Volume distribution definition

We believe that, as the very definition of free-volume characterizes the state of ordering in the system (especially for the cases when we consider the free-volume distribution), it may be preferable to apply the thermodynamic description of the processes at glass temperature. 

Abstract Makrolon , a commercially available polycarbonate with a glassy ultramicroporous structure (mean pore-volume 0.1 nm3), was often employed as sensitive layer for optical sensors in recent years. Due to the definite pore volume-distribution, it can be used as a size-selective sensitive layer. The interaction behaviour of Makrolon of different layer-thicknesses under the influence of methanol, ethanol and 1-propanol is characterized by Spectral El-lipsometry (SE), Surface Plasmon Resonance Spectroscopy (SPR)... 

An important feature of atmospheric aerosol size distributions is their multimodal character. Mass distributions, measured in urban centers, are characterized by three modes with a minimum between 1.0 and 3 The size range of particles larger than the minimum (supermicron particles) is termed coarse, while the smaller particles are called fine. The three modes present in the mass distribution of Figure 7.14 correspond to the nuclei mode (particles below 0.1 /zm), accumulation mode (0.1 < Dp < /.tm), and coarse mode Dp > )Lim) (Whitby and Sverdrup, 1980). Thus the fine particles include both accumulation and nuclei modes. The boundaries between these sections are not precise (recall in Chapter 2 that we divided fine and coarse modes at 2.5 /zm diameter). Note that our definition of modes has been based on the mass (or volume distribution). The location of modes may be different if they are based on the number or surface distribution. 

The net retention volume, Vn, (definition (7.1.99])), for species i can also be expressed in terms of Pf- and yf. Consider the distribution coefficient kh first and assume ideal gas behavior ... 

The particle size distribution of a given dust or mist can be reported as a number, length, surface, volume or mass (weight) distribution. Figure 2.3.3 shows number and volume distribution curves for a sample powder. The curves in the figure are density curves the function values /(x) represent the fraction of particles in a given interval divided by the width of that interval. The definition of the number density distribution fN x) is thus ... 

The appropriate quantum mechanical operator fomi of the phase has been the subject of numerous efforts. At present, one can only speak of the best approximate operator, and this also is the subject of debate. A personal historical account by Nieto of various operator definitions for the phase (and of its probability distribution) is in [27] and in companion articles, for example, [130-132] and others, that have appeared in Volume 48 of Physica Scripta T (1993), which is devoted to this subject. (For an introduction to the unitarity requirements placed on a phase operator, one can refer to [133]). In 1927, Dirac proposed a quantum mechanical operator tf), defined in terms of the creation and destruction operators [134], but London [135] showed that this is not Hermitean. (A further source is [136].) Another candidate, e is not unitary. 

When we have to deal with charge distributions rather than point charges, the definitions have to be generalized. What we do is to divide continuous charge distributions into differential charge elements /o(r)dr, and then apply the basic formula for the electrostatic field, and so on. Flere, dr is a differential volume element. Finally, we would have to integrate over the coordinates of the charge... 

Assuming that the distribution of masses inside the volume V is given, this vector function g p) depends only on the coordinates of the observation point p, and by definition it is a field. It is appropriate to treat the masses in the volume V as sources of the field g p). In other words, these masses generate the field at any point of the space, and this field may be supposed to exist whether a mass is present or absent at this point. When we place an elementary mass at some point p, it becomes subject to a force equal to... 

The behavior of g as a function of R is shown in Fig. 1.12c, and, of course, it is a continuous function. Now let us mentally decrease the thickness h and increase the volume density so that the mass remains the same. In such a way we arrive at a distribution of masses with a surface density, and this replacement does not change the field outside the shell, but it leads to a discontinuity of the field at the surface masses. It is instructive to demonstrate why the field inside the shell, Relementary surfaces dS and dS2- By definition we have ... 

The AUC is a measure of bioavailability, i.e. the amount of substance in the central compartment that is available to the organism. It takes a maximal value under intravenous administration, and is usually less after oral administration or parenteral injection (such as under the skin or in muscle). In the latter cases, losses occur in the gut and at the injection sites. The definition also shows that for a constant dose D, the area under the curve varies inversely with the rate of elimination kp and with the volume of distribution V. Figure 39.6 illustrates schematically the different cases that can be obtained by varying the volume of distribution Vp and the rate of elimination k both on linear and semilogarithmic diagrams. These diagrams show that the slope (time course) of the curves are governed by the rate of elimination and that elevation (amplitude) of the curve is determined by the volume of distribution. 

Fig. 2. Illustration of the definitions of conformational coordinate 7Zn, e.g., 7Zn = ri, r2,. .., rn. The conformational distribution s (7U1) is sampled for the single molecule in the absence of interactions with solvent by suitable simulation procedures using coordinates appropriate for those procedures. The normalization adopted in this development is/sf (7Zn) dn1Z = V, the volume of the system. Thus, the conformational average that corresponds to adding the second brackets in going from Eq. (4) to Eq. (3) is evaluated with the distribution function sf (7Zn) = V.

The subscripts m, L, S, and G will represent the local two-phase mixture, liquid phase, solid phase and gas phase, respectively. The definitions below are given in terms of solid-liquid (S-L) mixtures, where the solid is the more dense distributed phase and the liquid the less dense continuous phase. The same definitions can be applied to gas-liquid (G-L) flows if the subscript S is replaced by L (the more dense phase) and the L by G (the less dense phase). The symbol

volume fraction of the more dense phase, and s is the volume fraction of the less dense phase (obviously (p = 1 — e). An important distinction is made between ([Pg.444]

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