Bifurcations of a creeping air–water flow in a conical container

This numerical study describes the eddy emergence and transformations in a slow steady axisymmetric air–water flow, driven by a rotating top disk in a vertical conical container. As water height \(H_{\mathrm{w}}\) and cone half-angle \(\beta \) vary, numerous flow metamorphoses occur. They are investigated for \(\beta =30^{\circ }, 45^{\circ }\), and \(60^{\circ }\). For small \(H_{\mathrm{w}}\), the air flow is multi-cellular with clockwise meridional circulation near the disk. The air flow becomes one cellular as \(H_{\mathrm{w}}\) exceeds a threshold depending on \(\beta \). For all \(\beta \), the water flow has an unbounded number of eddies whose size and strength diminish as the cone apex is approached. As the water level becomes close to the disk, the outmost water eddy with clockwise meridional circulation expands, reaches the interface, and induces a thin layer with anticlockwise circulation in the air. Then this layer expands and occupies the entire air domain. The physical reasons for the flow transformations are provided. The results are of fundamental interest and can be relevant for aerial bioreactors.     

Stochastic upscaling of random microstructures

In this work we present an upscaling technique for multi-scale computations based on random microstructures modelled as realisations of lognormally distributed random fields, or described by randomly distributed inclusions in a homogeneous matrix. Their corresponding coarse-scale model parameters are considered as uncertain, and are approximated by random variables, the distributions of which are obtained via polynomial chaos based Bayesian procedures in which the fine-scale energy is used as an observation. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Radial oscillations of nonhomogeneous,thick-walled cylindrical and spherical shells subjected to finite deformations

The infinitesimal breathing motions of long cylindrical tubes and hollow spherical shells of arbitrary wall thickness subjected to a finite deformation field caused by uniform internal and/or external pressures are investigated. A neo-Hookean material with a material constant varying continuously along the radial direction is used. The shell is first subjected to finite static deformations and is then exposed to a secondary dynamic displacement field. Based on the theory of small deformations superposed on large deformations, closed form expressions are obtained for the frequency of small oscillations about the highly prestressed state. Frequency versus initial deformation parameter curves are given for several nohomogeneity functions and for various wall thicknesses.     

Dual and tetraelectrode QCMs using imprinted polymers as receptors for ions and neutral analytes

Polymers as coating materials were combined with quartz crystal microbalances (QCMs) to design sensor devices for the detection of both ionic and neutral analytes in liquid phase. The design and geometry of dual and tetraelectrode QCMs have been optimized to reduce electric field interferences. An unusual Sauerbrey effect was observed while exposing potassium salt solution to 10- and 20-MHz QCMs, i.e. increase in the frequency shifts by a factor of seven, which is attributed to electro-acoustic phenomena. Non-functionalized sol-gel materials were synthesized by templating with hydrophobic salt such as tetraethyl ammonium picrate. Imprinting with these ions of low charge density leads to sensitive layers, and UV–Vis spectroscopy was used to check re-inclusion of this analyte. In the next strategy, functionalized polyurethane for potassium ions and sol-gel materials with aminopropyl group as ligand were generated to tune selectivity and sensitivity towards Ni²⁺ and Cu²⁺. Methacrylic acid polymers were optimized for the detection of atrazine by hydrogen bonding; double molecular imprinted polyurethane approach was followed for pyrene recognition. Finally, these imprinted polymers were combined with tetraelectrode QCM to develop sensor platform.     

Accuracy and convergence of element-by-element iterative solvers for incompressible fluid flows using penalty finite element model

The ability of two types of Conjugate Gradient like iterative solvers (GMRES and ORTHOMIN) to resolve large-scale phenomena as a function of mesh density and convergence tolerance limit is investigated. The flow of an incompressible fluid inside a sudden expansion channel is analysed using three meshes of 400, 1600 and 6400 bilinear elements. The iterative solvers utilize the element-by-element data structure of the finite element technique to store and maintain the data at the element level. Both the mesh density and the penalty parameter are found to influence the choice of the convergence tolerance limit needed to obtain accurate results. An empirical relationship between the element size, the penalty parameter, and the convergence tolerance is presented. This relationship can be used to predict the proper choice of the convergence tolerance for a given penalty parameter and element size.     

