The anisotropic formation of elongated metal-oxide aggregates in water under intensive stirring is analyzed. It is treated in terms of anisotropic ballistically mediated aggregation kinetics in open systems. The basic kinetic equations describing the stages of homogeneous nucleation, independent growth, and ripening of the aggregates are formulated for the open system under the external influence with the stirring intensity as the main parameter governing the process. The most significant elongation of the aggregates is shown to evolve at the ripening stage.
Well-known predator-prey model is modified in two ways. First, regular adding or regular deleting of preys or/and predators is considered. Steady-state and stability diagram is found. Second, random fluctuations of the birthrate and other kinetic coefficients are studied -parabolic law of random walk in (X,Y)-space is found and proved for small deviations from steady-state.MSC 2010. 34A34, 34F05, 34D08
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