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研究生:吳哲維
研究生(外文):Che-Wei Wu
論文名稱:蝴蝶斑紋之有限元素模擬與分析
論文名稱(外文):Finite Element Modeling and Analyses on Pattern Formation of Butterfly Wings
指導教授:林達德林達德引用關係
指導教授(外文):Ta-Te Lin
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:生物產業機電工程學研究所
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2006
畢業學年度:94
語文別:中文
論文頁數:108
中文關鍵詞:涂林系統生物斑紋形成擴散反應方程式
外文關鍵詞:Turing systemBiological Pattern FormationDiffusion Reaction
相關次數:
  • 被引用被引用:3
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摘要

涂林系統是用來解釋生物形態發生(Morphogenesis)的一種可行理論,也就是說生物的成長發育或生物斑紋圖案形成可用涂林系統描述。生物形態發生的動力來自形態素的擴散和反應,而造成圖案形成的原因在於使用兩種以上的化學物質,經由濃度擴散以及化學物之間的交互作用與自我催化而形成圖案。本研究藉由涂林系統模擬蝴蝶翅膀上的斑紋,模擬之蝴蝶對象包括蛇目蝶科(Satyrinae)和鳳蝶科(Papilionidae)翅膀上的斑紋,同時也討論翅膀上的翅脈和翅膀邊緣與活化劑的關係,以及涂林系統參數對系統的穩定度與波數關係。我們以2D和3D參數平面來表示穩定範圍及趨勢,另外討論系統的邊界條件對圖案形成的影響,還有以Source-Source、Source-Sink和擴散反應方程式這三種方法模擬翅室內的基本斑紋。本研究主要探討Joakim Linde、眼斑Dilão、G-M、G-S與Schnakenberg五種涂林系統,用以模擬涂林系統的工具為FEMLAB有限元素軟體。我們分別討論這五個系統的收斂速度,利用收斂速度最近似的兩個或兩個以上之系統,配合翅脈與活化劑的關係來模擬與分析蝴蝶斑紋。本研究發現在系統收斂速度上以眼斑Dilão和G-M系統最接近,在同一翅膀上套用這兩個涂林系統模擬出台灣黑蔭蝶(Lethe butleri)和尖尾黛眼蝶(Lethe sinorix)的斑紋,另外利用Dilão、Schnakenberg和G-M系統三個涂林系統模擬出寬帶黛眼蝶(Lethe Helena Leech)的斑紋。本研究發現以翅脈為邊界條件會對斑紋形成造成影響,利用此關係我們可根據模擬的蝴蝶對象選擇適合之邊界條件,另外模擬斑紋時涂林系統的波數參數對斑紋形成樣式也會造成影響,所以模擬蝴蝶斑紋必須重複修正邊界條件和微調波數參數,直到模擬出相似的斑紋。過去前人研究模擬生物斑紋均以矩形或圓形和單一的涂林系統來模擬生物體上某一區域的斑紋,本研究則進一步以完整的蝴蝶翅膀和複合的涂林系統來模擬全區域的斑紋,得到更佳的模擬效果。

關鍵字:涂林系統、生物斑紋形成、擴散反應方程式
ABSTRACT

One of the elementary processes in morphogenesis is the formation of a spatial pattern of tissue structures. It has been shown that relatively simple molecular mechanisms based on auto and cross catalysis can account for a primary pattern of morphogens to determine pattern formation of the tissue. This study simulates and analyses butterfly wing pattern by using Turing system. The simulated wing patterns include Satyrinae and Papilionidae butterflies. We focus on the effect of key factors such as parameter values for mode selection, wave number, wing shape and boundary conditions. We express the stability and the tendency by constructing 2D and 3D parameter plane, and we discuss the boundary conditions of the system effect on pattern formation. Elementary patterns of butterfly wings are simulated by the source-sink, source-source and diffusion-reaction methods. This study utilizes five kinds of different Turing systems to simulate butterfly wing patterns. These systems are Joakim Linde Turing system, Dilão Turing system, Gierer-Meinhardt Turing system, Gray-Scott Turing system, and Schnakenberg Turing system. The finite element software FEMLAB was used for the simulation and analyses. Judging from their similar rate of convergence, Dilão and G-M systems were used to simulate wing patterns of Lethe butler and Lethe sinorix butterfly. We also used Dilão, G-M and Schnakenberg systems to simulate wing patterns of Lethe Helena Leech butterfly. In this study we found that wing pattern formation simulation is affected by two major factors of boundary condition and wave number parameters. The parameters are adjusted iteratively until the simulated pattern error is under a threshold. In contrast to simulate wing patterns of simple shape and using single Turing system, this study expands the scope to simulate whole butterfly wing patterns using composite Turing systems. As a result, more realistic butterfly wing patterns can be simulated and visualized.
Keywords: Turing system, Biological Pattern Formation, Diffusion Reaction
目錄
摘要 i
ABSTRACT ii
目錄 iii
圖目錄 v
表目錄 vii
第一章 前言與研究目的 1
1.1 研究背景 1
1.2 研究目的 2
第二章 文獻探討 4
2.1 形態發生學(MORPHOGENESIS) 4
2.1.1 動物斑紋 4
2.2 有限元素法的基本原理 5
2.2.1 有限元素法簡介 5
2.2.2 有限元素基本概念 6
2.2.3 FEMLAB有限元素軟體 6
2.2.4 FEMLAB解偏微分方程式 7
2.3 擴散反應系統(REACTION-DIFFUSION SYSTEM) 8
2.3.1 反應系統 8
2.3.2 涂林系統 9
2.3.3 涂林系統非線性方程式的線性化 12
2.4 蝴蝶翅膀之翅脈與花紋 17
2.4.1 蝴蝶簡介 17
2.4.2 蝶翅翅脈(Wing-veins) 17
2.4.3 蝶翅斑紋(Wing-pattern) 19
第三章 研究設備與方法 23
3.1 軟體架構與流程 23
3.1.1 有限差分法與有限元素法使用比較 23
3.1.2 蝴蝶翅脈影像 24
3.1.3 蝴蝶翅脈於FEMLAB有限元素軟體建模流程 26
3.2 有限元素法建立涂林系統之模組 30
3.2.1 擴散反應方程式係數穩定範圍 34
3.2.2 涂林系統波數 35
3.3 基本蝴蝶圖案模擬方法 37
3.3.1 基本圖案的建模方法 40
3.3.2 整合的模擬方法 40
3.4 涂林系統模擬蝴蝶斑紋之流程 41
第四章 結果與討論 43
4.1 涂林系統模擬範例 43
4.2 有限元素法與有限差分法之比較 53
4.3 涂林系統之分析理論 56
4.3.1 討論擴散反應方程式係數對圖案形成的影響 56
4.3.2 比較其它涂林系統 63
4.3.3 涂林系統之波數預測 70
4.3.4 涂林系統之邊界的影響 71
4-4 蝴蝶翅膀之基本花紋模擬 79
4-5 以翅脈模擬蝴蝶斑紋 86
第五章 結論與建議 101
5.1 結論 101
5.2 建議 104
參考文獻 105
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