The operation of a periodically forced chemostat (CSTR) in which two microbial populations compete for the same nutrient has been examined. Easily implemented criteria for the stability of the resulting cycles have been obtained, using the Floquet stability theory. After examining several possibilities it was found that stable periodic trajectories of coexistence can be achieved: (a) when the dilution rate of the chemostat is properly varied in a periodic manner between two values so chosen that the growth of one population is favored by the first and the growth of the other population is favored by the second, (b) when a certain percentage of biomass and growing medium is harvested periodically from the chemostat, and (c) when both the dilution rate and the concentration of the substrate in the feed are varied simultaneously and in a periodic manner. Both experiments and theories of growth show that competition of two populations for a single limiting nutrient leads to extinction of one of the populations, if they are grown in a spatially uniform environment that is subject to time-invariant external influences. This statement, or rather a less cautiously worded version of it, is known as the "competitive exclusion principle," (Hardin 1960). Its validity and applicability have been the subjects of much discussion among researchers. GREGORY STE PH ANOPOU LOSSome recent theoretical work based on models that give good description of the growth of microbial populations shows that the restricted version of the competitive exclusion principle given above must be modified if more than one nutrient is limiting. Thus, Taylor and Williams (1975) suggest that n competing populations can coexist with each other if a set of at least n nutrients is limiting. Similarly, Schuelke (1976) shows that two populations could coexist if the sets of limiting nutrients for the two populations overlapped only partially. In spite of these developments, it remains true that reduction of system diversity is Several schemes for sustaining microbial competitors in the same environment have appeared in the literature because of the importance of competitive interaction in practical applications involving microbial activities. One of the most common is that external influences are not time invariant but that they vary so as to provide an environment in which the competitive advantage alternates between the two populations. Unfortunately, all the above schemes have been based on non-mathematical arguments and there is no assurance that a proposed scheme of time varying external influences will, in fact, allow competitors to coexist.This study examined the effect of periodically varying inputs to coexisting competing microbial populations which grow in a continuous, well stirred vessel, usualIy referred to as chemostat. Criteria for the stability of the proposed cycles and examination of the effect of some operating parameters on their stability characteristics are based on Floquet stability theory. The results can be useful in establishing patte...
1 5) These monocyclizations were also conveniently performed by using a polystyrene-supported tributyltin hydride first prepared in this laboratory by Gary Tennyson, following essentially the route described for the related dihydride (Weinshenkcr, N. M.; Crosby, G. A.; Wong, J. YWe have succeeded in detecting by electron spin resonance spectroscopy an aromatic hydrocarbon, m-phenylenebis((di- phenylmethylen-3-y1)methylene) (l), which has eight parallelHiizu Iwamura* and Kazumasa Kobayashi 1 spins, Le., nonet spin multiplicity (S = 4) in the electronic ground state. This is the highest spin multiplicity observed in organic as well as inorganic compounds. The prototype of this molecule,
Filtration under constant D. C. electric field with constant hydraulic pressure, what is termed electrokinetic filtration, was discussed in this paper. Under these conditions it is considered that electrophoresis occurs in the slurry and causes less cake formation, and that electroosmosis occurs at the same time in the filter cake. Therefore, the flow rate of electrokinetic filtration is increased in comparison to filtration at the same hydraulic pressure. An equation taking account of both effects is presented. Experimental investigation of the characteristics of electrokinetic filtration is performed according to the theoretical equation. As a result, the flow rate of filtration is significantly increased for calcium carbonate slurry and [white clay slurry. For instance, at the electric field of 30 volt/cm under hydraulic pressure of 163.2 G/cm2, Ruth's filtration coefficient for calcium carbonate slurry was about 9.4 times as large as that of the filtration at the samehydraulic pressure, and Ruth's coefficient for white clay slurry was about 15 times at 12volt/ cmand 163.2 G/cm2. It is confirmed that the equation of electrokinetic filtration proposed in this paper is practically available.
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