Growth rate, concentration fluctuations

Although specific calculations for i and g are not made until Sect. 3.5 onwards, the mere postulate of nucleation controlled growth predicts certain qualitative features of behaviour, which we now investigate further. First the effect of the concentration of the polymer in solution is addressed - apparently the theory above fails to predict the observed concentration dependence. Several modifications of the model allow agreement to be reached. There should also be some effect of the crystal size on the observed growth rates because of the factor L in Eq. (3.17). This size dependence is not seen and we discuss the validity of the explanations to account for this defect. Next we look at twin crystals and any implications that their behaviour contain for the applicability of nucleation theories. Finally we briefly discuss the role of fluctuations in the spreading process which, as mentioned above, are neglected by the present treatment. 

Let us now choose the characteristic rate and concentration to make the point of intersection of/and g the point (1,1). We are going to put a random fluctuation on the flow rate of zero mean so we shall be particularly interested in the dynamics in the immediate neighborhood of the line x + y = z/ 1. Now, in this neighborhood, the linearization of the growth rates gives... 

In Anacystis nidulans, the intacellular PolyP level, which was manipulated by growth in the presence of various P concentrations in the medium (0.3-3 mM), increased with the Pi concentration up to 2.1 mM and decreased thereafter (Keyhani et al., 1996). Thus, the PolyP accumulation in cyanobacteria depended on the phosphorus content in the medium, as in other bacteria. The growth rate of cyanobacteria under phosphate starvation has been shown to be a function of the amount of previously accumulated PolyPs in the cells (Rhee, 1973). PolyP storage is a survival strategy under conditions of fluctuating phosphate supply characteristic of the environmental conditions, in which the cyanobacteria live (Falkner et al, 1995). 

The fluctuations in growth rate result from local variations in the temperature and in the concentrations of the gaseous species involved in gas-to-particle transformation processes. 

Historically, before the mid-19 " century, the methane concentration was approximately constant at about 0.75 ppm, but it has risen continually since then and had reached almost 1.75 ppm by 1994. In the 1970s, the rate of increase was twice as much as that in the 1980s, and in the early 1990s it temporarily became almost zero. It is not known with certainty why the growth rate decreased and has fluctuated recently, though some scientists have speculated that it is related to the air temperature decreases associated with the explosion of Mt. Pinatubo in the Philippines (Baird, 1999). 

In this concentration range the linear relationship can be seen, however, at higher L-Phen concentrations, the linear relationship between AL and Time was not established. The growth became much irregular and the growth rate fluctuated between intervals of no growth and intervals of growth. 

The solution to eqn (8.47) is usually written in terms of the growth in amplitude of the concentration fluctuation with growth rate of R(q) the scattering parameter which reflects phase separation ... 

The availability of Mg +, K+, and the folate coenzymes may also be considered. The two cations are probably not rate-limiting, although K+ concentrations do fluctuate in cells. Little is known about the concentrations of total folic acid or of individual folate coenzymes, relative to tissue requirements for them. That this cofactor may be in excess was suggested by a recent study (39) in which a 95% decrease in total H4-folate was induced without causing any change in growth rate of the cells concerned. Others have found, however, that dietary deficiency of folate or vitamin Bi2 leads to increased urinary excretion of aminoimidazole carboxamide (40, 4D-... 

The rate is positive between q = Q and q = q = cf and negative for all q>qc-All fluctuations with wave number less than q would grow exponentially. Since in molecular solutions is about of molecular size, it means that, essentially, all the concentration fluctuations will grow. The maximum growth rate is observed for fluctuations with a wave number = =... 

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