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rather than the spatially resolved velocities that are predicted by CFD. Further, an experimental RTD will include effects of eddy or molecular diffusion that are not reliability captured by current CFD codes. Most CFD codes use convergence acceleration techniques that cause numerical diffusion that is an artifact of the computation. Numerical diffusion mimics molecular or eddy diffusion, although to an indeterminate extent. Modern CFD codes are used routinely to calculate residence time distributions in complex ow systems such as static mixers. Care must be taken to sample according to ow rate rather than spatial position, and the number of particles must be surprisingly large for accurate results, particularly for the chaotic ow elds found in motionless mixers. The simulation of the recycle curve in Figure 1-2b used 218 tracer particles. The tail of the washout functions provides a demanding test for freedom from numerical diffusion. In the complete absence of diffusion, residence time distributions in laminar ow have slowly decreasing tails that give in nite variances. Speci cally, they have algebraic tails for which W(t) decreases as t 2 so that all moments higher than the rst diverge. Diffusion will cause the distributions to have rapidly decreasing exponential tails. The conclusion is that improvements in CFD codes and still faster computers are needed for accurate design calculations in complex geometries. Residence time calculations will be a useful tool for their validation. The situation becomes even more dif cult when the equations of motion are combined with convective diffusion equations to estimate reactions yields and heat transfer. We anticipate signi cant near-term improvements in CFD codes, but they are now at the cutting edge of technology and have not yet become everyday tools for the practicing engineer.

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q(=1) (0:6, 0:0, 0:3, 0:1) q(=3) (0:4, 0:4, 0:1, 0:1)

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Another factor to avoid is cross-colors, or overlapping patterns, that tend to confuse an analog video signal. This problem derives from fine patterns of similar color, which cause the chrominance and luminance elements of composite signals to leak into each other. The limited bandwidth of a composite signal causes luminance information to be interpreted as color. A comb filter can be applied to help separate the signals and compensate for minor variations in color. Comb filters are an essential part of a TV's composite input. They perform an important function, although they often degrade one part of a signal while improving another. If you are using Y/C, or S-Video inputs, then you won't have to worry about using a comb filter, because luminance and chrominance information is already separated. Next to color and brightness information, the relative size of a frame is an important element to consider.

16 or 17 + HA 15 + A-[

Purpose: This step scrolls the document window to the desired position or in the indicated direction.

where the term k2 in Equation (8.6) is replaced by the equivalent term kET in Equation (8.112) that is the rate constant for the actual electron transfer step, about which more later! Term /[D]0 represents the rate of the total electron transfer process described by the kinetic scheme above. Equation (8.112) neatly rearranges to k1 kET [A] = [D]0 kET + k 1 + k1 [A] k 1 + k1 [A], Equation (8.113) reduces to = k1 [A] [D]0 (8.114)

One way to select overlapping objects is by choosing Object Select and then choosing the appropriate command. Figure 9.2 shows the Select submenu and its options, as well as the equivalent buttons in the Control panel. The first four options let you select another object relative to the currently selected object: n First Object Above selects the topmost object. n Next Object Above selects the object immediately on top of the current object. n Next Object Below selects the object immediately under the current object. n Last Object Below selects the bottommost object. If no objects are selected, InDesign bases its selection on the creation order.

Excel enables you to use data from a variety of other sources for your PivotTable reports. There are two general ways to do this:

It s important to understand that you can t use worksheet functions that have an equivalent VBA function. For example, VBA can t access Excel s SQRT worksheet function because VBA has its own version of that function: Sqr. Therefore, the following statement generates an error:

If you press the Shift key while dragging the corner resizing handle, you maintain the current aspect ratio.

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