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Title: | 1. 多極展開法於粗粒化力場與分子動力學模擬
2. 波浪能受海底週期性結構之增益:模擬與實驗研究 1. Multipolar Expansion Methods for Coarse-Grained Force Fields and Molecular Dynamics Simulation 2. Enhancement of Sea Wave Potential Energy with Under-sea Periodic Structures: A Simulation and Laboratory Study |
Authors: | Shuo-Feng Chiu 邱碩峯 |
Advisor: | 趙聖德 |
Keyword: | 粗粒化力場,多極展開,分子動力學模擬,週期性圓柱陣列結構,淺水波方程式,波幅增益, coarse-grained force field,multipolar expansion,molecular dynamics simulation,periodic cylindrical array structure,shallow water wave equation,wave amplitude enhancement., |
Publication Year : | 2018 |
Degree: | 博士 |
Abstract: | 粗粒化 (Coarse-grained) 分子動力學模擬方面,本文提出了一種多極展開的粗粒化力場,該方法是通過轉化讓interblob的勢能近似於從第一原理計算、全原子經驗力場、實驗數據,或上述的任意組合得到之分子間相互作用勢能。這個級數提供了可控制的近似值,使我們能夠隨著展開項相次的增加而估計誤差,並接近原分子間的勢能,這樣我們可以只操作定義過的矩陣張量項,而不需重複於局部原子層級的計算。
我們分別對富勒烯 (Fullerene) 分子進行了全原子與粗粒化分子動力學模擬以比較其差異,在全原子經驗力場得到位勢能曲線後,將這兩個模型分別進行能量的擬合以建構其力場。在粗粒化過程中,將富勒烯當成一個等價的粒子來取代原本的原子團,此步驟可以有效減少計算量並可選用更大的時間步數。另外,我們從三相點沿著氣化曲線計算至臨界點,計算了不同溫度與密度下的徑向分佈函數(Radial Distribution Function) 、速度自相關函數 (Velocity Autocorrelation Function)與擴散係數 (Diffusion constant) 等,通過對富勒烯的模擬應用,可發現這個多極的粗粒化分子模型可有效地獲得原子級模擬的微觀細節,並且可以很容易地擴展到大規模的模擬。 在波浪能研究方面,波浪發電系統是藉由裝置把波浪能先轉換為機械能 (液壓能),然後轉成可利用之電能,對實際波浪而言,其能量潛能受到波高、週期所影響。本文提出一種增強波浪振幅之方法以期改善能流密度與地形水深的限制,使波浪能的擷取能更具廣泛性與效率性。其係在建構具週期性之圓柱陣列結構物,排列方式為三角晶格、四方晶格和六角晶格,由二維淺水波建立波浪之運動方程式,利用平面波展開法計算波在經過結構物後所增益之倍數。由於波浪之能量功率與波高的2次方成正比,根據此特性,歸納出圓柱半徑與晶格常數比值 (r/a) 和相對水深比值 (h0/h) 的相對關係,即可決定波高的增益分佈,模擬結果顯示,三角晶格和四方晶格相對於六角晶格能具有較高的波高的增益值。在數值模擬的基礎上,我們進行了一個縮小的水槽實驗,實驗結果顯示,經由參數 (r/a) 與 (h0/h)的設定,確實可以實現波高的增益現象,也可提供實際尺寸應用上的參考。 In the coarse-grained study, we presents a coarse-grained force field based on a multipolar expansion method developed previously. It is enabled by the construction of transferable united atoms potentials that approximate the full atomistic intermolecular interactions, as obtained from ab initio electronic structure calculations supplemented by empirical force fields and experimental data, or any combination of the above. This series involve controllable moment tensors that permit to estimate the errors and approaches the all-atom intermolecular potential as the expansion order increases. We can compute the united atoms potentials very efficiently with a few interaction moment tensors in order to implement a parallel algorithm on molecular interactions. We performed all-atom and coarse-grained molecular dynamics simulations of fullerene molecules to compare their differences. After obtaining the potential energy curves in the all-atom empirical force field, the two models were separately fitted with energy to construct its force field. In the coarse-grained process, the fullerene is replaced by an equivalent particle. This step can effectively reduce the amount of calculation and carry out larger time steps. Moreover, We calculate the radial distribution function, velocity autocorrelation function and diffusion constant at different temperatures and densities from the triple point along the gasification curve to the critical point. Our simulations describe the mechanism for the condensation of fullerenes and produce excellent agreement with benchmark fully atomistic molecular dynamics simulations. In the sea wave potential energy study, we have theoretically investigated the propagation of surface water wave enhancement by deploying under-sea periodic structures. It is constructed with a periodic cylindrical array structure arranged in a triangular, square, and hexagonal lattices. The two-dimensional shallow water wave is used to construct the equation of motion and solved by using the plane-wave expansion method. These structures determine the sea bottom topography and induce constructive interference on the surface waves, thus enhancing the potential energy. Based on the energy power which is proportional to the square of the wave height, the relationship between the cylindrical radius and the lattice spacing ratio (r/a) and the water depth ratio (h0/h) can be summarized to determine the enhancement factor distribution. Comparing the lattice types, the triangular and square lattice structures can induce more wave amplitude enhancement (and thus potential energy) than the hexagonal structures. Guided by numerical simulations, we have performed a reduced-scale water tank experiment to demonstrate the feasibility of the proposed idea. Preliminary experimental results show promising evidence of the predicted wave amplitude enhancement, suggesting perspective real scale nearshore deployment and test. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/78932 |
DOI: | 10.6342/NTU201803865 |
Fulltext Rights: | 有償授權 |
Appears in Collections: | 應用力學研究所 |
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