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Analyses and Numerical Simulations of Basic Two-Phase Flows
Published in Clement Kleinstreuer, Theory and Applications, 2017
The first array read is the ipijk pointer, which points from element-space to ijk-space. The next array is the iplocn array which stores two pieces of information, the reverse pointer from ijk-space back to element-space plus another remnant of CFX-4 topology — the local i, j, k location (related to the number of x, y, and z discretizations of a block) and block number. Although not strictly necessary, this was included for comparison purposes because the code of Hyun (1998) initialized variables this way and is convenient for generating regularly spaced positions in geometries. The ipvert array is defined, which points from element-space to vertex- space, thus for each control volume, the surrounding vertices are known. Finally, the ijkdex array is constructed. The ijkdex array is one of the features of the code used to increase performance. It stores two things in ijk-space, a boundary indicator and a pointer to the surrounding elements. The boundary indicator is zero everywhere except for along boundaries, in which case the nonzero integer defines the type of boundary it is for the subroutine domain_chk (used in the integration routine). The pointer to the surrounding elements is used in the local_move subroutine (again in integration) to avoid complete domain searches whenever possible. Associated with the boundary indicator is another variable storing the normal direction from the surface (again to be used in the domain_chk routine). Finally, before the topological stacks are complete, one modification must be made. Using the routines in CFX-4 and calling across block boundaries causes a problem for elements that differ by more than one integer location.
Spanning Trees
Published in Jonathan L. Gross, Jay Yellen, Mark Anderson, Graph Theory and Its Applications, 2018
Jonathan L. Gross, Jay Yellen, Mark Anderson
Analogous to the edge space WE(G), the collection of vertex subsets of VG under ring sum forms a vector space over GF(2), which is called the vertex space of G and is denoted WV (G). Each element of the vertex space WV (G) may be viewed as an n-tuple over GF(2).
Discrete Mathematics
Published in Dan Zwillinger, CRC Standard Mathematical Tables and Formulas, 2018
vertex space: The vertex space of a graph G is the vector space of all mappings from V to the two-element field GF(2) . The elements of the vertex space are called 0-chains.
Analysis and Evaluation of Cyber-attack Impact on Critical Power System Infrastructure
Published in Smart Science, 2021
Neeraj Kumar Singh, Vasundhara Mahajan
Using assumptions stated in subsection 3.2, TBCIF algorithm is developed while considering n agents equal to number of vertices. Using a graph G which consists of vertex and edges can be mapped using vertex space of G into reals. In a similar manner y mapped using edge space of G into real. Generally, Power system communication network follow single integrator dynamics, which can be expressed as follows: