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When confining pressure is low or absent, extensional fractures are typical, with fractures occurring on unloaded planes in rock. These “paradox” fractures can be explained by a phenomenological extension strain failure criterion. In the past, a simple empirical criterion for fracture initiation in brittle rock has been developed. But this criterion makes unrealistic strength predictions in biaxial compression and tension. A new extension strain criterion overcomes this limitation by adding a weighted principal shear component. The weight is chosen, such that the enriched extension strain criterion represents the same failure surface as the Mohr–Coulomb (MC) criterion. Thus, the MC criterion has been derived as an extension strain criterion predicting failure modes, which are unexpected in the understanding of the failure of cohesive-frictional materials. In progressive damage of rock, the most likely fracture direction is orthogonal to the maximum extension strain. The enriched extension strain criterion is proposed as a threshold surface for crack initiation CI and crack damage CD and as a failure surface at peak P. Examples show that the enriched extension strain criterion predicts much lower volumes of damaged rock mass compared to the simple extension strain criterion.
Inference on the basis of high-dimensional and functional data are two topics which are discussed frequently in the current statistical literature. A possibility to include both topics in a single approach is working on a very general space for the underlying observations, such as a separable Hilbert space. We propose a general method for consistently hypothesis testing on the basis of random variables with values in separable Hilbert spaces. We avoid concerns with the curse of dimensionality due to a projection idea. We apply well-known test statistics from nonparametric inference to the projected data and integrate over all projections from a specific set and with respect to suitable probability measures. In contrast to classical methods, which are applicable for real-valued random variables or random vectors of dimensions lower than the sample size, the tests can be applied to random vectors of dimensions larger than the sample size or even to functional and high-dimensional data. In general, resampling procedures such as bootstrap or permutation are suitable to determine critical values. The idea can be extended to the case of incomplete observations. Moreover, we develop an efficient algorithm for implementing the method. Examples are given for testing goodness-of-fit in a one-sample situation in [1] or for testing marginal homogeneity on the basis of a paired sample in [2]. Here, the test statistics in use can be seen as generalizations of the well-known Cramérvon-Mises test statistics in the one-sample and two-samples case. The treatment of other testing problems is possible as well. By using the theory of U-statistics, for instance, asymptotic null distributions of the test statistics are obtained as the sample size tends to infinity. Standard continuity assumptions ensure the asymptotic exactness of the tests under the null hypothesis and that the tests detect any alternative in the limit. Simulation studies demonstrate size and power of the tests in the finite sample case, confirm the theoretical findings, and are used for the comparison with concurring procedures. A possible application of the general approach is inference for stock market returns, also in high data frequencies. In the field of empirical finance, statistical inference of stock market prices usually takes place on the basis of related log-returns as data. In the classical models for stock prices, i.e., the exponential Lévy model, Black-Scholes model, and Merton model, properties such as independence and stationarity of the increments ensure an independent and identically structure of the data. Specific trends during certain periods of the stock price processes can cause complications in this regard. In fact, our approach can compensate those effects by the treatment of the log-returns as random vectors or even as functional data.
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.
An acetoin biosensor based on a capacitive electrolyte–insulator–semiconductor (EIS) structure modified with the enzyme acetoin reductase, also known as butane-2,3-diol dehydrogenase (Bacillus clausii DSM 8716ᵀ), is applied for acetoin detection in beer, red wine, and fermentation broth samples for the first time. The EIS sensor consists of an Al/p-Si/SiO₂/Ta₂O₅ layer structure with immobilized acetoin reductase on top of the Ta₂O₅ transducer layer by means of crosslinking via glutaraldehyde. The unmodified and enzyme-modified sensors are electrochemically characterized by means of leakage current, capacitance–voltage, and constant capacitance methods, respectively.
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.