of the produced microcapsules ranged between 10.4 and 39.0 μm, whereas EE% was found to be between 90.4% and 100%. The use of Span 85 resulted in mononuclear morphology while PGPR gave rise to polynuclear structures, regardless of the core material (vanillin or limonene). The obtained microcapsules demonstrated a sustained release pattern; namely the total cumulative release of the active agents after 7 days at 37 ± 1 °C was 75%, 52% and 19.4% for the polynuclear limonene microcapsules, the mononuclear limonene microcapsules and the polynuclear vanillin microcapsules, respectively. Grafting of the produced microcapsules onto cotton fabrics through na esterification reaction using citric acid as a nontoxic cross-linker followed by thermofixation and curing, was confirmed by SEM and FTIR spectroscopy. Standard antibacterial assays conducted on both microcapsules alone and impregnated onto the fabrics indicated a sustained antibacterial activity.info:eu-repo/semantics/publishedVersio

    Cardiac Involvement by Burkitt Lymphoma in a 49-Year-Old Man

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    Malignant metastases are among the most common cardiac masses. We report a rare case of cardiac involvement by Burkitt lymphoma in a 49-year-old man who presented with a 2-month history of dyspnea and palpitations. A transthoracic echocardiogram revealed 2 intracardiac masses in the right atrium (one of which partially encased the tricuspid valve), myocardial infiltration, and pericardial disease. Results of pleural fluid cytology and flow cytometry confirmed involvement by Burkitt lymphoma. Subsequent chemotherapy markedly reduced the intracardiac tumor burden and resolved the patient\u27s presenting symptoms. Our case highlights the importance of cardiac imaging in diagnosing systemic illness, initiating early and appropriate treatment, and monitoring disease progression in patients with intracardiac Burkitt lymphoma

    Global existence for semilinear reaction-diffusion systems on evolving domains

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    We present global existence results for solutions of reaction-diffusion systems on evolving domains. Global existence results for a class of reaction-diffusion systems on fixed domains are extended to the same systems posed on spatially linear isotropically evolving domains. The results hold without any assumptions on the sign of the growth rate. The analysis is valid for many systems that commonly arise in the theory of pattern formation. We present numerical results illustrating our theoretical findings.Comment: 24 pages, 3 figure

    A model for selection of eyespots on butterfly wings

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    The development of eyespots on the wing surface of butterflies of the family Nympalidae is one of the most studied examples of biological pattern formation.However, little is known about the mechanism that determines the number and precise locations of eyespots on the wing. Eyespots develop around signaling centers, called foci, that are located equidistant from wing veins along the midline of a wing cell (an area bounded by veins). A fundamental question that remains unsolved is, why a certain wing cell develops an eyespot, while other wing cells do not. We illustrate that the key to understanding focus point selection may be in the venation system of the wing disc. Our main hypothesis is that changes in morphogen concentration along the proximal boundary veins of wing cells govern focus point selection. Based on previous studies, we focus on a spatially two-dimensional reaction-diffusion system model posed in the interior of each wing cell that describes the formation of focus points. Using finite element based numerical simulations, we demonstrate that variation in the proximal boundary condition is sufficient to robustly select whether an eyespot focus point forms in otherwise identical wing cells. We also illustrate that this behavior is robust to small perturbations in the parameters and geometry and moderate levels of noise. Hence, we suggest that an anterior-posterior pattern of morphogen concentration along the proximal vein may be the main determinant of the distribution of focus points on the wing surface. In order to complete our model, we propose a two stage reaction-diffusion system model, in which an one-dimensional surface reaction-diffusion system, posed on the proximal vein, generates the morphogen concentrations that act as non-homogeneous Dirichlet (i.e., fixed) boundary conditions for the two-dimensional reaction-diffusion model posed in the wing cells. The two-stage model appears capable of generating focus point distributions observed in nature. We therefore conclude that changes in the proximal boundary conditions are sufficient to explain the empirically observed distribution of eyespot focus points on the entire wing surface. The model predicts, subject to experimental verification, that the source strength of the activator at the proximal boundary should be lower in wing cells in which focus points form than in those that lack focus points. The model suggests that the number and locations of eyespot foci on the wing disc could be largely controlled by two kinds of gradients along two different directions, that is, the first one is the gradient in spatially varying parameters such as the reaction rate along the anterior-posterior direction on the proximal boundary of the wing cells, and the second one is the gradient in source values of the activator along the veins in the proximal-distal direction of the wing cell
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