trunk/tengDissertation/Conclusion.tex

\chapter{\label{chapt:conclusion}CONCLUSION}

The primary goal of this research has been to develop and apply
computational methods to study the structure and dynamics of soft
condensed matters. As underlying physical law behind molecular
modeling of soft condensed matters, statistical mechanical principle
used in this dissertation is briefly reviewed in
Chapt.~\ref{chapt:introduction}. Following that, an introduction to
molecular simulation techniques including newtonian dynamics and
Langevin dynamics was provided. Even though the motions of soft
condensed system are characterized by different ODEs between
Newtonian dynamics and Langevin dynamics, they all preserve some
underlying geometric properties. These properties are built into
geometric integration method, which gives the method remarkable
performance and stability, especially during long simulations. Thus,
theory of geometric integration and the methods to construct
symplectic integrators are also covered in
Chapt.~\ref{chapt:introduction}, as well as the mathematics behind
the elegant symplectic integration scheme involving rigid body
dynamics.

In Chapt.~\ref{chapt:methodology}, the basic methods used in this
work were discussed. An overview of the DLM method was given showing
that DLM distinguished itself by its accuracy and efficiency during
long time simulation. Following this, DLM method was extended to
produce canonical ensemble and isobaric-isothermal ensemble, as well
as special ensembles like $NPAT$ ensemble and $NP\gamma T$ ensemble
to alleviate the anisotropic effect of biological membrane systems.
In order to study slow transport in membrane systems, a new method
to study diffusion by measuring the constraint force was proposed
and verified.

Chapt.~\ref{chapt:lipid} provided a general background to the
transport phenomena in biological membrane system. All atomistic
simulations were applied to study the headgroup solvation for
different phosphorlipids, and it was shown that. A simple but
relative accurate and efficient coarse-grained model was developed
to capture essential features of the headgroup-solvent interactions.
It was then shown the structural properties of membrane bilayer are
well agreed with experimental data. Further studies combining
external force dragging method and z-constraint method may provide
insights into understanding of transport in large scale biological
systems.

The current status of experimental and theoretical approaches to
study phase transition in banana-shaped liquid crystal system was
first reviewed in Chapt.~\ref{chapt:liquidcrystal}. A new rigid body
model consisting of three identical Gay-Berne particles was then
proposed to represent the banana shaped liquid crystal. Starting
from an isotropic configuration, we successfully explored an unique
chevron structure. Calculations from various order parameters and
correlation functions also confirmed this discovery.

Lastly, Chapt.~\ref{chapt:langevin} summarized the applications of
Langevin dynamics and the development of Brownian dynamics. By
embedding hydrodynamic properties into the sophisticated rigid body
dynamics, we developed a new Langevin dynamics for
translation-rotation couplings systems. Molecular simulations with
different viscosities demonstrated the temperature control ability
of this new algorithm. It was also shown the dynamics was preserved
using this implicit solvent model in studying mixed systems of
banana shaped molecules and pentane molecules.

Overall, this work has shown the successful application of
statistical mechanics for study structure, dynamics and phase
behavior of soft condensed matters. Beginning by developing coarse
grained models that could reproduce experimental observations, we
have extended molecular simulations to study self-assembly in soft
condensed systems. Finally, we have developed a new Langevin
dynamics algorithm for arbitrary rigid particles which can be used
as an implicit solvent model to explore slow processes in soft
condensed system.
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#	User	Rev	Content
1	tim	2685	\chapter{\label{chapt:conclusion}CONCLUSION}
2	tim	2880
3			The primary goal of this research has been to develop and apply
4			computational methods to study the structure and dynamics of soft
5			condensed matters. As underlying physical law behind molecular
6			modeling of soft condensed matters, statistical mechanical principle
7			used in this dissertation is briefly reviewed in
8			Chapt.~\ref{chapt:introduction}. Following that, an introduction to
9			molecular simulation techniques including newtonian dynamics and
10			Langevin dynamics was provided. Even though the motions of soft
11			condensed system are characterized by different ODEs between
12			Newtonian dynamics and Langevin dynamics, they all preserve some
13			underlying geometric properties. These properties are built into
14			geometric integration method, which gives the method remarkable
15			performance and stability, especially during long simulations. Thus,
16			theory of geometric integration and the methods to construct
17			symplectic integrators are also covered in
18			Chapt.~\ref{chapt:introduction}, as well as the mathematics behind
19			the elegant symplectic integration scheme involving rigid body
20			dynamics.
21
22			In Chapt.~\ref{chapt:methodology}, the basic methods used in this
23			work were discussed. An overview of the DLM method was given showing
24			that DLM distinguished itself by its accuracy and efficiency during
25			long time simulation. Following this, DLM method was extended to
26			produce canonical ensemble and isobaric-isothermal ensemble, as well
27			as special ensembles like $NPAT$ ensemble and $NP\gamma T$ ensemble
28			to alleviate the anisotropic effect of biological membrane systems.
29			In order to study slow transport in membrane systems, a new method
30			to study diffusion by measuring the constraint force was proposed
31			and verified.
32
33			Chapt.~\ref{chapt:lipid} provided a general background to the
34			transport phenomena in biological membrane system. All atomistic
35			simulations were applied to study the headgroup solvation for
36			different phosphorlipids, and it was shown that. A simple but
37			relative accurate and efficient coarse-grained model was developed
38			to capture essential features of the headgroup-solvent interactions.
39			It was then shown the structural properties of membrane bilayer are
40			well agreed with experimental data. Further studies combining
41			external force dragging method and z-constraint method may provide
42			insights into understanding of transport in large scale biological
43			systems.
44
45			The current status of experimental and theoretical approaches to
46			study phase transition in banana-shaped liquid crystal system was
47			first reviewed in Chapt.~\ref{chapt:liquidcrystal}. A new rigid body
48			model consisting of three identical Gay-Berne particles was then
49			proposed to represent the banana shaped liquid crystal. Starting
50			from an isotropic configuration, we successfully explored an unique
51			chevron structure. Calculations from various order parameters and
52			correlation functions also confirmed this discovery.
53
54			Lastly, Chapt.~\ref{chapt:langevin} summarized the applications of
55			Langevin dynamics and the development of Brownian dynamics. By
56			embedding hydrodynamic properties into the sophisticated rigid body
57			dynamics, we developed a new Langevin dynamics for
58			translation-rotation couplings systems. Molecular simulations with
59			different viscosities demonstrated the temperature control ability
60			of this new algorithm. It was also shown the dynamics was preserved
61			using this implicit solvent model in studying mixed systems of
62			banana shaped molecules and pentane molecules.
63
64			Overall, this work has shown the successful application of
65			statistical mechanics for study structure, dynamics and phase
66			behavior of soft condensed matters. Beginning by developing coarse
67			grained models that could reproduce experimental observations, we
68			have extended molecular simulations to study self-assembly in soft
69			condensed systems. Finally, we have developed a new Langevin
70			dynamics algorithm for arbitrary rigid particles which can be used
71			as an implicit solvent model to explore slow processes in soft
72			condensed system.