Idealized profile

In fig. 2 an ideal profile across a pipe is simulated. The unsharpness of the exposure rounds the edges. To detect these edges normally a differentiation is used. Edges are extrema in the second derivative. But a twofold numerical differentiation reduces the signal to noise ratio (SNR) of experimental data considerably. To avoid this a special filter procedure is used as known from Computerised Tomography (CT) /4/. This filter based on Fast Fourier transforms (1 dimensional FFT s) calculates a function like a second derivative based on the first derivative of the profile P (r) ... 

Figure 1. Idealized Profile of a Blast Wave from a Condensed High Explosive.(Courtesy Oyez Scientific and Technical Services Ltd.)...

In sediments that lie in coastal waters, organic carbon levels are high enough to support denitrification, iron respiration, sulfate reduction and methanogenesis. As shown in the idealized profile presented in Figure 12.3b, the depth of O2 penetration in organic-rich sediments is typically so shallow as to make the zones of aerobic respiration. 

Figure 4 indicates the ranking of similarity of the 16 Pd catalysts with respect to the hypothetical ideal profile shown in Figure 3. Accordingly, catalyst DEG-3 appears to be the preferable catalyst for the selective hydrogenation of hydroxy-olefin. DEG-16, DEG-14 and DEG-12 are also expected to give high yield of the saturated alcohol.

The condition for the practical implementation of such a feed control is the availability of a computer controlled feed system and of an on-line measurement of the accumulation. The later condition can be achieved either by an on-line measurement of the reactant concentration, using analytical methods or indirectly, by using a heat balance of the reactor. The amount of reactant fed to the reactor corresponds to a certain energy of reaction and can be compared to the heat removed from the reaction mass by the heat exchange system. For such a measurement, the required data are the mass flow rate of the cooling medium, its inlet temperature, and its outlet temperature. The feed profile can also be simplified into three constant feed rates, which approximate the ideal profile. This kind of semi-batch process shortens the time-cycle of the process and maintains safe conditions during the whole process time. This procedure was shown to work with different reaction schemes [16, 19, 20], as long as the fed compound B does not enter parallel reactions. 

Figure 7.3 Illustration of possible injection profiles, (a) ideal profile (theoretical) (b) ideal situation (practical) (c) practical profile (d) practical profile with tail cut off .

The temperature usually rises towards the end of a project, as the deadline approaches (Figure N2-10). This seems natural and unavoidable. However, if you start early, and try to have some result at any moment, the problems will be less acute. What would the ideal profile be like We suggest that it would have the highest degree of activity (temperature) in the beginning. As a result, you would have time to perfect things at the end, and to feel comfortable at the hnal presentation. Do you remember the time that you had prepared that examination early enough ... 

The potent, prolonged vasoconstrictor effects of endothelin (particularly ET-1), in addition to its mitogenic action, constitutes the ideal profile for a potential pathological role in the cardiovascular system. Thus, in disease states where elevated local or plasma levels of endothelin have been found, the question of whether endothelin plays a causative role has been addressed. 

Fig. 7 (A) Idealized profile of the concentration gradient near the surface of the electrode and (B) an illustration of a deposition instability in the presence of an asperity.

Eor the Plateau border we have z > / , 11 -> 0, o -> o = const., and both Equations 5.150 and 5.151 rednce to Eqnation 5.101 with AP = P. The macroscopic contact angle, a, is defined as the angle at which the extrapolated meniscns, obeying Equation 5.101, meets the extrapolated film snrface (see the dashed line in Fignre 5.16). The real surface, shown by solid line in Figure 5.16, differs from this extrapolated (idealized) profile, because of the interactions between the two film snrfaces, which is taken into acconnt in Eqnation 5.150, but not in Eqnation 5.101. To compensate for the difference between the real and idealized system, the line and transversal tensions are ascribed to the contact line in the macroscopic approach. In particnlar, the line tension makes up for the differences in snrface tension and running slope angle ... 

