Error estimation and adaptivity for incompressible, non–linear (hyper–)elasticity

A Galerkin finite element method is developed for non–linear, incompressible (hyper) elasticity, and a posteriori error estimates are derived for both linear functionals of the solution and linear functionals of the stress on a boundary where Dirichlet boundary conditions are applied. A second, higher order method for calculating a linear functional of the stress on a Dirichlet boundary is also presented together with an a posteriori error estimator for this approach. An implementation for a 2D model problem with known solution demonstrates the accuracy of the error estimators. Finally the a posteriori error estimate is shown to provide a basis for effective mesh adaptivity

Error bounds on block Gauss Seidel solutions of coupled\ud multiphysics problems

Mathematical models in many fields often consist of coupled sub–models, each of which describe a different physical process. For many applications, the quantity of interest from these models may be written as a linear functional of the solution to the governing equations. Mature numerical solution techniques for the individual sub–models often exist. Rather than derive a numerical solution technique for the full coupled model, it is therefore natural to investigate whether these techniques may be used by coupling in a block Gauss–Seidel fashion. In this study, we derive two a posteriori bounds for such linear functionals. These bounds may be used on each Gauss–Seidel iteration to estimate the error in the linear functional computed using the single physics solvers, without actually solving the full, coupled problem. We demonstrate the use of the bound first by using a model problem from linear algebra, and then a linear ordinary differential equation example. We then investigate the effectiveness of the bound using a non–linear coupled fluid–temperature problem. One of the bounds derived is very sharp for most linear functionals considered, allowing us to predict very accurately when to terminate our block Gauss–Seidel iteration.\ud \ud Copyright c 2000 John Wiley & Sons, Ltd

Numerical and Experimental Investigation of Circulation in Short Cylinders

In preparation for an experimental study of magnetorotational instability (MRI) in liquid metal, we explore Couette flows having height comparable to the gap between cylinders, centrifugally stable rotation, and high Reynolds number. Experiments in water are compared with numerical simulations. Simulations show that endcaps corotating with the outer cylinder drive a strong poloidal circulation that redistributes angular momentum. Predicted azimuthal flow profiles agree well with experimental measurements. Spin-down times scale with Reynolds number as expected for laminar Ekman circulation; extrapolation from two-dimensional simulations at $Re\le 3200$ agrees remarkably well with experiment at $Re\sim 10^6$. This suggests that turbulence does not dominate the effective viscosity. Further detailed numerical studies reveal a strong radially inward flow near both endcaps. After turning vertically along the inner cylinder, these flows converge at the midplane and depart the boundary in a radial jet. To minimize this circulation in the MRI experiment, endcaps consisting of multiple, differentially rotating rings are proposed. Simulations predict that an adequate approximation to the ideal Couette profile can be obtained with a few rings

Continuously variable diffraction gratings using electroconvection in liquid crystals for beam steering applications

There is a great technological need for the development of devices capable of producing wide-angle and efficient, transmissive optical beam steering. In this article, variable pitch phase diffraction gratings using electroconvection in liquid crystals are considered for applications in electrically controllable beam-steerers. The devices contain thin layers of nematic liquid crystal mixtures of negative dielectric anisotropy, which are doped with different concentrations of an ionic species to determine the effect of conductivity on the beam-steering characteristics. The devices are seen to act as continuously variable diffraction gratings, where the pitch increases with the frequency of the applied electric field. The second order diffraction peak is found to be the most efficient, with absolute efficiency ranging from 5% to 15%, and continuous steering from 4° to 8° within 20 μm spaced devices. Devices with thinner layers of liquid crystal were also examined; these demonstrated wider angle steering but had substantial losses of efficiency due to lowering of optical contrast. Suggestions for possible methodologies for optimizing such devices are discussed

Thaliporphine Preserves Cardiac Function of Endotoxemic Rabbits by Both Directly and Indirectly Attenuating NFκB Signaling Pathway

Cardiac depression in sepsis is associated with the increased morbidity and mortality. Although myofilaments damage, autonomic dysfunction, and apoptosis play roles in sepsis-induced myocardial dysfunction, the underlying mechanism is not clear. All of these possible factors are related to NFκB signaling, which plays the main role in sepsis signaling. Thaliporphine was determined to possess anti-inflammatory and cardioprotective activity by suppressing NFκB signaling in rodents. The purpose of this study is to further prove this protective effect in larger septic animals, and try to find the underlying mechanisms. The systolic and diastolic functions were evaluated in vivo by pressure-volume analysis at different preloads. Both preload-dependent and -independent hemodynamic parameters were performed. Inflammatory factors of whole blood and serum samples were analyzed. Several sepsis-related signaling pathways were also determined at protein level. Changes detected by conductance catheter showed Thaliporphine could recover impaired left ventricular systolic function after 4 hours LPS injection. It could also reverse the LPS induced steeper EDPVR and gentler ESPVR, thus improve Ees, Ea, and PRSW. Thaliporphine may exert this protective effect by decreasing TNFα and caspase3 dependent cell apoptosis, which was consistent with the decreased serum cTnI and LDH concentration. Thaliporphine could protect sepsis-associated myocardial dysfunction in both preload-dependent and -independent ways. It may exert these protective effects by both increase of “good”-PI3K/Akt/mTOR and decrease of “bad”-p38/NFκB pathways, which followed by diminishing TNFα and caspase3 dependent cell apoptosis

