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Interior transmission eigenvalue problems for the Helmholtz equation play an important role in inverse wave scattering. Some distribution properties of those eigenvalues in the complex plane are reviewed. Further, a new scattering model for the interior transmission eigenvalue problem with mixed boundary conditions is described and an efficient algorithm for computing the interior transmission eigenvalues is proposed. Finally, extensive numerical results for a variety of two-dimensional scatterers are presented to show the validity of the proposed scheme.
We present new numerical results for shape optimization problems of interior Neumann eigenvalues. This field is not well understood from a theoretical standpoint. The existence of shape maximizers is not proven beyond the first two eigenvalues, so we study the problem numerically. We describe a method to compute the eigenvalues for a given shape that combines the boundary element method with an algorithm for nonlinear eigenvalues. As numerical optimization requires many such evaluations, we put a focus on the efficiency of the method and the implemented routine. The method is well suited for parallelization. Using the resulting fast routines and a specialized parametrization of the shapes, we found improved maxima for several eigenvalues.
Motile cilia are hair-like cell extensions present in multiple organs of the body. How cilia coordinate their regular beat in multiciliated epithelia to move fluids remains insufficiently understood, particularly due to lack of rigorous quantification. We combine here experiments, novel analysis tools, and theory to address this knowledge gap. We investigate collective dynamics of cilia in the zebrafish nose, due to its conserved properties with other ciliated tissues and its superior accessibility for non-invasive imaging. We revealed that cilia are synchronized only locally and that the size of local synchronization domains increases with the viscosity of the surrounding medium. Despite the fact that synchronization is local only, we observed global patterns of traveling metachronal waves across the multiciliated epithelium. Intriguingly, these global wave direction patterns are conserved across individual fish, but different for left and right nose, unveiling a chiral asymmetry of metachronal coordination. To understand the implications of synchronization for fluid pumping, we used a computational model of a regular array of cilia. We found that local metachronal synchronization prevents steric collisions and improves fluid pumping in dense cilia carpets, but hardly affects the direction of fluid flow. In conclusion, we show that local synchronization together with tissue-scale cilia alignment are sufficient to generate metachronal wave patterns in multiciliated epithelia, which enhance their physiological function of fluid pumping.
Lignite biosolubilization and bioconversion by Bacillus sp.: the collation of analytical data
(2021)
The vast metabolic potential of microbes in brown coal (lignite) processing and utilization can greatly contribute to innovative approaches to sustainable production of high-value products from coal. In this study, the multi-faceted and complex coal biosolubilization process by Bacillus sp. RKB 7 isolate from the Kazakhstan coal-mining soil is reported, and the derived products are characterized. Lignite solubilization tests performed for surface and suspension cultures testify to the formation of numerous soluble lignite-derived substances. Almost 24% of crude lignite (5% w/v) was solubilized within 14 days under slightly alkaline conditions (pH 8.2). FTIR analysis revealed various functional groups in the obtained biosolubilization products. Analyses of the lignite-derived humic products by UV-Vis and fluorescence spectrometry as well as elemental analysis yielded compatible results indicating the emerging products had a lower molecular weight and degree of aromaticity. Furthermore, XRD and SEM analyses were used to evaluate the biosolubilization processes from mineralogical and microscopic points of view. The findings not only contribute to a deeper understanding of microbe–mineral interactions in coal environments, but also contribute to knowledge of coal biosolubilization and bioconversion with regard to sustainable production of humic substances. The detailed and comprehensive analyses demonstrate the huge biotechnological potential of Bacillus sp. for agricultural productivity and environmental health.
A new formulation to calculate the shakedown limit load of Kirchhoff plates under stochastic conditions of strength is developed. Direct structural reliability design by chance con-strained programming is based on the prescribed failure probabilities, which is an effective approach of stochastic programming if it can be formulated as an equivalent deterministic optimization problem. We restrict uncertainty to strength, the loading is still deterministic. A new formulation is derived in case of random strength with lognormal distribution. Upper bound and lower bound shakedown load factors are calculated simultaneously by a dual algorithm.
Cardiopulmonary bypass (CPB) is a standard technique for cardiac surgery, but comes with the risk of severe neurological complications (e.g. stroke) caused by embolisms and/or reduced cerebral perfusion. We report on an aortic cannula prototype design (optiCAN) with helical outflow and jet-splitting dispersion tip that could reduce the risk of embolic events and restores cerebral perfusion to 97.5% of physiological flow during CPB in vivo, whereas a commercial curved-tip cannula yields 74.6%. In further in vitro comparison, pressure loss and hemolysis parameters of optiCAN remain unaffected. Results are reproducibly confirmed in silico for an exemplary human aortic anatomy via computational fluid dynamics (CFD) simulations. Based on CFD simulations, we firstly show that optiCAN design improves aortic root washout, which reduces the risk of thromboembolism. Secondly, we identify regions of the aortic intima with increased risk of plaque release by correlating areas of enhanced plaque growth and high wall shear stresses (WSS). From this we propose another easy-to-manufacture cannula design (opti2CAN) that decreases areas burdened by high WSS, while preserving physiological cerebral flow and favorable hemodynamics. With this novel cannula design, we propose a cannulation option to reduce neurological complications and the prevalence of stroke in high-risk patients after CPB.
Thrombogenic complications are a main issue in mechanical circulatory support (MCS). There is no validated in vitro method available to quantitatively assess the thrombogenic performance of pulsatile MCS devices under realistic hemodynamic conditions. The aim of this study is to propose a method to evaluate the thrombogenic potential of new designs without the use of complex in-vivo trials. This study presents a novel in vitro method for reproducible thrombogenicity testing of pulsatile MCS systems using low molecular weight heparinized porcine blood. Blood parameters are continuously measured with full blood thromboelastometry (ROTEM; EXTEM, FIBTEM and a custom-made analysis HEPNATEM). Thrombus formation is optically observed after four hours of testing. The results of three experiments are presented each with two parallel loops. The area of thrombus formation inside the MCS device was reproducible. The implantation of a filter inside the loop catches embolizing thrombi without a measurable increase of platelet activation, allowing conclusions of the place of origin of thrombi inside the device. EXTEM and FIBTEM parameters such as clotting velocity (α) and maximum clot firmness (MCF) show a total decrease by around 6% with a characteristic kink after 180 minutes. HEPNATEM α and MCF rise within the first 180 minutes indicate a continuously increasing activation level of coagulation. After 180 minutes, the consumption of clotting factors prevails, resulting in a decrease of α and MCF. With the designed mock loop and the presented protocol we are able to identify thrombogenic hot spots inside a pulsatile pump and characterize their thrombogenic potential.