where [E.sub.p] is a scalar variable
denoting z component of the electric field on the surface of the polymer film under the line patterns and [E.sub.l] is a scalar variable
denoting z component of the electric field on the surface of the polymer film under the template cavity in right side of these patterns.
If the box showing the linkages between the Categorical variable and the Scalar variable shows the following connection as definitely checked:
There is only one value of the scalar variable remaining, and so [P.sub.1] must be associated with it:
For a problem whose structure was [PCS], this meant that the participant would always see statements in the problem's text that connected a value on the Person variable, (i.e., a name) with a value on the Scalar variable, and statements that connected a value on the Categorical variable with a value on the Scalar variable, or [P-S, C-S].
There are three scalar variables in its composition: [D.sub.2], [D.sub.3] and [D.sub.5], besides [D.sub.4], related to pre-existing tensile effects.
where [[??].sub.T] [not equal to] 0 or [[??].sub.C] [not equal to] 0, it is necessary to update the damage scalar variables values which appear in the tensors [D.sub.T] and [D.sub.C], considering their laws of evolution.
Based in model (3), the objective function consists of (3+1) x K = 4 K scalar square terms, and the number of scalar variables
in Z is 3K+4.
New information has been added on such topics as droplet-droplet interactions, the use of the mass-flux potential, conserved scalar variables
, spatial averaging and the formulation of the multicontinua equations, the confluence of spatial averagings for sprays and filtering for turbulence, direct numerical simulations and large-eddy simulations for turbulent sprays, and high-pressure vaporization processes.