A posteriori error control for discontinuous Galerkin methods for parabolic problems

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

A finite element method for fully nonlinear elliptic problems

We present a continuous finite element method for some examples of fully nonlinear elliptic equation. A key tool is the discretisation proposed in Lakkis & Pryer (2011, SISC) allowing us to work directly on the strong form of a linear PDE. An added benefit to making use of this discretisation method is that a recovered (finite element) Hessian is a biproduct of the solution process. We build on the linear basis and ultimately construct two different methodologies for the solution of second order fully nonlinear PDEs. Benchmark numerical results illustrate the convergence properties of the scheme for some test problems including the Monge-Amp\`ere equation and Pucci's equation.Comment: 22 pages, 31 figure

Exhibiting cross-diffusion-induced patterns for reaction-diffusion systems on evolving domains and surfaces

The aim of this manuscript is to present for the first time the application of the finite element method for solving reaction-diffusion systems with cross-diffusion on continuously evolving domains and surfaces. Furthermore we present pattern formation generated by the reaction-diffusion systemwith cross-diffusion on evolving domains and surfaces. A two-component reaction-diffusion system with linear cross-diffusion in both u and v is presented. The finite element method is based on the approximation of the domain or surface by a triangulated domain or surface consisting of a union of triangles. For surfaces, the vertices of the triangulation lie on the continuous surface. A finite element space of functions is then defined by taking the continuous functions which are linear affine on each simplex of the triangulated domain or surface. To demonstrate the role of cross-diffusion to the theory of pattern formation, we compute patterns with model kinetic parameter values that belong only to the cross-diffusion parameter space; these do not belong to the standard parameter space for classical reaction-diffusion systems. Numerical results exhibited show the robustness, flexibility, versatility, and generality of our methodology; the methodology can deal with complicated evolution laws of the domain and surface, and these include uniform isotropic and anisotropic growth profiles as well as those profiles driven by chemical concentrations residing in the domain or on the surface

Optimal processings design for synthetic aperture radar

Synthetic aperture radar (SAR) is a microwave imagery system capable ofproducing high resolution images by processing properly data collected by a relatively small antenna. In this papet the bi-dimensionnal received signal, using spatial coordinates, is formulated. The image is reconstructed by a two- dimensionnal filtering operation . We propose a straightforward derivation for the coherent sommation method (or bock-projection of range responses) and the 2-D azimuth matched filtering . The image quality is determined by that of the ambiguity fonction. This latter is analyzed and optimized for two performance criteria. First, for a matched filter receiver (maximal signal-to-noise ratio receiver), the optimal waveform is shown ta be a non linear FM pulse which autocorrelationfunction is a Taylor . The optimal azmiuth weighting fonction is related to that of Taylor by a Fourier transform . Second, for a Wiener filter (least mean-squares receiver), we show that the optimal waveform is the firstprolate spheroidal fonction . The single-hit measurement of the scattering matrix by mean of two optimal orthogonal waves is discussed . Resolutions, SNR as well as ambiguities, are specified .Le radar à visée latérale et à ouverture synthétique est un système d'imagerie micro-onde capable de produire des images de très haute résolution des terrains, et ceci à partir d'un traitement approprié des signaux reçus par une antenne de faible dimension, Dans cet article, nous présentons la formulation exacte du signal reçu, ainsi que les traitements associés afin de former l'image. On met en évidence l'équivalence entre la méthode de la sommation cohérente et le filtrage adapté bidimensionnel en azimut. La qualité de l'image ainsi formée est déterminée par celle de la fonction d'ambiguït

Global existence for semilinear reaction-diffusion systems on evolving domains

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

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

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

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

A model for selection of eyespots on butterfly wings

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

Impediments to eye transplantation: Ocular viability following optic-nerve transection or enucleation

Maintenance of ocular viability is one of the major impediments to successful whole-eye transplantation. This review provides a comprehensive understanding of the current literature to help guide future studies in order to overcome this hurdle. A systematic multistage review of published literature was performed. Three specific questions were addressed: (1) Is recovery of visual function following eye transplantation greater in cold-blooded vertebrates when compared with mammals? (2) Is outer retina function following enucleation and reperfusion improved compared with enucleation alone? (3) Following optic-nerve transection, is there a correlation between retinal ganglion cell (RGC) survival and either time after transection or proximity of the transection to the globe? In a majority of the studies performed in the literature, recovery of visual function can occur after whole-eye transplantation in cold-blooded vertebrates. Following enucleation (and reperfusion), outer retinal function is maintained from 4 to 9 h. RGC survival following optic-nerve transection is inversely related to both the time since transection and the proximity of transection to the globe. Lastly, neurotrophins can increase RGC survival following optic-nerve transection. This review of the literature suggests that the use of a donor eye is feasible for whole-eye transplantation.published_or_final_versio