Three different algorithms, as implemented in three different computer programs, were put to the task of extracting direct space lattice parameters from four sets of synthetic images that were per design more or less periodic in two dimensions (2D). One of the test images in each set was per design free of noise and, therefore, genuinely 2D periodic so that it adhered perfectly to the constraints of a Bravais lattice type, Laue class, and plane symmetry group. Gaussian noise with a mean of zero and standard deviations of 10 and 50% of the maximal pixel intensity was added to the individual pixels of the noise-free images individually to create two more images and thereby complete the sets. The added noise broke the strict translation and site/point symmetries of the noise-free images of the four test sets so that all symmetries that existed per design turned into pseudo-symmetries of the second kind. Moreover, motif and translation-based pseudo-symmetries of the first kind, a.k.a. genuine pseudo-symmetries, and a metric specialization were present per design in the majority of the noise-free test images already. With the extraction of the lattice parameters from the images of the synthetic test sets, we assessed the robustness of the algorithms’ performances in the presence of both Gaussian noise and pre-designed pseudo-symmetries. By applying three different computer programs to the same image sets, we also tested the reliability of the programs with respect to subsequent geometric inferences such as Bravais lattice type assignments. Partly due to per design existing pseudo-symmetries of the first kind, the lattice parameters that the utilized computer programs extracted in their default settings disagreed for some of the test images even in the absence of noise, i.e., in the absence of pseudo-symmetries of the second kind, for any reasonable error estimates. For the noisy images, the disagreement of the lattice parameter extraction results from the algorithms was typically more pronounced. Non-default settings and re-interpretations/re-calculations on the basis of program outputs allowed for a reduction (but not a complete elimination) of the differences in the geometric feature extraction results of the three tested algorithms. Our lattice parameter extraction results are, thus, an illustration of Kenichi Kanatani’s dictum that no extraction algorithm for geometric features from images leads to definitive results because they are all aiming at an intrinsically impossible task in all real-world applications (Kanatani in Syst Comput Jpn 35:1–9, 2004). Since 2D-Bravais lattice type assignments are the natural end result of lattice parameter extractions from more or less 2D-periodic images, there is also a section in this paper that describes the intertwined metric relations/holohedral plane and point group symmetry hierarchy of the five translation symmetry types of the Euclidean plane. Because there is no definitive lattice parameter extraction algorithm, the outputs of computer programs that implemented such al...

A new series of introductory physics experiments for teaching the kinematics and dynamics of falling bodies is presented. These learning activities are enabled by newly available position-tracking technology that allows for the direct acquisition of coordinate data from moving objects. Students are led through an iterative inquiry process that explores both free fall and drag-enhanced physical models, for different velocity regimes, emphasizing a comparative modeling approach to science. Learners discover how the experimental design, including the properties of the dropped objects, the dropping distance, and the uncertainty of the measuring device, impacts the ability to explore the validity of physical models with or without drag.

The BINSYN program suite, a collection of programs for analysis of binary star systems with or without an optically thick accretion disk, is available for download from a wiki. This article describes the package, including download instructions. BINSYN produces synthetic spectra of individual binary star components plus a synthetic spectrum of the system. If the system includes an accretion disk, BINSYN also produces a separate synthetic spectrum of the disk face and rim. A system routine convolves the synthetic spectra with filter profiles of several photometric standards to produce absolute synthetic photometry output. The package generates synthetic light curves and determines an optimized solution for system parameters. This article includes illustrative literature references that have used the suite, including mass transfer rates in several cataclysmic binary systems.

Tracking the motion of an object in 2D as a demonstration in a physics classroom or as a laboratory activity is difficult to accomplish in real time with traditional equipment used by educators. A local positioning system (LPS), like the Pozyx Creator series LPS, has a potentially wide range of educational applications for introductory physics courses. In a previous article we reported using this product to track one-dimensional motion, pressure, rotation, and magnetic field data, but here we discuss how such systems can provide location information (to within approximately ±10 cm) in one, two, and potentially three dimensions both indoors and outdoors.

Recently available local positioning systems (LPS) have the potential to be used for interactive physics laboratory activities and classroom demonstrations. The Pozyx LPS combines multiple sensors with position data for any object that one of the devices is attached to. Devices referred to as “tags” (Fig. 1[a]) are mobile devices that can be tracked, and those referred to as “anchors” are stationary devices that are employed to calculate the tag’s position. At data rates of 30 Hz (2D and 3D tracking) to 200 Hz (1D tracking), the position is measured to an accuracy of about ±10 cm. We have found that this particular LPS works best for physics laboratory setups at distance scales of at least two meters and up to tens of meters.