臺灣國際科展

模擬複雜系統的演化

科展類別
臺灣國際科展
屆次
2004年
科別
物理科
學校名稱
國立臺灣師範大學附屬高級中學
指導老師
胡進錕、陳忠城
作者
郭韋震
關鍵字
複雜系統,臨界現象

摘要或動機

複雜系統廣泛地存在每個人生活的周遭,儘管這些系統在表象上有明顯的差異,卻不約而同的都呈現出臨界現象。一個簡單的物理概念卻能廣泛地使用在許多不同的場合當中,這是令人始料未及的。這份報告在尋找,是什麼原因導致這許多似乎與物理沒什麼關聯的系統,都呈現出臨界現象?以及這類系統是如何演化的?臨界現象在系統的演化歷史中,又是扮演怎樣的一個角色?一開始,先介紹臨界現象在實際系統中表現的形式,在這以文字系統作為範例。接下來,進入思考的階段,猜測系統個體間存有的關聯性,提出如何影響的假設,並建立模型。從模型結果,可以了解複雜系統隨時間演化的趨勢改變,並發現臨界現象在系統中扮演的角色以及代表的意義。這份報告有三項結論:1. 臨界現象在複雜系統中呈現的形式 2. 模型結果與實際系統十分相似 3. 臨界現象代表著系統的穩定態。The theory of Scaling Law and Universality was originally used in researching Critical phenomena, and now we find it existing in our normal life. A simple physical concept can be used extensively in different courses. This study try to find out the relation between individuals which causes Critical phenomena appear in such different courses in our normal life, and figure out the effect time brings about. To begin with, we introduce the sights of Scaling Law and Universality by exploring the formation of complicated system. Facing a complicated word system as a real example, we observe an extraordinary phenomena, and find out the Universality and Scaling Law in different kinds of linguistics. In the main part, to think further, what’s the relation between the individuals that leads to Critical phenomena? We will give hypotheses and build a model to simulate complicated system from the view of Universality, trying to find out the cause of the interaction of complicated system. From this model, we could understand: When a complicated system evolves with time, the Critical phenomena will naturally occur in this system that could be considered as dynamic equilibrium. From this study we found out(1) The Universality and Scaling Law in complicated systems, here we use linguistics as an example.(2) Under the hypotheses, the simulation is almost as same as the real result of linguistics system.(3) Time plays an important part in the Critical phenomena which can be found in many different complicated systems, and Critical phenomena symbolize a stable state of such systems.


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