The Study About The Kinetics Of Aggregation With Fragmentation

Aggregate growth phenomenon occurs very widely in the fields of natural sci-ence and social economics such as cloud formation, dust accumulation in atmosphere, coacervation of erythrocyte, chemical reaction, distribution of wealth in a society, spread of germs, evolution of biotic population and so on. Aggregation is a phenome-non that homogeneous individuals come together temporarily through certain connec-tion in the system. There are many elements which influence the evolution of aggrega-tion, for example: aggregation, fragment, exchange, self-birth, self-death, annihilation, injection and so on. Generally speaking, for real-world aggregation systems, there al-ways exist multi-elements effecting in the system, thus, aggregation is a very compli-cated phenomenon. The phenomenon of aggregation has become a hot research spot in the last few decades, people have researched comprehensively and systematically by experimental method, theoretical arithmetic method and computer simulation method. We propose corresponding dynamic model of some real-world systems to investigate phenomena such as animal species evolution, economic and population distribution. The kinetic evolution behaviors of some systems in real world have some characters similar to the aggregate growth process, so the investigation on the kinetic behaviors of aggregate growth has positive effect to the nature and social systems. These predic-tive researches contribute active impetus to the developments of nature and human society.In this paper, we study the kinetic evolution behaviors of aggregates by using the Smoluchowski rate equation based on the mean field theory and considering the in-fluence of fragmentations.The main contexts are as followings: In chapter one, we introduce the history of aggregate growth, research approaches and several typical aggregation models. The second chapter we study the kinetic evolution behaviors of pest aggregates, mainly underlying the conditions of pest propagation, pest control with pesticide and pest control with natural enemy. It finds that: In the pest propagation model, the amount of pest increases as the exponential function e^Itin a long time; In the pest control with pesticide, pests can be perished only when the initial condition of the pesticide satis-fies to a certain condition; In the pest control with natural enemy, the pests will be perished totally in despite of the initial amount of the enemy. In the third chapter, we study the kinetic evolution behavior of aggregates through exchange-driven growth and finite-size fragmentation. It mainly studies the aggregates distribution from dif-ferent fragmentation. It finds that the aggregate distribution has different forms under the different fragmentations. The forth chapter gives a comprehensive conclusion and makes outlook.