Geometrically, a vector often encompasses coordinates in an n-dimensional space (n refers to the quantity of dimensions, for instance, two). It signifies the position of a coordinate in an n-dimensional space. In the Cartesian coordinate system, vector quantities are represented in a space with...
The Cartesian base vectors i1,i2,n and the corresponding coordinates x1,x2 and z are used to specify the position vectors in the reference state. l1 and l2 designate the length and the width of the plate while hT,hC, and hB denote the thicknesses of the top, core and bottom layers,...
where Φ represents interatomic force constants (IFCs) within a cluster of atoms (e.g.,a,b) in their respective Cartesian displacement directions (e.g.,i,j). The second-order IFCs describe pairwise interactions and thus define harmonic phonons. These can be easily obtained using the now wide...
In practice, the choice of the selection box size is left to the user, and it is straightforward in the case of a uniform Cartesian grid, for which the box should be slightly larger than a cell so that CS cells are always located. VOF models are also known to suffer from the ...
where Φ represents interatomic force constants (IFCs) within a cluster of atoms (e.g.,a,b) in their respective Cartesian displacement directions (e.g.,i,j). The second-order IFCs describe pairwise interactions and thus define harmonic phonons. These can be easily obtained using the now wide...
From Tranquility one passes to Admiration (Fig. 4), then to Amazement until reaching, through a gradual increase 10 Inspired by the Cartesian theories exposed in the treatise Les pas- sions de l'âme del 1649. 11 We shall illustrate, throughout this essay, how the concept of "...
It was to get over this very difficulty that the Cartesians invented the system of Occasional Causes. They could not conceive that thoughts in a mind could produce movements in a body, or that bodily movements could produce thoughts. They could see no necessary connexion, no relation à ...
To describe the surface-based lattice structures of FLatt Pack, some basic nomenclature must be introduced. The lattice design space is a simple Cartesian frame, with axes x, y and z. ki are the lattice function periodicities, defined by(1)ki=2πni,where i = x, y, z, and ni are...
Sensor position is delineated using the Cartesian coordinate system that specifies each point uniquely in a plane (X, Y, Z), whilst its orientation is captured using a combination of three angular quantities: azimuth, pitch and roll. Data is gathered from the tracking sensors through space, ...
To analyze two-dimensional scanpaths projected onto the screen in a typical Cartesian coordinate plane, the data was standardized via a cleaning procedure. Tobii Analyzer’s automated gaze mapping uses pattern analysis of the ongoing video and still image of the scene, ascribing fixations to a snap...