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Morphogenesis
Published in A. Šiber, P. Ziherl, Cellular Patterns, 2018
respectively. Here X is the coordinate along the azimuthal direction and Y is the radial coordinate. The magnitudes of the two modes are controlled by dimensionless parameters τ1 and τ2. In the apical constriction, a square domain of edge length a is transformed into an isosceles trapezoid of base lengths (1 + τ1a/2)a and (1 - τ1a/2)a and the apico‐basal contraction/elongation is an example of a pure‐shear deformation which changes the aspect ratio of a rectangular cell, turning, e.g., a square domain into a rectangle of sides (1 + τ2)a and a/(1 + τ2) . In both modes the area of the epithelium is locally preserved.
Shear behavior and acoustic emission characteristics of regular dentate joints
Published in Charlie C. Li, Xing Li, Zong-Xian Zhang, Rock Dynamics – Experiments, Theories and Applications, 2018
C.D. Su, H.Z. Zang, J.Q. Guo, Y.N. Sun, C.S. Song, W. Wang
Due to the complexity and difficulties in making in-situ joint, artificial joint with simple geometrical characteristics is generally adopt in laboratory research (Zhang et al. 2016). In this paper, concrete-made dentate joint with different teeth height are adopted. Customized mould with isosceles trapezoid teeth whose height and addendum width are 0 mm, 2 mm, 3 mm, 4 mm. Also, 45o teeth angle are designed for making dentate joint (Figure 1), the specimen number A2–1 means 2 mm teeth height for the 1st test.
A fast detection method for tunnel surface defects based on video processing
Published in Daniele Peila, Giulia Viggiani, Tarcisio Celestino, Tunnels and Underground Cities: Engineering and Innovation meet Archaeology, Architecture and Art, 2019
Figure 4 shows the result of the edge identification of the tunnel rings by Canny operator with image dodging. The red border in Figure on the left is the result of the Isosceles trapezoid fitting of the edge identified by of Canny operator. Figure on the right shows the image processed by uniform light, which is the original image in this part.
Scattering of SH waves by an isosceles flat-topped hill with multistage slopes
Published in Waves in Random and Complex Media, 2021
Zailin Yang, Yunqiu Song, Yong Yang, Xinzhu Li, Menghan Sun
The second approach of verification is to make so that the hill is shaped as an isosceles trapezoid. The span of the hill is set to 2.0, the height is 1.0, the width of the hill is 1.0, and the SH wave is incident vertically, considering both and . As can be seen in Figure 4(a), the auxiliary boundary (green line) delineated from the hillside is non-essential. But the redundant auxiliary boundary that does not exist in Ref. [29] is due to the introduction of MRMT in this paper and must be taken into account when validating the results. The comparison between our results and published numerical results of Shyu and Teng [31] is shown in Figure 4(b). The surface displacement amplitudes corresponding to the two dimensionless frequencies are in good agreement with those of Shyu and Teng [31], then it can be argued that the redundant auxiliary boundaries have no effect on the correctness of the calculations. In other words, the individual hill model can be decomposed by MRMT and it is feasible to set the slope value for each subregion separately.
Tailoring surface patterns to direct the assembly of liquid crystalline materials
Published in Liquid Crystals Reviews, 2019
Yu Xia, Apiradee Honglawan, Shu Yang
Shojaei-Zadeh et al. [94] also investigate the 3D confinement effect of 8CB using a closed rectangular microchannel system with three PDMS surfaces to impose homeotropic anchoring and the fourth one as plasma-oxidized PDMS for planar anchoring (Figure 20). Both toroidal and non-toroidal FCDs are formed, and the transparent PDMS cell allowed for direct observation of interesting LC textures under POM. The formation of FCDs is strongly affected by the channel size (Figure 20), which effectively tunes the balance between surface anchoring energy and layer bending energy. Kim et al. [95] further investigate the effect of shapes of 1D channels, including rectangle, V-shape, and isosceles trapezoid (Figure 21). More complex FCD textures, including half FCDs, circular FCDs, and diminished FCDs are generated due to the variation in surface anchoring energy from the bottom and side walls of channels. Since the growth of FCDs must be accommodated by bending smectic layers around the axial defect core, highly regular TFCDs are formed in the trapezoidal channels with antagonistic boundary conditions, and the size of TFCDs is dependent on the channel depth.
Comparing the concept images and hierarchical classification skills of students at different educational levels regarding parallelograms: a cross-sectional study
Published in International Journal of Mathematical Education in Science and Technology, 2022
In this study, the participants were asked whether the scalene quadrilateral (Figure F) and isosceles trapezoid (Figure A) were parallelograms along with their reasoning behind their determination. Thus, the results regarding the answers of the participants were provided in Table 4 as well as their reasoning was given in Table 5. The percentages of participants who gave the correct hierarchical classification regarding non-parallelogram shapes are given in Figure 4.