Geometrically, a vector often encompasses coordinates in ann-dimensional space (nrefers to the quantity of dimensions, for instance, two). It signifies the position of a coordinate in ann-dimensional space. In theCartesian coordinate system, vector quantities are represented in a space with an x ...
As noted above, the equations governing the dynamics of a two-dimensional weakly nematic fluid subject to linear friction have been derived in our previous publication [45]. They can be projected into Cartesian coordinates as $$\begin{aligned} p_{,x} -\nu _3 \left( \lambda _+ v_{x,...
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,...
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...
chess set - checkerboard and a set of 32 pieces used to play chess manicure set - a set of implements used to manicure join, sum, union - a set containing all and only the members of two or more given sets; "let C be the union of the sets A and B" Cartesian product, intersection...
such as a Cartesian grid. Participants appropriated the artifacts as strategic or discursive means of accomplishing their goals. Yet, so doing, they found themselves attending to and engaging certain other embedded affordances in these artifacts that they had not initially noticed yet were supporting ...
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...
18. The system according to claim 17, further including: a three-dimensional image memory for storing image data indicative of a three-dimensional region of a portion of a subject which is disposed on the subject support; a plane selector for selecting planar slices of data from the three-di...
The boundaries of the halfspaces are defined in a three-dimensional, mathematical object space 28 (FIG. 3) by mathematical functions expressed in the Cartesian coordinate system variables x, y, and z. Linear functions of the variables x, y, and z define the boundaries of planar halfspaces; ...