Students as toolmakers: refining the results in the accuracy and precision of a trigonometric activity

Smartphones used as tools provide opportunities for the teaching of the concepts of accuracy and precision and the mathematical concept of arctan. The accuracy and precision of a trigonometric experiment using entirely mechanical tools is compared to one using electronic tools, such as a smartphone clinometer application and a laser pointer. This research has demonstrated how two classroom activities based on tool-making can enhance student measurement and application of accuracy and precision considerations through a trigonometric activity investigating arctan.     

Central Schur rings over the projective special linear groups

In [1 Bannai, E. (1991). Subschemes of some association schemes. J. Algebra 14:167–188.[Crossref], [Web of Science ®] , [Google Scholar]], Bannai presents a fusion condition and uses this to consider central Schur rings (S-rings) over the simple groups PSL(2,q) where q is a prime power. In this paper, we concretely describe all such S-rings in terms of symmetric S-rings over cyclic groups. The final section discusses counting these.     

Eine Metallfilmsonde zur Messung von kleinen und schnellen Strömungstemperaturschwankungen

Measurements of the temperature fluctuations in flows are restricted to low fluctuation frequencies, if the temperature probes which have been available and which have a relative high thermal inertia are used. A newly constructed metalfilm probe, which works in principle as a resistance thermometer, overcomes this restriction to a large degree so that temperature fluctuations in the order of 0.01 °C can be measured up to fluctuation frequencies of about 5 kHz. The construction, the procedure of manufacture, and a method of calibration are presented for the newly developed probe, and its applicability for the measurement of temperature fluctuations in flows is demonstrated by some examples (measurements of the natural temperature fluctuations in the wake of a circular rod in air flow at a Reynolds number of about 5 · 10⁴). Some further applications of the probe are mentioned, in which its high sensitivity and its low thermal inertia is especially advantageous (measurement of flow velocities and measurement of fast temperature variations by infra-red detectors).     

Silanols cured by borates as lubricants in extrusion of LLDPE. Impact of elasticity of the lubricant on sliding friction

Addition of a viscoelastic material based on silanols cured by boron oxide was used to delay sharkskin and stick–slip instabilities in extrusion of linear low-density polyethylene (LLDPE). Delay of flow instabilities to rates of extrusion 25–35 times higher than without additive and about 40% less extrusion pressure at the same throughput are achieved by the use of this material as an additive (∼0.1%) to LLDPE or as a coating of the extrusion die. Mechanical properties of the lubricant were changed by small variations of composition to investigate the impact of elasticity on lubrication and sharkskin delay. Both lubrication and sharkskin delay were considerably improved when more elastic lubricants were used while the chemical composition of the lubricants was nearly the same. Filling the lubricants with powders of metal oxides or especially particulates having plate-like particles (kaolin, mica, BN) helped to delay the flow instabilities further to even higher throughputs. Together with experimental results, we present a tentative explanation for the importance of elasticity of polymer processing aids in the delay of sharkskin and the stabilization of slip. This paper was presented at Annual European Rheology Conference (AERC) held in Hersonisos, Crete, Greece, April 27–29, 2006.     

On drag, Strouhal number and vortex-street structure

A phenomenological model for the vortex-shedding process behind bluff cylindrical bodies is proposed. Relationships between Strouhal frequency St, drag coefficient c_D, Reynolds number Re and geometric wake parameters are obtained from mass conservation, momentum conservation in the transverse direction and energy considerations. For the first time, Roshko's (Technical Report TN 3169, NACA, US Government Printing Office, Washington DC, 1954) experimental discovery of vortex-street similarity behind different cylinders is analytically derived. In addition, the empirically obtained Strouhal-frequency laws of Roshko (Technical Report TN1191, NACA, US Government Printing Office, Washington DC, 1954) and Fey (Phys. fluids A 10 (1998) 1547) are also reproduced. Measurements of St and c_D including their Re dependency for flows around cylinders with circular, square, triangular, semi-circular and other cross sections agree favorably with the proposed model.     

A Nonlinear Deterministic Mode Decomposition Strategy for High-Dimensional Monte Carlo Simulations

We present a new reduced Monte Carlo simulation strategy for nonlinear high-order systems based on an extension of the proper orthogonal decomposition for transient excited structures. This novel approach enables the evaluation of the response statistics in a fractional amount of time compared to the full Monte Carlo simulation procedure. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)