scholarly journals The ⊥-Illusion Is Not a T-Illusion

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1330
Author(s):  
Klaus Landwehr
Keyword(s):  
J Curve ◽  
S Curve ◽  

Variants of the capital Latin letter T were prepared with the straight strokes replaced by J-, C-, or S-curves, mimicking handwritten Ts. These were used to test the hypothesis that the overestimation of the length of the T’s undivided line, relative to the length of its divided line may be understood as an adaptation to a corresponding letter schema. The illusion was greater for S-curve Ts than for C- and J-curve Ts, suggesting that approximate bilateral mirror symmetry is more important for the illusion to occur than letterness. Despite the illusion, observers were quite sensitive to the different lengths of the Ts’ curves.

Author(s):  
Jeanne C. Samuel

This article proposes a hypothetical model for determining rate of diffusion of an innovation in a system. The model modifies Everett Rogers’ S-curve using an index created from Gartner’s hype cycle phases. Rogers’ model for technology innovation adoption demonstrates that cumulative technology diffusion in a system from zero through the late majority adopters’ phase forms a curve resembling the letter “S”. Hype cycles analyze the five emotional stages technology adopters go through from over-enthusiasm (hype) though disappointment until it plateaus (beginning of mainstream adoption). When numbers assigned to the phases of adoption from the hype cycle are used as multipliers and applied to the cumulative adoption data of an innovation (Rogers’ S-curve), the “S” becomes a “J”. With the J-curve you can determine the rate of innovation diffusion in an organization.


Author(s):  
Yoichi Ishida ◽  
Hideki Ichinose ◽  
Yutaka Takahashi ◽  
Jin-yeh Wang

Layered materials draw attention in recent years in response to the world-wide drive to discover new functional materials. High-Tc superconducting oxide is one example. Internal interfaces in such layered materials differ significantly from those of cubic metals. They are often parallel to the layer of the neighboring crystals in sintered samples(layer plane boundary), while periodically ordered interfaces with the two neighboring crystals in mirror symmetry to each other are relatively rare. Consequently, the atomistic features of the interface differ significantly from those of cubic metals. In this paper grain boundaries in sintered high-Tc superconducting oxides, joined interfaces between engineering ceramics with metals, and polytype interfaces in vapor-deposited bicrystal are examined to collect atomic information of the interfaces in layered materials. The analysis proved that they are not neccessarily more complicated than that of simple grain boundaries in cubic metals. The interfaces are majorly layer plane type which is parallel to the compound layer. Secondly, chemical information is often available, which helps the interpretation of the interface atomic structure.


Author(s):  
Hamish L. Fraser

The topic of strain and lattice parameter measurements using CBED is discussed by reference to several examples. In this paper, only one of these examples is referenced because of the limitation of length. In this technique, scattering in the higher order Laue zones is used to determine local lattice parameters. Work (e.g. 1) has concentrated on a model strained-layer superlattice, namely Si/Gex-Si1-x. In bulk samples, the strain is expected to be tetragonal in nature with the unique axis parallel to [100], the growth direction. When CBED patterns are recorded from the alloy epi-layers, the symmetries exhibited by the patterns are not tetragonal, but are in fact distorted from this to lower symmetries. The spatial variation of the distortion close to a strained-layer interface has been assessed. This is most readily noted by consideration of Fig. 1(a-c), which show enlargements of CBED patterns for various locations and compositions of Ge. Thus, Fig. 1(a) was obtained with the electron beam positioned in the center of a 5Ge epilayer and the distortion is consistent with an orthorhombic distortion. When the beam is situated at about 150 nm from the interface, the same part of the CBED pattern is shown in Fig. 1(b); clearly, the symmetry exhibited by the mirror planes in Fig. 1 is broken. Finally, when the electron beam is positioned in the center of a 10Ge epilayer, the CBED pattern yields the result shown in Fig. 1(c). In this case, the break in the mirror symmetry is independent of distance form the heterointerface, as might be expected from the increase in the mismatch between 5 and 10%Ge, i.e. 0.2 to 0.4%, respectively. From computer simulation, Fig.2, the apparent monocline distortion corresponding to the 5Ge epilayer is quantified as a100 = 0.5443 nm, a010 = 0.5429 nm and a001 = 0.5440 nm (all ± 0.0001 nm), and α = β = 90°, γ = 89.96 ± 0.02°. These local symmetry changes are most likely due to surface relaxation phenomena.


