Break-even concentration

A competitor x, for which A, > 1 is an inadequate competitor, since its break-even concentration equals or exceeds the reservoir concentration of nutrient. Our first result makes this mathematically precise. 

On the other hand, competitive success is determined solely by having the smaller break-even concentration A,. Since A, decreases (and so the /th... 

Because of the ozone depletion that occurs by photolysis, the NO, break-even concentration at which net O, production occurs is somewhat larger than the value based just on the ratio of the rate constants of reactions 5.47 and 5.25. The approximate crossover point for NO, between O destruction and production is usually considered to be at about 30 ppt. Ozone mixing ratios in the planetary boundary layer over the remote Pacific Ocean are only about 5 to 6 ppb NO, levels are about 10 ppt. Thus, this region of the atmosphere is probably below the crossover point. 

The key parameter associated with (3.6), as observed in Chapters 1 and 2, is the break-even nutrient concentration A, defined to be the solution of... 

NOW, YOU might be feeling overloaded with new words, and even a bit hesitant to use any words you already know. Learning new vocabulary is intense work. This lesson provides a break by concentrating on two common vocabulary problems. 

Unmodified PBT is a fairly ductile material exhibiting high elongation at break, even after crystallization. However, as to be expected of all rigid semi-crystalline polymers, molded parts of PBT show low notched Izod impact strength indicating that under conditions of stress concentration, the... 

The soft segment content is a major variable in this system. Table 4, as it is in the case of polystyrene/polybutadiene/poly styrene triblock polymer. A comparison of the data in Tables 3 and 4 shows that at the same "B" segment content these polymers have similar tensile elongations at break, even though their chemical composition is in no way similar. The arrangement of glassy and rubbery segments and their concentrations dominate. 

Conventional elution chromatography has the serious disadvantage of dilution, and usually a concentration step must follow. The technique of displacement chromatography circumvents dilution and may even result in an eluant more concentrated than the feed. A displacer compound breaks the desired product from the chromatographic material sharply, and a column heavily loaded with several biochemicals will release them one at a time depending on their adsorption equilibria. However, the displacers tena to be expensive and can be troublesome to remove from the product. 

In addition to impurities, other factors such as fluid flow and heat transfer often exert an important influence in practice. Fluid flow accentuates the effects of impurities by increasing their rate of transport to the corroding surface and may in some cases hinder the formation of (or even remove) protective films, e.g. nickel in HF. In conditions of heat transfer the rate of corrosion is more likely to be governed by the effective temperature of the metal surface than by that of the solution. When the metal is hotter than the acidic solution corrosion is likely to be greater than that experienced by a similar combination under isothermal conditions. The increase in corrosion that may arise through the heat transfer effect can be particularly serious with any metal or alloy that owes its corrosion resistance to passivity, since it appears that passivity breaks down rather suddenly above a critical temperature, which, however, in turn depends on the composition and concentration of the acid. If the breakdown of passivity is only partial, pitting may develop or corrosion may become localised at hot spots if, however, passivity fails completely, more or less uniform corrosion is likely to occur. 

Chromate ions, when used as inhibitors in aqueous solutions, passivate by maintaining a coherent oxide film on the metal surface. Passivation is maintained even in a boiling concentrated chromic acid solution, in which many of the oxides in bulk form are soluble. The passivity breaks down rapidly, however, once the chromate is removed. 

The two models commonly used for the analysis of processes in which axial mixing is of importance are (1) the series of perfectly mixed stages and (2) the axial-dispersion model. The latter, which will be used in the following, is based on the assumption that a diffusion process in the flow direction is superimposed upon the net flow. This model has been widely used for the analysis of single-phase flow systems, and its use for a continuous phase in a two-phase system appears justified. For a dispersed phase (for example, a bubble phase) in a two-phase system, as discussed by Miyauchi and Vermeulen, the model is applicable if all of the dispersed phase at a given level in a column is at the same concentration. Such will be the case if the bubbles coalesce and break up rapidly. However, the model is probably a useful approximation even if this condition is not fulfilled. It is assumed in the following that the model is applicable for a continuous as well as for a dispersed phase in gas-liquid-particle operations. 

The principal characteristic of induced reactions of this type which have not been stressed so far, is that the extent of the induced change greatly decreases and in most cases reaction even ceases in the presence of chain-breaking substances. The induced reaction can be suppressed by any substances reacting with chain carriers at a higher rate than does the acceptor, and the product of the reaction of the suppressor can easily react with the inductor. Since the concentration of the chain carriers is generally low, the supressors of induced chain reactions exert considerable effect even in small quantity. The effect is particularly pronounced when the suppressor reacts reversibly. 

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