The Study On The Kinetic Evolution Behavior Of The Economic And Chemical Systems Under The Catalytic-competitive Effects

Aggregate growths are a very common phenomenon in the real life andproduction, which is the individual of the system come together by the cetrainconnection. For example cloud formation, aggregate of wealth and population, islandformation, coacervation of erythrocyte, the evolution of biotic population and so on.In order to obtain what of rule and mechanism in the aggregate process people haveresearched the aggregate system by expeirmental method, computer simulationmethod and theoretical airthmetic method. Now, aggregation growth is the main studycontents in the growth mechanisms, and the study of aggregation growth dynamicshas been set out to the character of rfactal growth, besides, much attention has beendevoted to the study of aggregation growth dynamics and the size distirbution ofaggregates. In the recent years, the dynamics of catalysis aggregation growth hasbecome a hot spot of research，it exists not only the physic, biological, economic,chemical system, but also many social knowledge cross discipline.In this paper, we frame the kinetic model of catalytic competitive underaggregate evolution with the background of the aggregation behavior of the catalyst inthe economic and chemical systems, consider the aggregate growth, the catalyst ofcatalytic exchange migration, as well as complete annihilation processevolutionarybehavior of the aggregation of groups dirven by different mechanisms。Theinvestigation is performed by using the Smoluchowski rate equation based on themean-field theory. We mainly study the influences of some mechanisms, such asself-aggregation, exchange migration under the catalysis, annihilated of completelyand by analysing the conclusion, we discuss the scaling law which aggregation systemmay satisfy in the long-time limit.The paper is organized as follows: In chapter1，We introduce several typicalaggregation growths models, the history of aggregate growth and research approaches.In chapter)2，we devote to studying the kinetic evolutional behaviors of electmigration under the catalysis process. It is by the generalized Smoluchowski rateequation approach. The results show that the trend of aggregate group was catalysed, depends on the concentration of the size and number of catalyst catalyst rate nuclear.In chapter3，we study the kinetic evolutional behaviors of annihilated of completely.It finds that the size of the reactants changes mainly dependent on the number ofcatalytic group changes. In the last chapter, we summairze the results of theseinvestigations.