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\chapter{\label{chapt:conclusion}CONCLUSION} |
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The primary goal of this research has been to develop and apply |
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computational methods to study the structure and dynamics of soft |
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condensed matters. As underlying physical law behind molecular |
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modeling of soft condensed matters, statistical mechanical principle |
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used in this dissertation is briefly reviewed in |
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Chapt.~\ref{chapt:introduction}. Following that, an introduction to |
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molecular simulation techniques including newtonian dynamics and |
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Langevin dynamics was provided. Even though the motions of soft |
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condensed system are characterized by different ODEs between |
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Newtonian dynamics and Langevin dynamics, they all preserve some |
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underlying geometric properties. These properties are built into |
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geometric integration method, which gives the method remarkable |
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performance and stability, especially during long simulations. Thus, |
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theory of geometric integration and the methods to construct |
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symplectic integrators are also covered in |
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Chapt.~\ref{chapt:introduction}, as well as the mathematics behind |
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the elegant symplectic integration scheme involving rigid body |
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dynamics. |
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In Chapt.~\ref{chapt:methodology}, the basic methods used in this |
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work were discussed. An overview of the DLM method was given showing |
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that DLM distinguished itself by its accuracy and efficiency during |
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long time simulation. Following this, DLM method was extended to |
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produce canonical ensemble and isobaric-isothermal ensemble, as well |
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as special ensembles like $NPAT$ ensemble and $NP\gamma T$ ensemble |
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to alleviate the anisotropic effect of biological membrane systems. |
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In order to study slow transport in membrane systems, a new method |
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to study diffusion by measuring the constraint force was proposed |
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and verified. |
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Chapt.~\ref{chapt:lipid} provided a general background to the |
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transport phenomena in biological membrane system. All atomistic |
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simulations were applied to study the headgroup solvation for |
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different phosphorlipids, and it was shown that. A simple but |
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relative accurate and efficient coarse-grained model was developed |
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to capture essential features of the headgroup-solvent interactions. |
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It was then shown the structural properties of membrane bilayer are |
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well agreed with experimental data. Further studies combining |
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external force dragging method and z-constraint method may provide |
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insights into understanding of transport in large scale biological |
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systems. |
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The current status of experimental and theoretical approaches to |
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study phase transition in banana-shaped liquid crystal system was |
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first reviewed in Chapt.~\ref{chapt:liquidcrystal}. A new rigid body |
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model consisting of three identical Gay-Berne particles was then |
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proposed to represent the banana shaped liquid crystal. Starting |
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from an isotropic configuration, we successfully explored an unique |
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chevron structure. Calculations from various order parameters and |
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correlation functions also confirmed this discovery. |
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Lastly, Chapt.~\ref{chapt:langevin} summarized the applications of |
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Langevin dynamics and the development of Brownian dynamics. By |
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embedding hydrodynamic properties into the sophisticated rigid body |
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dynamics, we developed a new Langevin dynamics for |
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translation-rotation couplings systems. Molecular simulations with |
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different viscosities demonstrated the temperature control ability |
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of this new algorithm. It was also shown the dynamics was preserved |
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using this implicit solvent model in studying mixed systems of |
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banana shaped molecules and pentane molecules. |
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Overall, this work has shown the successful application of |
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statistical mechanics for study structure, dynamics and phase |
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behavior of soft condensed matters. Beginning by developing coarse |
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grained models that could reproduce experimental observations, we |
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have extended molecular simulations to study self-assembly in soft |
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condensed systems. Finally, we have developed a new Langevin |
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dynamics algorithm for arbitrary rigid particles which can be used |
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as an implicit solvent model to explore slow processes in soft |
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condensed system. |
