Ultimate distribution

Eig. 1. Bags of oyster shell used as cultch for the settling of oyster spat. The spat-laden shell is ultimately distributed on leased oyster beds. 

The three principal domestic uses for rice in 1988 were direct food (61%), processed food (18%), and beer (20%). The direct food use figure includes the conventional white milled rice plus specialty rice products (parboiled, precooked, aromatic, brown, and prepackaged mixes) shipped directly from the rice mills. The specialty products account for approximately one-fifth of the direct food use. Approximately two-thirds of the direct food use rice is ultimately distributed to consumers through retail outlets and one-third through food service outlets. 

The ultimate distribution after an infinite number of passes is also shown in Fig. 22-6 and can be calculated for x < L — 1) From the following equation (Pfann, op. cit., p. 42) ... 

The ultimate distribution represents the maximum separation that can be attained without cropping the ingot. Equation (22-5) is approximate because it does not include the effect of progressive freezing in the last zone length. 

Continuous-zone-melting apparatus has been described by Pfann (op. cit., p. 171). This technique offers the advantage of a close approach to the ultimate distribution, which is usually impractical for batch operation. 

To this point, we have emphasized that the cycle of mobilization, transport, and redeposition involves changes in the physical state and chemical form of the elements, and that the ultimate distribution of an element among different chemical species can be described by thermochemical equilibrium data. Equilibrium calculations describe the potential for change between two end states, and only in certain cases can they provide information about rates (Hoffman, 1981). In analyzing and modeling a geochemical system, a decision must be made as to whether an equilibrium or non-equilibrium model is appropriate. The choice depends on the time scales involved, and specifically on the ratio of the rate of the relevant chemical transition to the rate of the dominant physical process within the physical-chemical system. 

The Earth formed as a set of elements and compounds, ultimately distributed in zones, with a large gradient of temperature and consequently providing an enormous store of energy. 

Data from phase-modulation fluorometry have been analyzed using an alternative approach to those described above, as expounded by Gratton and co-workers(14 12 13,22) and Lakowicz et al. W> Here, Lorentzian or Gaussian distribution functions with widths and centers determined by least-squares analysis are used to model the unknown distribution function. While this approach may introduce assumptions about the shape of the ultimate distribution function since these trial functions are symmetric, it has the advantage of minimizing the number of parameters involved in the fit. Here, a minimum x2 is sought, where... 

It may readily be seen by averaging the equation for o that the form given for mi. in equation (23) agrees with that previously derived in equation (21). It is interesting that the ultimate distribution of Ci is independent of 0-, physically this is because circumferential diffusion brings a molecule into a stream of precisely the same speed and so contributes nothing to the movement of the centre of gravity. 

These are the relations which exist between the moments of the normal distribution and in this sense the mean concentration is ultimately distributed about a point moving with the mean speed of the stream according to the normal law of error, the variance being 2(1 + kh2)t. It should be noted that the approach to normality is as r 1, a very much slower process than the vanishing of terms in the expressions for the moments, which is as exp(-Air). 

Carbon-14 atoms produced in the upper atmosphere combine with oxygen to yield 14CC>2, which slowly diffuses into the lower atmosphere, where it mixes with ordinary 12CC>2 and is taken up by plants during photosynthesis. When these plants are eaten, carbon-14 enters the food chain and is ultimately distributed evenly throughout all living organisms. 

It is assumed that radium that has been deposited in the lung as a radium salt enters the systemic circulation either as that salt or as individual radium atoms at a rate dependent upon the solubility and chemical characteristics of the specific radium salt involved. Subsequently, these salts or radium atoms would be systemically transported in the same manner as radium acquired by oral or parenteral administration. However, some of the radium in the lung could be retained for a long time before this process is completed. The ultimate distribution, many years after an inhalation exposure, would probably be very similar to that of other routes of administration that is, most of the radium that was retained in the body would eventually be deposited in the skeleton (Marinelli et al. 1953). 

The random fracture of brittle solids was studied by Griffith (1920), Sunatuni (1922), Hirata (1931), Terada (1931), Lienau (1936), and others. The problem is complicated by ma y factors and a satisfactory theory is lacking, especially with regard to ultimate distribution of sizes. Lienau, while devoting considerable attention to the nature of the force... 

Nucleation, or the formation of a crystalline phase from the liquid state, is probably the most important factor in controlling crystallization. The nucleation rate is the major determining factor in the number and size of crystals formed, their polymorphic form, and the ultimate distribution of crystalline solids. Crystallization cannot occur until the phase is supersaturated or subcooled. However, attaining the supersaturated or subcooled state is not necessarily sufficient to promote crystallization because a certain energy barrier exists to formation of nuclei. 

With subsequent zone passes, back-mixing becomes increasingly significant. When the number of zone passes becomes very large, the concentration profile reaches the ultimate distribution and subsequent passes have no influence. The number of zone passes required to approach the ultimate distribution is about twice the number of zone masses in the rod for small effective distribution coefficients. Thus, longer zones permit the attainment of the ultimate distribution sooner. On the other hand, the attainable separation increases as the zone size becomes smaller (permitting less back-mixing) (1,4). 

In the early stages of reaction the distribution (16) differs considerably from the Poisson form, althou with increasing conversion the difference decreases. If the final value of P is lai e the ultimate distribution may be effectively Poissonian. 

Systemic absorption of venom is dependent on lymphatic transport following subcutaneous envenomation. The onset of local symptoms such as swelling and ecchymosis occurs within several hours. Cardiovascular, neurological, or hematological compromise varies in onset but may occur within 10-15 min following intravenous or intraarterial envenomation. The metabolism of venom components is not well understood. It is likely that venom components are inactivated by enzymes within tissues where the venom is ultimately distributed. The distribution of... 

The timing of the stressor s interaction with the biological system is another important consideration. If the stressor is episodic in nature, different species and life stages may be affected. In addition, the ultimate distribution of a stressor is rarely homogeneous it is important to quantify such heterogeneity whenever possible. 

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