An easy-to-use estimate of the energy-release rate for crack arrays

Formation of crack arrays plays an increasing role in several fields of applied physics. The energy-release rate of the cracks controls the development of the array. Therefore, following the concept of configurational forces, a simplified analytical expression is provided for the energy-release rate, which is based both on numerical studies and on a specially adapted beam model. Comparisons of this easy-to-use estimate of the energy-release rate with established results from the literature as well as detailed numerical results are presented. The provided estimate of the energy-release rate can easily be extended to non-equidistant cracks and an anisotropic material.     

Cholesterol complexes with some proton acceptors in benzene and toluene solutions

Abstract  Cholesterol complexes with tri-n-butyl phosphate, tri-n-octylamine, N,N-dimethylacetamide, and cyclohexanone in benzene and toluene solutions were studied using conventional IR spectroscopy. The spectra were recorded in the region of fundamental OH stretching (3,700–3,100 cm⁻¹) at 298 K. The experimental spectra were resolved into bands corresponding to the cholesterol monomer and particular oligomeric and complex species. The formation constants of complexes were determined from the-least squares plots of the linearized expressions of Bjerrum’s formation function. The stoichiometry of complexes was also identified in this way. The identification of the particular resolved bands was performed from their location, and from the dependence of their intensity on the cholesterol monomer and free base concentration. Graphical Abstract        

Global exponential stability of a class of retarded impulsive differential equations with applications

This paper studies the dynamics of a class of retarded impulsive differential equations (IDE), which generalizes the delayed cellular neural networks (DCNN), delayed bidirectional associative memory (BAM) neural networks and some population growth models. Some sufficient criteria are obtained for the existence and global exponential stability of a unique equilibrium. When the impulsive jumps are absent, our results reduce to its corresponding results for the non-impulsive systems. The approaches are based on Banach’s fixed point theorem, matrix theory and its spectral theory. Due to this method, our results generalize and improve many previous known results such as [3], [5], [6], [9], [17], [18], [23], [32], [38], [43], [51], [52]. Some examples are also included to illustrate the feasibility and effectiveness of the results obtained.     

Turbulent Couette–Taylor flows with endwall effects: A numerical benchmark

The accurate prediction of fluid flow within rotating systems has a primary role for the reliability and performance of rotating machineries. The selection of a suitable model to account for the effects of turbulence on such complex flows remains an open issue in the literature. This paper reports a numerical benchmark of different approaches available within commercial CFD solvers together with results obtained by means of in-house developed or open-source available research codes exploiting a suitable Reynolds Stress Model (RSM) closure, Large Eddy Simulation (LES) and a direct numerical simulation (DNS). The predictions are compared to the experimental data of Burin et al. (2010) in an original enclosed Couette–Taylor apparatus with endcap rings. The results are discussed in details for both the mean and turbulent fields. A particular attention has been turned to the scaling of the turbulent angular momentum G with the Reynolds number Re. By DNS, G is found to be proportional to Re^α, the exponent α = 1.9 being constant in our case for the whole range of Reynolds numbers. Most of the approaches predict quite well the good trends apart from the k–ω SST model, which provides relatively poor agreement with the experiments even for the mean tangential velocity profile. Among the RANS models, even though no approach appears to be fully satisfactory, the RSM closure offers the best overall agreement.     

Coenzyme Regeneration in Hexanol Oxidation Catalyzed by Alcohol Dehydrogenase

The enzymatic ways of coenzyme regeneration include the addition of a second enzyme to the system or the addition of the co-substrate. In the present study, both methods of enzymatic coenzyme (NAD⁺) regeneration were studied and compared in the reaction of hexanol oxidation catalyzed by alcohol dehydrogenase (ADH). As a source of ADH, commercial isolated enzyme and the whole baker??s yeast cells were used. First, coenzyme regeneration was employed in the reaction of acetaldehyde reduction catalyzed by the same enzyme that catalyzed the main reaction, and then NAD⁺ regeneration was applied in the reaction of pyruvate reduction catalyzed by l-lactate dehydrogenase (l-LDH). Hexanal was obtained as the product of hexanol oxidation catalyzed by isolated ADH while hexaonic acid was detected as a product of the same reaction catalyzed by baker??s yeast cells. All of the used biocatalysts were kinetically characterized. The mass reactions were described by the mathematical models. All models were validated in the batch reactor. One hundred percent hexanol conversion was obtained using permeabilized yeast cells using both methods of cofactor regeneration. By using isolated enzyme ADH, the higher conversion was achieved in a system with cofactor regeneration catalyzed by l-LDH.     

A finite element analysis of the bending of crystalline plates due to anisotropic surface and film stress applied to magnetoelasticity

The bending of crystalline plates in response to a non-isotropic stress on one of the two surfaces is investigated with special attention to magnetoelastic effects. The crystalline plates are assumed to have cubic symmetry, expose either (1 0 0) or (1 1 1) surfaces, and be clamped along one edge. It is shown that the effect of clamping can be described by a dimensionless parameter, the “dimensionality” D, which in general depends on the length-to-width ratio of the sample, the Poisson ratio ν, and the elastic anisotropy A. Using a finite element analysis we find that the dimensionality parameters for anisotropic and isotropic surface stresses are identical. The theory is applied to the bending caused by magnetoelastic stresses in deposited thin films. Expressions are derived to calculate the magnetoelastic coupling constants of films with cubic, tetragonal, or hexagonal symmetry from a measurement of the change of radius of curvature of the film–substrate composite upon an in-plane reorientation of the film magnetization.