Growth rate, logarithmic

Figure C2.8.7. Principal oxide growth rate laws for low- and high-temperature oxidation inverse logarithmic, linear, paralinear and parabolic.

Most normal animal cells in culture grow at a logarithmic rate until they achieve a particular density (i.e., their saturation density) (Figure 11). A typical growth rate for animal cells in culture is one doubling per day, and a typical saturation density... 

An exponential (or logarithmic) growth phase follows the lag phase, and during this period the cell mass increases exponentially. The growth rate is at a maximum during this phase, and the population of cells are fairly uniform with respect to chemical composition and metabolic composition. 

Where i is determined from the logarithmic growth rate. 

Fig. 3.6. Semi-logarithmic plot of agglomerate growth rate in laboratory balling drum as a function of moisture content. (Data of Capes [2] sand particles of average sizes 70/im (o), 97 jum (A) and 49 jUm ( ).)...

In the case of some metals such as magnesium below a temperature of 200°C, a thin oxide layer is formed, which resists diffusion of oxygen and as a result an initial formation of oxide is followed by practically zero growth of the oxide. The rate law governing this type of oxide growth is logarithmic.75... 

Oxidation of metals includes all reactions in which the charge is transported through a film of reaction product on the metal surface. Parabolic, logarithmic, asymptotic, rates involve the presence of a rate-determining film, while linear growth rates correspond to the absence of such films. These reactions are generally considered as dry reactions. 

Paris [75] showed in 1964 that a linear relationship predicted by a simple power law for a double-logarithmic scale exists between the FCP rate da/dN and the applied AK (Fig. 6). The linear dependence is frequently observed only over an intermediate range of growth rates. On the double-logarithmic scale, the region of stable crack growth is usually satisfactorily described by the Paris-Erdogan equation... 

Logarithmic growth rate—Unlimited rate of growth rate. 

Figure 4.2.2 A pH step change continuous culture experiment. The reactor pH was decreased from 7.6 to 7.1 at time zero. The dilution rate was maintained at 0.41 day throughout the experiment, (a) Natural logarithm of total cell concentration versus culture time. Tangent lines are shown for slope determination. Error bars represent the standard deviation based on four replicate cell counts, (b) Apparent (1X3 , ) and true ((jl, ) specific growth rates calculated from (a) and Equations 4.2.7 and 4.2. Adapted from Miller et al. (1988) by permission of Biotechnology and Bioengineering.

Figure 10. The logarithm of the linear growth rate G, based on polarized light microscopy measurements, plotted versus l/[T(T°i-T)] for HPX-C11 2 main direction ( ) lateral (O).

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