Effect of a Heterogeneous Site Size Distribution on the Branch Size Distribution of Tree Networks

作者：Kim Yup^*; Chae Huiseung; Yook Soon Hyung

来源：Journal of the Korean Physical Society, 2012, 60(4): 595-598.

DOI：10.3938/jkps.60.595

• Critical tree
• River network

In this study, we investigate how the heterogeneous site size distribution affects the behavior of the branch size distribution of critical trees. By assuming a power-law, P(s) similar to s(-alpha), for the site size distribution, we find that the exponent tau for the branch size distribution is smaller than that of a critical tree when alpha %26lt; 3. When alpha %26gt;= 3, we find tau = 1.5, which is the value of the critical tree for P(s) = delta(s - 1). We also find tau = 1.5 for other P(s)%26apos; s with finite %26lt; s(2)%26gt;. Based on our measurement, the physical origin of the discrepancy between the measured branch size distribution in real river networks and that of the critical tree is suggested. As an extension of our study, we also measure the directory size distribution of computer operating systems and discuss the effect of the heterogeneity of the site size distribution tau of a supercritical tree.

• 出版日期2012-2