The Study Of Cell's Growth-death In One-dimensional Model Based On Self-organized Criticality

This dissertation is concerned with the distribution law of clusters with different sizes in a simple one-dimensional(lD) cell's growth-death model.The terminology cluster is applied to the model. The size s of a cluster is the number of contiguous occupied neighboring sites. We record the number n(s) of the cluster with different sizes. We adopt the computer simulation to mimic this model. It is obvious there are many different permutation cases for occupied sites when p takes a certain value, which doesn't affect the research about the two variables interest us. After all, Our concern is not which position a special occupied site is located, but the statistical property about the clusters with different sizes. Each site in the ID model takes independent value, and the random numbers taken value to the sites satisfy the independence in some degree.The BS model is introduced in detail, and some different definitions and research about the model are compared. We discuss the power-law and interaction's influence on the SOC in real world or model. Besides that, we present the positive meaning and puzzles in the SOC. Some problem to be considered and solved is pointed out. In the physiology and medicine field, the seminal breakthrough in our understanding of cell programmed cell death is introduced. The important discovery is very important for medical research and have shed new light on the pathogenesis and cure of many diseases, which is also the biological background of this dissertation.Searching for the self-organization mechanism, we intend to analyze thedata in the dual-logarithm plot, we find that in the neighborhood of p = 0.5, n(s) and s in the dual-logarithm plot have approximate linear relation, however, for relatively large or small p, there is not ideal linear relation. It is undeniable that there are boundary effect, because our actual operation is in a limited-size model. For some large p, seemingly there are multi-fractal property, which is needed to be discussed forward.In further consideration, by definition we obtain an exact probability equation, which describes the relation between the above two quantity and is in agreement with the numerical simulation. Finally, through three different methods to take the same p, we find that the distributions almost makes no difference, which shows that the distribution of clusters with different sizes depend little on the process of taking value to p, and p itself decides the distribution.