A self-consistent boundary element, parametric dislocation dynamics formulation of plastic flow in finite volumes

We present a self-consistent formulation of 3-D parametric dislocation dynamics (PDD) with the boundary element method (BEM) to describe dislocation motion, and hence microscopic plastic flow in finite volumes. We develop quantitative measures of the accuracy and convergence of the method by considering a comparison with known analytical solutions. It is shown that the method displays absolute convergence with increasing the number of quadrature points on the dislocation loop and the surface mesh density. The error in the image force on a screw dislocation approaching a free surface is shown to increase as the dislocation approaches the surface, but is nevertheless controllable. For example, at a distance of one lattice parameter from the surface, the relative error is less than 5% for a surface mesh with an element size of 1000×2000 (in units of lattice parameter), and 64 quadrature points. The Eshelby twist angle in a finite-length cylinder containing a coaxial screw dislocation is also used to benchmark the method. Finally, large scale 3-D simulation results of single slip behavior in cylindrical microcrystals are presented. Plastic flow characteristics and the stress-strain behavior of cylindrical microcrystals under compression are shown to be in agreement with experimental observations. It is shown that the mean length of dislocations trapped at the surface is the dominant factor in determining the size effects on hardening of single crystals. The influence of surface image fields on the flow stress is finally explored. It is shown that the flow stress is reduced by as much as 20% for small single crystals of size less than .     

Optimally growing boundary layer disturbances in a convergent nozzle preceded by a circular pipe

We report the findings from a theoretical analysis of optimally growing disturbances in an initially turbulent boundary layer. The motivation behind this study originates from the desire to generate organized structures in an initially turbulent boundary layer via excitation by disturbances that are tailored to be preferentially amplified. Such optimally growing disturbances are of interest for implementation in an active flow control strategy that is investigated for effective jet noise control. Details of the optimal perturbation theory implemented in this study are discussed. The relevant stability equations are derived using both the standard decomposition and the triple decomposition. The chosen test case geometry contains a convergent nozzle, which generates a Mach 0.9 round jet, preceded by a circular pipe. Optimally growing disturbances are introduced at various stations within the circular pipe section to facilitate disturbance energy amplification upstream of the favorable pressure gradient zone within the convergent nozzle, which has a stabilizing effect on disturbance growth. Effects of temporal frequency, disturbance input and output plane locations as well as separation distance between output and input planes are investigated. The results indicate that optimally growing disturbances appear in the form of longitudinal counter-rotating vortex pairs, whose size can be on the order of several times the input plane mean boundary layer thickness. The azimuthal wavenumber, which represents the number of counter-rotating vortex pairs, is found to generally decrease with increasing separation distance. Compared to the standard decomposition, the triple decomposition analysis generally predicts relatively lower azimuthal wavenumbers and significantly reduced energy amplification ratios for the optimal disturbances.     

Pre-service Teachers’ Developing Conceptions about the Nature and Pedagogy of Mathematical Modeling in the Context of a Mathematical Modeling Course

Adopting a multitiered design-based research perspective, this study examines pre-service secondary mathematics teachers’ developing conceptions about (a) the nature of mathematical modeling in simulations of “real life” problem solving, and (b) pedagogical principles and strategies needed to teach mathematics through modeling. Unlike other studies that have focused on single-topic and lesson-sized research sites, a course-sized research site was used in this study. Having been through several iterations over three teaching semesters, the 15-week long course was implemented with 25 pre-service secondary mathematics teachers. Findings revealed that pre-service teachers developed ideas about the nature of mathematical modeling involving what mathematical modeling is, the relationship between mathematical modeling and meaningful understanding, and the nature of mathematical modeling tasks. They also realized the changing roles of teachers during modeling implementations and diversity in students’ ways of thinking. The researchers’ conceptual development, on the other hand, involved realizing the critical aspect of the “teacher role” played by the instructor during modeling implementations, and the need for more experience of modeling implementations for pre-service teachers.     

Eigenvalues of Two Parameter Polynomial Operator Pencils of Waveguide Type

The spectral structure of two parameter unbounded operator pencils of waveguide type is studied. Theorems on discreteness of the spectrum for a fixed parameter are proved. Variational principles for real eigenvalues in some parts of the root zones are established. In the case of n = 1 (quadratic pencils) domains containing the spectrum are described (see Fig. 1–3). Conditions in the definition of the pencils of waveguide type arise naturally from physical problems and each of them has a physical meaning. In particular a connection between the energetic stability condition and a perturbation problem for the coefficients is given.     

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.     

Monosize microbeads for pseudo-affinity adsorption of human insulin

Affinity adsorption technique is increasingly used for protein purification, separation and other biochemical applications. Therapeutic molecules such as antibodies, cytokines, therapeutic DNA and plasma proteins must be purified before characterization and utilization. The aim of this study was to prepare micronsized spherical polymeric beads and to investigate the extent of their human insulin adsorption capability. Monosize poly(ethylene glycol dimethacrylate-N-methacryloyl-(L)-histidine) [poly(EDMA-MAH)] beads were prepared by modified suspension copolymerization. Functional monomer (MAH) was synthesized using methacryloyl chloride and L-histidine. The beads were characterized using scanning electron microscopy (SEM), Fourier transform infrared spectroscopy, swelling test and elemental analysis. MAH incorporation into monosize polymeric beads, having an average size around 2-3 μm, was estimated as 55.3 μmol MAH/g bead. Equilibrium swelling ratios of poly(EDMA-MAH) and poly(EDMA) beads were 65% and 55%, respectively. Adsorption experiments were performed under different conditions (i.e., pH, temperature, protein concentration and ionic strength). It was found that adsorption characteristics are strongly depend on these conditions. Maximum insulin adsorption capacity was achieved as 24.7 mg insulin/g poly(EDMA-MAH) beads. Results were well fitted to the Langmuir isotherm model. Compared with poly(EDMA-MAH), nonspecific insulin adsorption onto poly(EDMA) beads was very low (0.61 mg insulin/g bead) and can be negligible. It was observed that insulin could be repeatedly adsorbed and desorbed (at least 10 times) without significant loss in adsorption capacity.     

Monitoring and Exposure Assessment of Fosetyl Aluminium and Other Highly Polar Pesticide Residues in Sweet Cherry

Cherries are popular fruits due to their health benefits, organoleptic quality, and attractive appearance. Since highly polar pesticides are of low mass and amphoteric character, and are not amenable to traditional multi-residue extraction methods, they are more commonly not included in the pesticide monitoring program. This study aims to determine twelve highly polar pesticide residues in cherry samples intended for export from Turkey. A total of 16,022 cherry samples from 2018–2020 harvests in four production areas of Turkey were analyzed using a modification of the Quick Polar Pesticides method and liquid chromatography-tandem mass spectrometry. The method was validated at two fortification levels (0.01 and 0.05 mg kg⁻¹), and good recoveries (87.4–111.4%) and relative standard deviations (<6%) were achieved for all analytes. The limits of quantification were in the range of 1.08–2.55 μg kg⁻¹. Overall, 28.4% of the analyzed cherry samples were detected with phosphonic acid, calculated as fosetyl aluminium (fosetyl-Al) in amounts up to 77.7 mg kg⁻¹. For 2304 samples (14.4%), the residues exceeded the European Union maximum residue level of 2 mg kg⁻¹. There is no reason to be concerned about long-term exposure to phosphonic acid/fosetyl-Al, and the other highly polar pesticides through the consumption of sweet cherry.