Geometrical representation of scattering cross section in cylindrical conductor: Apparent Poynting vectordoi:10.1002/(SICI)1520-6432(199907)82:7<31::AID-ECJB5>3.0.CO;2-Vcylindrical conductorscattering problemscattering cross sectionPoynting vector
––A simple independent method for geometrical construction of two-dimensional coincidence site lattices (CSL) based on vector representation of lattice sites is put forward. In this method, the construction of such CSLs is achieved by mutual rotation of a unique vector, termed a sigma generating...
32 comes from its uniquitous use in representing geometric properties of materials, for example: to estimate coordination numbers33, to capture structural heterogeneity34, to define degenerate Delaunay clusters to study crystallization35, and to generate the representation of crystalline compounds in ...
计算机图形学课件：8 Geometrical Transformations Chapter4GeometricalTransformations MathematicsPreparationfortransformation 1.Vector(矢量）2.Matrix（矩阵）矢量运算(Vector)（1）两个矢量之和：V1V2(x1x2,y1y2,z1z2)（2）两个矢量的点积：V1•V2x1x2y1y2z1z2 （3）矢量的长度：1 1 V1(V1V1)2(x1x1...
In real magnetic lenses the paraxial approximation, which leads to point-to-point representation in the Gaussian focal plane (i.e., the focal plane considered in geometrical optics), breaks down. This is due to the fact that the value of sin β, which enters into the expression for the Lo...
Although, such simulations can be informative in providing understanding of the flow field, they are not very useful in design process and optimisation where the input into surrogate model would need to be the 3D surface mesh representation of the geometry and the design engineers are interested ...
Persistence images: a stable vector representation of persistent homology. J. Mach. Learn. Res. 18, 218–252 (2017). MathSciNet Google Scholar Pun, C. S., Xia, K. & Lee, S. X. Persistent-homology-based machine learning and its applications – a survey. Preprint at https://arxiv....
R 3 - a vector space of dimension 3 over the field R of real numbers. ∧ - exterior product or wedge product The GA representation is implemented in python as G ∘ M . Code is written in TensorFlow 2.4 using Keras high-level API and supports Python 3.6 or higher. Data representation...
microstructure representation dimension reduction 1. Introduction The effective macroscopic properties of a material are significantly affected by the material's microstructure (Olson, Citation1997). Modeling microstructure-properties relationships is, therefore, of great interest in research and industry. In ...
Lower dimensional approximate representation is used for Big Data visualization. The cross-field between topology and Big Data will bring huge opportunities, as well as challenges, to Big Data communities. This survey aims at bringing together state-of-the-art research results on geometrical and ...