Browse

Fractal dimensions of bridge bonds in directed percolation models
방향성 스미기 모형에서 다리본드의 쪽거리 차원

Cited 0 time in Web of Science Cited 0 time in Scopus
Authors
최상민
Advisor
강병남
Major
자연과학대학 물리·천문학부
Issue Date
2015-02
Publisher
서울대학교 대학원
Keywords
percolation transitiondirected percolationbridge bonddiscontinuous percolation transitionfractal dimension
Description
학위논문 (석사)-- 서울대학교 대학원 : 물리·천문학부, 2015. 2. 강병남.
Abstract
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.
Language
English
URI
https://hdl.handle.net/10371/131631
Files in This Item:
Appears in Collections:
College of Natural Sciences (자연과학대학)Dept. of Physics and Astronomy (물리·천문학부)Physics (물리학전공)Theses (Master's Degree_물리학전공)
  • mendeley

Items in S-Space are protected by copyright, with all rights reserved, unless otherwise indicated.

Browse