Unstable capillary flow of reinforced polymer melts

The injection capillary flow of various unfilled and glass fibre or calcium carbonate filled polypropylene and nylon 6.6 melts is studied using either a single capillary of five capillaries in series, separated by small reservoirs. Only unfilled nylon 6.6 yields instability during flow through a single capillary due to mechanochemical degradation in the capillary at extremely high shear rates above 5 × 10⁵ s^?1. It is found that only short glass fibre reinforced polypropylene yields high frequency oscillations in the reservoir pressure and extrudate diameter and has discontinuity in the flow curve when the apparent shear rate is above 4 × 10⁵ s^?1 and the flow is through multiple capillaries. Further increase in the shear rate restores the stable flow. The intensity of the oscillations and the range of shear rate during which unstable flow occurs are increased with increasing melt temperature. The mechanism of this unstable flow is investigated by studying fibre orientation at the capillary entrance and exit using mouldings simulating capillary entry-exit flows.     

Characterizing student mathematics teachers’ levels of understanding in spherical geometry

This article presents an exploratory study aimed at the identification of students’ levels of understanding in spherical geometry as van Hiele did for Euclidean geometry. To do this, we developed and implemented a spherical geometry course for student mathematics teachers. Six structured, task-based interviews were held with eight student mathematics teachers at particular times through the course to determine the spherical geometry learning levels. After identifying the properties of spherical geometry levels, we developed Understandings in Spherical Geometry Test to test whether or not the levels form hierarchy, and 58 student mathematics teachers took the test. The outcomes seemed to support our theoretical perspective that there are some understanding levels in spherical geometry that progress through a hierarchical order as van Hiele levels in Euclidean geometry.     

Mathematical analysis of an influenza epidemic model,formulation of different controlling strategies using optimal control and estimation of basic reproduction number

In this article, a deterministic model is formulated to perform a thorough investigation of the transmission dynamics of influenza. In particular, our model takes into account the effects of medication as well as hospitalization. An in-depth stability analysis of the model is performed, and it is subsequently shown that the model is locally, as well as globally asymptotically stable, when R₀ > 1. It is also shown that there exists a unique endemic equilibrium whenever R₀ > 1. After estimating the effective contact rate, we estimate the basic reproduction number, using both an ordinary least squares and generalized least squares methodology. We also estimated confidence intervals for the effective contact rate using parametric bootstrapping. Furthermore, we perform uncertainty and sensitivity analysis to recognize the impact of crucial model parameters on R₀. In addition, using ideas from the optimal control theory, optimal medication and hospitalization strategies are proposed to eliminate the disease.     

Thiourea Derivatives,Simple in Structure but Efficient Enzyme Inhibitors and Mercury Sensors

In this study six unsymmetrical thiourea derivatives, 1-isobutyl-3-cyclohexylthiourea (1), 1-tert-butyl-3-cyclohexylthiourea (2), 1-(3-chlorophenyl)-3-cyclohexylthiourea (3), 1-(1,1-dibutyl)-3-phenylthiourea (4), 1-(2-chlorophenyl)-3-phenylthiourea (5) and 1-(4-chlorophenyl)-3-phenylthiourea (6) were obtained in the laboratory under aerobic conditions. Compounds 3 and 4 are crystalline and their structure was determined for their single crystal. Compounds 3 is monoclinic system with space group P2₁/n while compound 4 is trigonal, space group R³:H. Compounds (1–6) were tested for their anti-cholinesterase activity against acetylcholinesterase and butyrylcholinesterase (hereafter abbreviated as, AChE and BChE, respectively). Potentials (all compounds) as sensing probes for determination of deadly toxic metal (mercury) using spectrofluorimetric technique were also investigated. Compound 3 exhibited better enzyme inhibition IC₅₀ values of 50, and 60 µg/mL against AChE and BChE with docking score of −10.01, and −8.04 kJ/mol, respectively. The compound also showed moderate sensitivity during fluorescence studies.     

Shear deformation plate continua of large double layered space structures

A simple method is presented to model large rigid-jointed lattice structures as continuous elastic media with couple stresses using energy equivalence. In our analysis the transition from the discrete system to the continuous media is achieved by expanding the displacements and the rotations of the nodal points in a Taylor series about a suitable chosen origin. The strain energy of the continuous media with couple stresses is then specialized to obtain shear deformation plate continua. Equivalent continua for single layered grids, double layered grids and three-dimensional lattices are then obtained.