Volume-normalized

Hugoniot curve A curve representing all possible final states that can be attained by a single shock wave passing into a given initial state. It may be expressed in terms of any two of the five variables shock velocity, particle velocity, density (or specific volume), normal stress (or pressure), and specific internal energy. This curve it not the loading path in thermodynamic space. 

Some systems normally do not have any specific supply airflow, though they could have some air supply. These are used when a volume (normally a room) is intended to have a lower pressure than the surrounding rooms. This so-called pressurization of zones is used when a high level of safety against spreading of contaminants is needed. A high pressure difference between two rooms causes the air to flow into the room with the lowest pressure if some cracks exist or some connection between the two rooms is opened. 

Figure 3 shows a plot of the volume normalized nucleation time constant as a function of isothermal crystallization temperature for PEO droplets, taken from the work of Massa and Kalnoki-Veress [84]. As expected, droplets of different volumes have the same value of r V. The inset in Fig. 3 is a plot consistent with classical nucleation theory (see Eqs. 1, 4) only the last four data points correspond to the work of Massa and Kalnoki-Veress. The first... 

Containment (pressure rating, gas-phase volume, normal and emergency venting)... 

Depending on its subtraction from or addition to the buoyancy force, the continuous phase velocity can either increase or decrease the bubble volume. Normally, this velocity is such that the bubble detaches prematurely from the nozzle tip. Maier (M2) has shown that the shear force experienced by the bubble, which causes its premature detachment, is a maximum when the continuous phase flows at right angles to the nozzle axis. 

Fig. 14.9 Total energy curves for seven structures of Si as a function of volume normalized to the experimental volume. The dashed line is the common tangent between the diamond and the p-tin phase.

For small particles (R < as) the overlap integral I U(0) l of the electron and hole wave functions increases with decreasing nanoparticle volume as a result /is only weakly dependent on the particle size [113], However, volume normalized oscillator strength fA/) increases with decreasing nanoparticle size and can be estimated as [126] ... 

Normalization is performed in order to remove. systematic variation. iisuaHy a.ssociatcd with the total amount of sample. common example of this is normalizing to the largest nt/e peak in mass spectrometry (Howe ct at., 19S1, p. 19). In chromatography, normalization of the entire chromatogram to unit area is used to remove the effect of variable injection volume. Normalizing to... 

Closed wakes have been modeled as completing the sphere or spheroid of which the particle forms the cap [e.g. (C5, P2)]. However, the wake is smaller than that required to complete a spheroid for Re < 5 and greater for larger Re (B3). The wake becomes more nearly spherical as Re 100, but is still somewhat egg-shaped (B3, H5). Wake volumes, normalized with respect to the volume of the fluid particle, are shown in Fig. 8.6 for Re up to 110. Note the close agreement with results (Kl) for solid spherical caps of the same aspect ratio. This is not surprising since separation necessarily occurs at the rim of the... 

Pick s Law. Pick s law is a physically meaningful mathematical description of diffusion that is based on the analogy to heat conduction (Pick, 1855). Let us consider one side of our control volume, normal to the x-axis, with an area 4r, shown in Figure 2.3. Pick s law describes the diffusive flux rate as... 

Volume-normalized extinction is plotted in Fig. 11.2 as a function of photon energy for several polydispersions of MgO spheres both scales are logarithmic. For comparison of bulk and small-particle properties the bulk absorption coefficient a = Airk/X is included. Some single-particle features, such as ripple structure, are effaced by the distribution of radii. The information contained in these curves is not assimilated at a glance they require careful study. 

Figure 11.14 Volume-normalized extinction as a function of size calculated for spheres of (a) ater (after Carlon ct al.. 1977) and (b) aluminum (from Rathmann, 1981). The optical constants used arc those appropriate to the wavelengths noted on the curves.

As an example of extinction by spherical particles in the surface plasmon region, Fig. 12.3 shows calculated results for aluminum spheres using optical constants from the Drude model taking into account the variation of the mean free path with radius by means of (12.23). Figure 9.11 and the attendant discussion have shown that the free-electron model accurately represents the bulk dielectric function of aluminum in the ultraviolet. In contrast with the Qext plot for SiC (Fig. 12.1), we now plot volume-normalized extinction. Because this measure of extinction is independent of radius in the small size... 

Fuchs s (1975) result for volume-normalized absorption by randomly oriented cubes in the electrostatics approximation is... 

This is shown semiquantitatively for a series of polyimides, where hydrogen/ fluorine, and symmetric/asyirunetric analogues were synthesized and measured. The free-volume contribution is estimated by a free-volume normalization method developed for this purpose.In these materials, the contribution of changes in free volume to the observed change in dielectric constant ranged from 25 to 95% in moisture-free materials. ... 

Figure 9.26 illustrates two types of three-dimensional elements, the prisms and the tetrahe-drals. The prisms shown are of the serendipity family and the coordinates for these elements are normalized the same way as the rectangular two-dimensional elements and the shape functions are just simple extensions of the 2D elements. The tetrahedral elements have volume normalized coordinates, which again are an extension of the 2D area normalized coordinates. 

The volume normalized coordinates for the tetrahedral elements are defined as... 

The weight of soil used in the measurement depends on the initial soil microbial biomass concentration and the flask volume. Normally, 20-40 g moist soil is suitable for this measurement. Lin and Brookes (1999a) showed that SIR can give reliable estimates of microbial biomass in unamended soils, soils that contain actively decomposing plant residues, or soils recently treated with pesticides or fumigants. The final results are usually expressed as the SIR rate (tl C02 evolved g soil h Biomass carbon (Bc) is estimated by Bc (gig C g l soil) = 15 SIR (Lin and Brookes 1999a). 

The area is the cross-area of the control volume normal to the heat flow, i.e. the x direction. In this case where the temperature gradient is constant, the equation becomes... 

There have been recent efforts to predict, or at least rationalize, the x parameters of these and other polyolefin-polyolefin blends. Bates et al. (1992) and Fredrickson et al. (1994) suggest that the x parameter is correlated to a difference in statistical segment length of the polymer molecules, on a volume-normalized basis. The volume normalization is required because the definition of the statistical segment length depends on how the monomer unit... 

Fig. 5. Comparison of volume normal distribution function with data for = 0.001 0.005 [after Chen and Middleman (C8)].

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