Differential Responses of Calcifying and Non-Calcifying Epibionts of a Brown Macroalga to Present-Day and Future Upwelling pCO2

Seaweeds are key species of the Baltic Sea benthic ecosystems. They are the substratum of numerous fouling epibionts like bryozoans and tubeworms. Several of these epibionts bear calcified structures and could be impacted by the high pCO2 events of the late summer upwellings in the Baltic nearshores. Those events are expected to increase in strength and duration with global change and ocean acidification. If calcifying epibionts are impacted by transient acidification as driven by upwelling events, their increasing prevalence could cause a shift of the fouling communities toward fleshy species. The aim of the present study was to test the sensitivity of selected seaweed macrofoulers to transient elevation of pCO2 in their natural microenvironment, i.e. the boundary layer covering the thallus surface of brown seaweeds. Fragments of the macroalga Fucus serratus bearing an epibiotic community composed of the calcifiers Spirorbis spirorbis (Annelida) and Electra pilosa (Bryozoa) and the non-calcifier Alcyonidium hirsutum (Bryozoa) were maintained for 30 days under three pCO2 conditions: natural 460±59 µatm, present-day upwelling1193±166 µatm and future upwelling 3150±446 µatm. Only the highest pCO2 caused a significant reduction of growth rates and settlement of S. spirorbis individuals. Additionally, S. spirorbis settled juveniles exhibited enhanced calcification of 40% during daylight hours compared to dark hours, possibly reflecting a day-night alternation of an acidification-modulating effect by algal photosynthesis as opposed to an acidification-enhancing effect of algal respiration. E. pilosa colonies showed significantly increased growth rates at intermediate pCO2 (1193 µatm) but no response to higher pCO2. No effect of acidification on A. hirsutum colonies growth rates was observed. The results suggest a remarkable resistance of the algal macro-epibionts to levels of acidification occurring at present day upwellings in the Baltic. Only extreme future upwelling conditions impacted the tubeworm S. spirorbis, but not the bryozoans

Biodegradation kinetics of 4-fluorocinnamic acid by a consortium of Arthrobacter and Ralstonia strains

Arthrobacter sp. strain G1 is able to grow on 4-fluorocinnamic acid (4-FCA) as sole carbon source. The organism converts 4-FCA into 4-fluorobenzoic acid (4-FBA) and utilizes the two-carbon side-chain for growth with some formation of 4-fluoroacetophenone as a dead-end side product. We also have isolated Ralstonia sp. strain H1, an organism that degrades 4-FBA. A consortium of strains G1 and H1 degraded 4-FCA with Monod kinetics during growth in batch and continuous cultures. Specific growth rates of strain G1 and specific degradation rates of 4-FCA were observed to follow substrate inhibition kinetics, which could be modeled using the kinetic models of Haldane–Andrew and Luong–Levenspiel. The mixed culture showed complete mineralization of 4-FCA with quantitative release of fluoride, both in batch and continuous cultures. Steady-state chemostat cultures that were exposed to shock loadings of substrate responded with rapid degradation and returned to steady-state in 10–15 h, indicating that the mixed culture provided a robust system for continuous 4-FCA degradation

MicroRNA Involvement in Immune Activation During Heart Failure

Heart failure is one of the common end stages of cardiovascular diseases, the leading cause of death in developed countries. Molecular mechanisms underlying the development of heart failure remain elusive but there is a consistent observation of chronic immune activation and aberrant microRNA (miRNA) expression that is present in failing hearts. This review will focus on the interplay between the immune system and miRNAs as factors that play a role during the development of heart failure. Several studies have shown that heart failure patients can be characterized by a sustained innate immune activation. The role of inflammatory signaling is discussed and TLR4 signaling, IL-1β, TNFα and IL-6 expression appears to coincide with the development of heart failure. Furthermore, we describe the implication of the renin angiotensin aldosteron system in immunity and heart failure. In the past decade microRNAs (miRNAs), small non-coding RNAs that translationally repress protein synthesis by binding to partially complementary sequences of mRNA, have come to light as important regulators of several kinds of cardiovascular diseases including cardiac hypertrophy and heart failure. The involvement of differentially expressed miRNAs in the inflammation that occurs during the development of heart failure is still subject of investigation. Here, we summarize and comment on the first studies in this field and hypothesize on the putative involvement of certain miRNAs in heart failure. MicroRNAs have been shown to be critical regulators of cardiac function and inflammation. Future research will have to point out if dampening the immune response, and the miRNAs associated with it, during the development of heart failure is a therapeutically plausible route to follow