為了避免奈米力學模擬中所產生的假性波傳反射及改進其計算效率，本論文進行了一系列關於晶體奈米材料之學理研究，包括單原子晶格之奈米力學分析、恆溫非反射性邊界條件、相鄰列表之快速更新，以及前述各項研究在雷射輔助奈米壓印模擬之應用。
首先，本論文介紹了單原子晶格之奈米力學及統計力學特性，其將作為非反射性邊界條件開發及相關奈米材料模擬之基礎。在原子間勢能諧和近似假設下，本文給出了晶格的運動方程式及波傳色散關係。進一步地，從聲子及晶格能量的角度出發我們將給出晶格溫度的定義及各溫度下之熱運動振幅，此結果含括了先前研究者在高溫下之結論。
廣義Langevin方程式是非反射性邊界條件之廣義形式，其中Time-History-Kernel (THK)方法及吸收邊界層方法(ABL)為獲得此式之兩種主要方法。在THK方法部分，內文中將介紹其一般形式、核函數產生方法、時間卷積、性能評估及數值驗證。本文提議使用Crump方法來產生指數形式之核函數，如此可使得時間卷積之計算量從 降為 。從THK方法在晶格鬆弛過程及系統承受外部加熱或受力的模擬中，顯示了其確實能在奈米力學計算中提供恆溫非反射性邊界條件的功能。在ABL方法部分，本文提出了兩種主要的映射轉換來獲得吸收層的運動方程式，同時在解析上及數值上討論了其相關係收性能。從 映射轉換出發，本文發展了一系列的延伸轉換來改進波動吸收性能；並在最後獲得一種ABL延伸方法使得其低頻反射率可以降到最低。最後，我們針對所有提及的非反射性邊界條件做了廣泛的比較。
在Verlet半徑基於溫度及相鄰列表更新間隔的嚴謹定義下，本文給出了分子動力學計算時間的估計公式；由此公式我們可以決定不同系統總原子數、系統平均密度及平均溫度下最佳的列表更新演算法。其中，Verlet 元胞連結列表 (Verlet Cell-linked List, VCL)演算法在高原子總數情形下可證明是相較於其他方法為最佳的。進一步地分析及模擬結果指出，廣義的元胞連結列表(GVCL)演算法在搭配最佳的列表更新間隔及元胞分割數時，相較於VCL演算法可將計算時間減少百分之三十至六十。
最後，本文使用了佐以恆溫非反射邊界條件之分子動力模擬來分析雷射輔助壓印製程中之材料物理行為。結果指出所使用之邊界條件不僅可以良好地鬆弛原子晶格，更可以在加熱及壓印過程中逐漸地吸收動量及能量的波動傳遞。此外，本文還討論了製程中底材溫度與應力的變化、壓模/脫膜間隔控制的影響以及模具表面處理之效應。

In order to prevent the spurious wave reflections and to improve the computational efficiency in nanomechanical simulation, this dissertation performs a series of theoretical/numerical studies on the crystalline solid material, including nanomechanics of monatomic lattice, isothermally non-reflecting boundary condition, fast updating of neighbor list, and the application/simulation in laser-assisted nano-imprinting.
Firstly, the nanomechanical and statistical behavior of monatomic crystal lattice are introduced, which is the foundation for the development of non-reflecting boundary condition and the simulation of corresponding nano materials. Based on the assumptions and the harmonic approximation for the utilized inter-atomic potential, the equation of motion as well as dispersive relation will be given. Furthermore, from the statistical properties of phonon and lattice energy, the thermal amplitude can be calculated and lattice temperature can be defined, which covers the result previously derived by other researchers at high temperatures.
Method of Time-History-Kernel (THK) and method of absorbing boundary layer (ABL) are two main philosophies to derive the generalized Langevin equation, which is a general form of non-reflecting boundary conditions. The general concepts of THK method, including the formulation, kernel generation, time convolution, application assessments and numerical verification, are given. Based on the Crump’s method to express the THK function in the exponential form, a recursive algorithm for THK time-convolution has been proposed to reduce the computational cost from down to . By applying the THK method in lattice relaxation and the system under external forcing or heating, it is demonstrated that the THK method indeed provides an isothermally non-reflecting boundary condition in nanomechanical computation.
In ABL methods, two major mapping formulations are proposed and the corresponding performances are discussed analytically as well as verified numerically. Starting from the -mapping formulation, a series of extensive ABL methods are developed and investigated to improve the performance of wave absorption, and one ABL method is recommended due to its lower reflection at low frequency. Finally, the general comparison for all non-reflecting boundary condition is addressed.
Based on a rigorous definition of Verlet radius with respect to temperature and list-updating interval, this study gives an estimation formula of computation time, with which the best algorithm can be chosen according to different total number of atoms, system average density and system average temperature in the nanomechanical system. It has been shown that the Verlet Cell-linked List (VCL) algorithm is better than other algorithms for a system with a large number of atoms. Furthermore, a generalized VCL (GVCL) algorithm optimized with a list-updating interval and cell-dividing number is analyzed and shows the reduction of the computation time by 30% ~ 60%, which is verified by the molecular-dynamics simulation for a two-dimensional system.
Finally, the molecular dynamics simulation accompanied with the isothermally non-reflecting boundary condition is performed to analyze the related material physics in laser-assisted nano-imprinting. Results show that the implemented boundary condition relax the lattice well, and eventually absorb the wave propagation of momentum/energy during heating and imprinting process. Besides, the temperature/force evolution in substrate, effect of the molding-demolding interval, and surface situation of mold are discussed.

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