In reality, few systems are Newtonian, and some of the other principal rheological profiles are also shown in Figure 5.1. In many cases a Newtonian behavior is not desirable for a formulated product. This can be illustrated by the case of a spray cleaner. A certain minimum viscosity is often required such that the material appears to be concentrated in the bottle. The visual appearance is referred to in this chapter as the apparent viscosity and is generally considered to correspond to a shear rate of the order of 10 sec-1 (reciprocal seconds). If the formulation is Newtonian, then the viscosity will remain the same even at the relatively high shear rates corresponding to spraying (Figure 5.2). This is not desirable, as the spray pattern obtained varies considerably with the viscosity of the fluid in the spray nozzle, and better atomization is observed when the viscosity is low. Consequently, an ideal profile for such a formulation is one in which the viscosity decreases as... 

D, including acidic titrant from Table 4) courses. The shape for the ideal profile was computed from data on the statistical distribution of protein p/s (Gianazza and Righetti, 1980). The relevant histogram is redrawn in the figure inset. (From Gianazza et al., 1985b. Reproduced with permission of the publisher.)... 

The need to simulate the atmospheric dispersion of a gas cloud in order to determine extension and lifetime the flammable portions as realistically as possible has led to a lot of approaches, however, with different degrees of success in reaching the ideal profile of a mathematical model. 

A subbottom acoustic profile appears to give a cross section of the strata beneath the seafloor. However, it is really a plot of time that it takes the sound to pass from a ship to a reflector and back again versus clock time. An ideal profile is obtained if the spacing of soimd pulses is always the same, pulses are short, and little drift in the electronics is experienced. These conditions are usually satisfied by modem profiling systems. 

Figure 2 shows an idealized profile of the subsurface. From the surface down to the water table, the soil void space is partially filled with water and is termed the unsaturated zone. Below the water table, the soil void space is completely filled with water. This zone is termed the... 

Eventually, it should be stressed that rapid does not necessarily mean instantaneous. Rather, one should consider rapid proflling methods as ways to acquire data more rapidly than with their conventional equivalents. In Chapter 20, Blumenthal and Herbeth report that in order to evaluate sensations while driving, each assessor in their study drove a total of more than 25 h and 600 km, even if they used a quicker approach than conventional proflling. The same goes with other methods TDS is not as rapid, but it is much faster than traditional time-intensity measurements the Ideal Profile Method may also take some time for the panellists, but it is clearly more rapid than a full external preference mapping study. 

If consumers can profile products, and if consumers can rate the products relative to their own ideal (as with the JAR scale), then we could ask consumers to rate their ideal directly on a predefined list of attributes. This is the essence of the Ideal Profile Method (IPM) (Worch et al, 2013) that is presented here. As will be shown, the data obtained from this approach are directly actionable for product development and/ or product improvement (Hoggan, 1975). However, since these particular data are obtained from consumers who are rating a fictive ideal product, they require particular attention from the practitioners. 

The concepts, as well as the corresponding step-by-step methodology for the analysis of the IPM data (called the Ideal Profile Analysis (IPA)), will be presented. Finally, the advantages/inconveniences of the IPM and its practical use compared to other methods (such as the Preference Mapping or JAR scale) will be discussed. 

In the IPM, consumers are asked to rate both the perceived and ideal intensities of products on a predefined list of sensory attributes. In this case, P tested products will yield P sensory profiles and P ideal profiles per consumer. Additionally, the consumers rate the products on overall liking. In this sense, the IPM can be seen as a mix between a classical profiling task (such as QDA , except that it is performed by consumers) and a JAR task in which the ideal intensities are asked explicitly. 

On the left side, the sensory profiles of the products in the middle, the ideal profiles on the right side, the vector of hedonic scores. Here, j indicates the consumer, p the product and a the attribute. 

Respondents Perceived intensity Liking scores Ideal Profiles Deviation (perceived- ideal)... 

At the end of the test, each consumer has thus generated three blocks of data (Table 14.1) the sensory profiles of the products (noted the ideal profiles (noted Zjpa) and the vector of hedonic scores (noted hp). 

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