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 the underlying physical law behind molecular
modeling of soft condensed matter, statistical mechanical principles
used in this dissertation are 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 systems are characterized by different ODEs between
Newtonian dynamics and Langevin dynamics, they all preserve some
underlying geometric properties. These properties are built into a
geometric integration method, which gives the method remarkable
performance and stability, especially during long simulations. Thus,
the 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, the 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 transport
phenomena in biological membranes. Atomistic simulations were
applied to study the headgroup solvation for different
phospholipids. A simple but relatively accurate and efficient
coarse-grained model was developed to capture essential features of
the headgroup-solvent interactions. It was then shown that the
structural properties of the simulated membrane bilayers agreed well
with experimental data. Further studies combining an 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 algorithms, 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 that 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 to study structure, dynamics and phase
behavior of soft condensed materials. 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 systems.
Revision:	2909
Committed:	Thu Jun 29 23:00:35 2006 UTC (18 years, 2 months ago) by tim
Content type:	application/x-tex
File size:	4032 byte(s)
Log Message:	more corrections
#	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	tim	2909	condensed matters. As the underlying physical law behind molecular
6			modeling of soft condensed matter, statistical mechanical principles
7			used in this dissertation are briefly reviewed in
8	tim	2880	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	tim	2909	condensed systems are characterized by different ODEs between
12	tim	2880	Newtonian dynamics and Langevin dynamics, they all preserve some
13	tim	2909	underlying geometric properties. These properties are built into a
14	tim	2880	geometric integration method, which gives the method remarkable
15			performance and stability, especially during long simulations. Thus,
16	tim	2909	the theory of geometric integration and the methods to construct
17	tim	2880	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	tim	2909	long time simulation. Following this, the DLM method was extended to
26	tim	2880	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	tim	2909	Chapt.~\ref{chapt:lipid} provided a general background to transport
34			phenomena in biological membranes. Atomistic simulations were
35			applied to study the headgroup solvation for different
36			phospholipids. A simple but relatively accurate and efficient
37			coarse-grained model was developed to capture essential features of
38			the headgroup-solvent interactions. It was then shown that the
39			structural properties of the simulated membrane bilayers agreed well
40			with experimental data. Further studies combining an external force
41			dragging method and z-constraint method may provide insights into
42			understanding of transport in large scale biological systems.
43	tim	2880
44			The current status of experimental and theoretical approaches to
45			study phase transition in banana-shaped liquid crystal system was
46			first reviewed in Chapt.~\ref{chapt:liquidcrystal}. A new rigid body
47			model consisting of three identical Gay-Berne particles was then
48			proposed to represent the banana shaped liquid crystal. Starting
49			from an isotropic configuration, we successfully explored an unique
50			chevron structure. Calculations from various order parameters and
51			correlation functions also confirmed this discovery.
52
53			Lastly, Chapt.~\ref{chapt:langevin} summarized the applications of
54			Langevin dynamics and the development of Brownian dynamics. By
55			embedding hydrodynamic properties into the sophisticated rigid body
56	tim	2909	dynamics algorithms, we developed a new Langevin dynamics for
57	tim	2880	translation-rotation couplings systems. Molecular simulations with
58			different viscosities demonstrated the temperature control ability
59	tim	2909	of this new algorithm. It was also shown that the dynamics was
60			preserved using this implicit solvent model in studying mixed
61			systems of banana shaped molecules and pentane molecules.
62	tim	2880
63			Overall, this work has shown the successful application of
64	tim	2909	statistical mechanics to study structure, dynamics and phase
65			behavior of soft condensed materials. Beginning by developing coarse
66	tim	2880	grained models that could reproduce experimental observations, we
67			have extended molecular simulations to study self-assembly in soft
68			condensed systems. Finally, we have developed a new Langevin
69			dynamics algorithm for arbitrary rigid particles which can be used
70			as an implicit solvent model to explore slow processes in soft
71	tim	2909	condensed systems.