China
Africa
Explore chapters and articles related to this topic
Particle Morphological Analysis
Published in John Keith Beddow, T. P. Meloy, Advanced Particulate Morphology, 1980
but an m-sided regular polygon has m-fold rotational symmetry. According to Equation 22, Bk will be nonzero only if k is a whole numer multiple of m or k/2 = integer, i. e., only Bm, B2m, B3m, etc. are nonzero. When k/m is an interger, θ = 2πk/m will be a whole number multiple of 2π and cos 2nπ = 1 for any n. () Bk=−2km[1+1+1+…+1]=−2kmm=−2k
Building-integrated solar photovoltaic thermal (BIPVT) technology: a review on the design innovations, aesthetic values, performance limits, storage options and policies
Published in Advances in Building Energy Research, 2023
Vertical symmetry (V) is much easier to visualize by any observer while equilibrium is said to exist if a structure has vertical symmetry and a horizontal base. The rotational symmetry (R) is related to the characteristics during the rotation of the centre of the object. Usually, if a system has V as 1, then R could also be taken as 1. The object is pleasing if it has an equal vertical to horizontal (VH) network for which 1 is assigned. The aesthetic effect of curvilinear elements is measurable with characteristic tangents (T) whose value could be taken as 0 or 1 due to the absence or presence of curvilinear elements, respectively (Evangelinos & Tscharaktschiew, 2021). The unsatisfactory form (uF) has a negative value whose value is regarded as 0 (say for, satisfactory appearance) and 1 for unpleasing appearance. Based on these ideologies, the aesthetic value (M) could be represented as For simplicity and easy understanding to introduce the researchers about how to use this quantitative measure for the evaluation of the aesthetic appearance of the BIPVT systems, each of the influencing parameters considered in the order (O) may be assigned with the value of 1 or 0 based on whether they exist or not, respectively. The aesthetic value for façade, roof and concentrated PVT for building applications calculated using Equation (2) is tabulated in Table 3. The calculation of the values of vertical symmetry and complexity is shown in Figure 9.
Many-beam dynamical scattering simulations for scanning and transmission electron microscopy modalities for 2D and 3D quasicrystals
Published in Philosophical Magazine, 2019
Saransh Singh, William C. Lenthe, Marc De Graef
In the context of quasicrystals, the forward model for EBSD patterns introduced in Section 2.2 can be used to generate a pattern dictionary for a set of unique orientations. For the icosahedral quasicrystal with the rotational symmetry group of order 60, the fundamental zone in (i.e. the compact region containing all unique orientations) has volume , significantly smaller than that of the highest crystallographic rotational symmetry group , which has a volume of . In the Rodrigues rotation representation, the fundamental zone (RFZ) is bounded by planes normal to the five-fold rotation axes at a distance of from the origin, resulting in a regular dodecahedron. Similar fundamental zones for the cyclic , and rotational points groups (octahedral, decagonal and dodecagonal symmetries, respectively) can also be determined, resulting in prisms with 16, 20 and 24 vertical faces, respectively.
Exact solution of two collinear cracks normal to the boundaries of a 1D layered hexagonal piezoelectric quasicrystal
Published in Philosophical Magazine, 2018
As a new class of condensed matter having quasi-periodic translational symmetry and non-crystallographic rotational symmetry, quasicrystals (QCs) were discovered in 1984 [1]. This new discovery has pushed the material science into a new era. Due to the unique lattice structure, QCs have many special properties, such as low friction coefficients, low adhesion, high wear resistance, and low electrical and thermal conductivity. Therefore, QCs can be used as a surface coating of engines, containers of nuclear fuel, solar cells and thermoelectric converters. The study of QCs has attracted much attention of researchers in physics of condensed matter, materials science, mechanics and others.