S-Space College of Natural Sciences (자연과학대학) Dept. of Physics and Astronomy (물리·천문학부) Physics (물리학전공) Theses (Master's Degree_물리학전공)
Fractal dimensions of bridge bonds in directed percolation models
방향성 스미기 모형에서 다리본드의 쪽거리 차원
- 자연과학대학 물리·천문학부
- Issue Date
- 서울대학교 대학원
- percolation transition ; directed percolation ; bridge bond ; discontinuous percolation transition ; fractal dimension
- 학위논문 (석사)-- 서울대학교 대학원 : 물리·천문학부, 2015. 2. 강병남.
- Bond percolation is a mathematical model studying the emergence of a spanning cluster as bonds are occupied in Euclidean space without any preferred direction. Bonds are classified into two types: bridge bonds and non-bridge bonds. Bridge bonds are ones that once occupied, a spanning cluster is created in one direction of the system. When the occupation of bridge bonds is prohibited and only non-bridge bonds are occupied, the system is divided into two parts
the boundary composed of bridge bonds forms a fractal object. It has been revealed that the fractal dimension of that object is related to the continuity of the so-called explosive percolation transition. In the problem of directed percolation, however, where the bonds possess a preferred direction of flow, not much is known about these bridges. We obtain the fractal dimensions of the bridges in various dimensions and compare them to those of ordinary percolation. It will further be shown that these bridges relate to the continuity of the phase transition in the same way those of ordinary percolation do, and outline the implications of these results.