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研究生: 林宗憲
Lin, Tsung-Hsien
論文名稱: 量子氣泡奈米噴流結構
QUANTUM BUBBLE NANOJET STRUCTURES
指導教授: 邱輝煌
Chiu, Huei-Huang
學位類別: 碩士
Master
系所名稱: 工學院 - 航空太空工程學系
Department of Aeronautics & Astronautics
論文出版年: 2005
畢業學年度: 93
語文別: 英文
論文頁數: 81
中文關鍵詞: 量子奈米噴流量子氣泡奈米級設備量子擴散流
外文關鍵詞: quantum nanojet, quantum bubbles, quantum diffusive flow, nanodevices
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  • 中文摘要
    論文題目(中文):量子氣泡奈米噴流結構
    論文題目(英文):QUANTUM BUBBLE NANOJET STRUCTURES
    指導教授:邱輝煌

    粒子通過奈米級尺寸雙狹縫的量子力學模擬,定義「量子雷諾數(Quantum Reynolds Number)」為「慣性力除以因量子勢能所引發的量子力」,隨著量子雷諾數的增加,展現了複雜的演化結構:量子氣泡(quantum bubble)、延伸分流氣泡(stretch-splitting bubbles)、多分支奈米噴流(multi-branch nanojets)及最終的兩道主要噴流。主要的量子力學成形及量子氣泡與噴流的轉變過程為:高度調和波的激發(high harmonic wave excitation)、波傳遞(wave propagation)、交叉 (intersection)、干涉(interference)及穿隧(tunneling),每一過程皆影響動力、外形及氣泡與噴流的結構。我們將分析速度之橫向與軸向分佈,干涉條紋及粒子在噴嘴內的路徑,亦將討論量子勢能力所引起的動力機制。奈米噴流與氣泡的動力與其複雜的結構提供我們在奈米級設備上的應用:質量光譜儀(mass spectrometer)、成像(imaging)、感測器(sensors)、平版印刷(lithograghy)及奈米管(nanotubes)。

    QUANTUM BUBBLE NANOJET STRUCTURES

    Student : Tsung-Hsien Lin
    Advisor : Huei-Huang Chiu

    ABSTRACT

    Quantum mechanical simulations of particles ejected from two slits of nanoscales reveal complex evolutionary structure of: quantum bubble, stretched-splitting bubbles, multi-branch nanojets and ultimately, two primary jets, in the order of increasing quantum Reynolds number, defined by the ratio of the inertia force to the quantum force induced by quantum potential. Major quantum mechanical processes involved in formation and their transition of the quantum bubbles and jets are: high harmonic wave excitation, wave propagation, intersection, interference and tunneling, each of which affects the dynamics, configurations and structures of the bubbles and jets. Transverse and axial distributions of velocities, interference fringes and particle paths in jets are also examined and dynamic mechanisms attributed by the quantum potential force discussed. The dynamic and structural complexities of nanojets and bubbles lend themselves to potential applications for nanodevices: mass spectrometer, imaging, sensors, lithography and nanotubes.

    ABSTRACT i ACKNOWLEDGEMENT iii CONTENTS iv LIST OF TABLES vii LIST OF FIGURE viii NOMENCLATURE xii I INTRODUCTION 1 1.1 Introduction 1 1.2 Motivation 2 II MATHEMATICAL ANALYSIS OF SCHRÖDINGER WAVE EQUATION FOR QUANTUM BUBBLE JETS 4 2.1 Mathematical Formulation 4 2.2 Problem Postulat 7 2.3 Non-Dimensionalization 8 2.4 Wave Solutions 10 2.4.1 Sub-critical wave field 15 2.4.2 Super-critical wave field 18 III RESULTS AND DISSCUSIONS 21 3.1 Probability Density Distribution 21 3.1.1 Quantum Bubble Formation 22 3.1.2 Quantum Bubble Branching 23 3.1.3 Multi-Branching 23 3.2 Current Flux Distribution 24 3.2.1 Flux Distribution In Quantum Bubble Formation Stage 25 3.2.2 Flux Distribution In Quantum Bubble-Branching Stage 25 3.2.3 Flux Distribution In Multi-Branching Stage 26 3.3 Single Slit Distribution 26 3.4 Mean Kinetic Energy Distribution 27 3.5 Summary 28 3.6 Validity of Conservation Law 29 3.6.1 Validity of Quantum Continuity Equation 30 3.6.2 Validity of Quantum Bernoulli's Equation 31 3.7 Numerical Solution 34 IV CONCLUSIONS 36 4.1 Quantum Nano Jet 36 4.2 Quantum Bubble Structure for Low Quantum Reynolds Number 37 4.2.1 Quantum Bubble Formation 37 4.2.2 Quantum Bubble Branching and Multi-Branching 37 4.2.3 Mean Kinetic Energy 38 4.2.4 Density, Flux and Mean Kinetic Energy 39 4.3 Future Works 40 REFERENCES 42 TABLES 43 FIGURES 47 VITA 80

    【1】Born M., 1949 “Natural Philosophy of Cause and Chance”. Oxford, England: Clarendon Press.
    【2】C.D. Yang, 2003. “Pilot Waves of de Broglie”, Ch. 1 in Quantum Mechanics, IAA, NCKU, fall semester.
    【3】Chiu, H.H. Lin. C.T., Lin, S.Y. Hung T.C. & Mardarasz F., 2004.“Developments of Quantum nanojet based nanodevices,” ICEE11, S. Carolina US.
    【4】Chiu, H.H & C.T. Lin, 2003. “Structural and dynamics complexities of nanojets”, USAirforce/ Taiwan Nanoscience Initiative workshop Maui Hawaii.
    【5】Chiu H.H., 2002. “Fundamentals and Computational Aspects of Quantum Diffusive Fluid Dynamics” workshop presented at NCKU, Hsinchu, Tainwan December 13-14.
    【6】Chiu H.H., 2005. “Quantum fluid mechanical and electronic structure of a hydrogen-like atom” To appear in the Proceedings A of The. Royal Society of London.
    【7】R. Penrose and C.J. Isham, 1986. The paper by Smolin in Quantum concepts in space and time, p.156.

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