Dimensional Terms

In dimensional terms, this adiabatic ignition time is... 

Another group of similarity solutions corresponds to the initial discontinuity condition (3.2.4b), which might be rewritten in dimensional terms as... 

In dimensional terms the maximum value of the intermediate concentration is... 

If the problem were being done for a specific value of the pressure-gradient parameter in dimensional terms, the problem would be solved once the spreadsheet has completed its iterations. The correct velocities would be contained in each of the cells. However, for the... 

Because all the dimensional material and dynamic multiplexes are reported only for the LM or for the prototype, we can combine these r q dimensional multiplexes and the characteristic geometric parameters (so we have r q-tl dimensional terms) to formulate new dimensionless independent multiplexes. It is not difficult to observe that these independent dimensionless multiplexes are the dimensionless pi groups that characterize the evolution of the phenomenon. If III, n2,.ris represent the dimensionless groups that characterize the evolution of the phenomenon in the laboratory device or in the prototype, we transform the similitude postulate into the next new statement ... 

There are two other forms of pellet that allow a simple solution in one-dimensional terms. The first is the cylinder with sealed ends which has axial symmetry. Taking Z to be its radius, the effectiveness factor is given by the ratio of two modified Bessel functions (see Appendix)... 

Nevertheless, notice how the quoted definition is still structured in three dimensional terms the body is implicitly a vessel containing the psyche which is also a vessel containing a hierarchy of upper and lower worlds which are accessed via a central vertical axis. It is a kind of Chinese box image-- worlds within worlds within worlds. Given our physical restriction to three-dimensional space, this is probably as good... 

This makes the physical body a kind of vessel which "contains" higher dimensional constructs. In three-dimensional terms it is logically absurd for a vessel to be smaller than its contents, yet this is not an inevitable conclusion if other dimensions are factored into the equation. Another way to conceptualize this is to think of space/time as the "outer" projection of an inner infinity. Imagine what it would be like to be a two-dimensional entity living on one of the six faces of a cube. 

Since the sequence of dimensional terms in the covariance does not affect the results, that is, cov(x,y) = cov(y,x), the covariance matrix is a symmetric one. The main diagonal shows the self-products and, thus, the variances for the dimension. 

The remaining term, the dimensional term, is tq. Determine its value. 

The evolution of u with respect to 1 is plotted in Fig. 3-12. As in previous examples of start-up flows, we see that the momentum from the lower wall propagates across the gap by means of diffusion in a dimensionless time interval 1 = 0(1), or, in dimensional terms,... 

The governing equations for the coefficient functions gn(t) are obtained by the standard perturbation procedure of substituting expansion (4-227) into the Ray leigh-Plesset equation in the form (4—208) and then equating the sum of all terms at each order in s to zero. The result at 0(1), expressed in dimensional terms, is... 

If we convert (5-90) and (5-91) to dimensional terms, the pressure distribution becomes... 

Equations (6-83) and (6-85) govern the dynamics of any time-dependent changes in the shape of the thin film, subject of course to the long-wavelength approximation, (6-86). Hence, if we wish to study the stability of the thin film to some perturbation of shape from the uniform ho, we consider some specified initial shape that we can represent symbolically (in dimensional terms) as... 

Note In dimensional terms, the steady-state distribution of A in the liquid is governed by... 

The hydrostatic pressure variation at the bubble surface, in dimensional terms, is... 

Fig. 5 Non-dimensional flame standoff distance and Peclet number based on flame standoff distance (ratio of bulk-to-diffusion velocity) for benchmark case (Table 1). Note that in dimensional terms xg for small Eg is actually greater than that for large Eg for comparable...

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