政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/156604

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政大機構典藏 > 理學院 > 應用數學系 > 國科會研究計畫 > Item 140.119/156604

Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/156604

Title:	在高維度下定向滲流在體心立方晶格與具長域自我相斥隨機漫步在整數晶格的漸進行為 Asymptotic Behavior for Oriented Percolation on Body-Centered Cubic Lattice and Self-Avoiding Walk on Integer Lattice in High Dimensions
Authors:	陳隆奇
Contributors:	應數系
Keywords:	滲流;定向滲流;自我相斥隨機漫步;易辛模型;長域;BCC晶格;臨界行為;碎形模型;獨立集;分配函數;漸進行為;上臨界維度 Percolation;Oriented Percolation;Self-Avoiding Walk;Ising Model;Long-Range;BCC Lattice;Critical Behavior;Fractal Model;Independent Set;Partition Function;Asymptotic Behavior;Upper Critical Dimension
Date:	2023-09
Issue Date:	2025-04-16 14:28:07 (UTC+8)
Abstract:	此計畫主要是理論證明定向滲流在高維度下BCC晶格的臨界行為，具長域滲流，自我相斥隨機漫步與易辛模型在維度大於等於上臨界維度的臨界行為，最後想探討在一些碎形模型獨立集的分配函數的漸進行為。上述模型都是統計物理的經典模型且是描述相變現象的重要模型，此模型的臨界行為時我們無法用程式或數值分析其現象，只能用數學理論證明之，但直到如今我們得到的結果十分有限。所以此計劃有研究的重要性與必要性。
Relation:	科技部, MOST109-2115-M004-010-MY3, 109.08-112.07
Data Type:	report
Appears in Collections:	[應用數學系] 國科會研究計畫

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