Author(s):  
Jean-Luc Rouvière ◽  
Alain Bourret

The possible structural transformations during the sample preparations and the sample observations are important issues in electron microscopy. Several publications of High Resolution Electron Microscopy (HREM) have reported that structural transformations and evaporation of the thin parts of a specimen could happen in the microscope. Diffusion and preferential etchings could also occur during the sample preparation.Here we report a structural transformation of a germanium Σ=13 (510) [001] tilt grain boundary that occurred in a medium-voltage electron microscopy (JEOL 400KV).Among the different (001) tilt grain boundaries whose atomic structures were entirely determined by High Resolution Electron Microscopy (Σ = 5(310), Σ = 13 (320), Σ = 13 (510), Σ = 65 (1130), Σ = 25 (710) and Σ = 41 (910), the Σ = 13 (510) interface is the most interesting. It exhibits two kinds of structures. One of them, the M-structure, has tetracoordinated covalent bonds and is periodic (fig. 1). The other, the U-structure, is also tetracoordinated but is not strictly periodic (fig. 2). It is composed of a periodically repeated constant part that separates variable cores where some atoms can have several stable positions. The M-structure has a mirror glide symmetry. At Scherzer defocus, its HREM images have characteristic groups of three big white dots that are distributed on alternatively facing right and left arcs (fig. 1). The (001) projection of the U-structure has an apparent mirror symmetry, the portions of good coincidence zones (“perfect crystal structure”) regularly separate the variable cores regions (fig. 2).


Author(s):  
Elena Makarycheva

The aim of the article is to develop a method for calculating water losses from irrigation channels in determining the permeability of rock in the zone of filtration flow on the basis of the law of infiltration A.N. Kostyakov using the results of studies of free filtration from pits and foundation pits in loess loams. Pressure movement of water in irrigation canals is subject to the laws of two-phase flow, in which – in contrast to the Darcy law for the zone of saturation plays an important role, the volume and its change in time. The filtration rate (VF) increases with increasing rock moisture (θ) along the S-curve, while the pressure gradient (I = dh/dz) decreases. The dependences of these parameters on the pressure are represented by power functions, and their product CDP = VFI does not change in time and can serve as a characteristic of the filtration flow under the channel. When installing paired piezometers near the water chore line in the channel and determining the graph I(t) by the value of the twophase flow constant CDP, it is possible to calculate the filtration rate at a number of times and the water losses during unsteady filtration. Water losses from the channels at equilibrium humidity increases with increasing head according to the formula A.N. Kostyakova, in which the water permeability of rocks is characterized by a steady filtration rate at a head of 1.0 m, and the gradient is the function of pressure. The application of the proposed method of calculating losses in the design of irrigation systems will increase the reliability of the justification of the volume of anti-filtration measures and the forecast of the groundwater level.


2011 ◽  
Vol 29 (supplement) ◽  
pp. 283-304 ◽  
Author(s):  
Timothy R. Brick ◽  
Steven M. Boker

Among the qualities that distinguish dance from other types of human behavior and interaction are the creation and breaking of synchrony and symmetry. The combination of symmetry and synchrony can provide complex interactions. For example, two dancers might make very different movements, slowing each time the other sped up: a mirror symmetry of velocity. Examining patterns of synchrony and symmetry can provide insight into both the artistic nature of the dance, and the nature of the perceptions and responses of the dancers. However, such complex symmetries are often difficult to quantify. This paper presents three methods – Generalized Local Linear Approximation, Time-lagged Autocorrelation, and Windowed Cross-correlation – for the exploration of symmetry and synchrony in motion-capture data as is it applied to dance and illustrate these with examples from a study of free-form dance. Combined, these techniques provide powerful tools for the examination of the structure of symmetry and synchrony in dance.


This volume provides the first comprehensive overview of the extant Greek and Latin letter collections of late antiquity (ca. 300-600 C.E.). Bringing together an international team of historians, classicists, and scholars of religion, it illustrates how letter collections advertised an image of the letter writer and introduces the social and textual histories of each collection. Nearly every chapter focuses on the letter collection of a different late ancient author—from the famous (or even infamous) to the obscure—and investigates its particular issues of content, arrangement, and publication context. On the whole, the volume reveals how late antique letter collections operated as a discrete literary genre with its own conventions, transmission processes, and self-presentational agendas while offering new approaches to interpret both larger letter collections and the individual letters contained within them. Each chapter contributes to a broad argument that scholars should read letter collections as they do representatives of other late antique literary genres, as single texts made up of individual components, with larger thematic and literary characteristics that are as important as those of their component parts.


2018 ◽  
Vol 26 (2) ◽  
Author(s):  
Dean A. Forbes

In a recent essay published in this journal, I illustrated the limitations one may encounter when sequencing texts temporally using s-curve analysis. I also introduced seriation, a more reliable method for temporal ordering much used in both archaeology and computational biology. Lacking independently ordered Biblical Hebrew (BH) data to assess the potential power of seriation in the context of diachronic studies, I used classic Middle English data originally compiled by Ellegård. In this addendum, I reintroduce and extend s-curve analysis, applying it to one rather noisy feature of Middle English. My results support Holmstedt’s assertion that s-curve analysis can be a useful diagnostic tool in diachronic studies. Upon quantitative comparison, however, the five-feature seriation results derived in my former paper are found to be seven times more accurate than the single-feature s-curve results presented here. 


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