trunk/mattDisertation/Introduction.tex



\chapter{\label{chapt:intro}Introduction and Theoretical Background}


\section{\label{introSec:theory}Theoretical Background}

The techniques used in the course of this research fall under the two main classes of 
molecular simulation: Molecular Dynamics and Monte Carlo. Molecular Dynamic simulations
integrate the equations of motion for a given system of particles, allowing the researher
to gain insight into the time dependent evolution of a system. Diffusion phenomena are 
readily studied with this simulation technique, making Molecular Dynamics the main simulation
technique used in this research. Other aspects of the research fall under the Monte Carlo
class of simulations. In Monte Carlo, the configuration space available to the collection
of particles is sampled stochastichally, or randomly. Each configuration is chosen with
a given probability based on the Maxwell Boltzman distribution. These types of simulations
are best used to probe properties of a system that are only dependent only on the state of
the system. Structural information about a system is most readily obtained through
these types of methods.

Although the two techniques employed seem dissimilar, they are both linked by the overarching
principles of Statistical Thermodynamics. Statistical Thermodynamics governs the behavior of 
both classes of simulations and dictates what each method can and cannot do. When investigating
a system, one most first analyze what thermodynamic properties of the system are being probed,
then chose which method best suits that objective.

\subsection{\label{introSec:statThermo}Statistical Thermodynamics}

ergodic hypothesis

enesemble averages

\subsection{\label{introSec:monteCarlo}Monte Carlo Simulations}

Stochastic sampling

detatiled balance

metropilis monte carlo

\subsection{\label{introSec:md}Molecular Dynamics Simulations}

time averages

time integrating schemes

time reversible

symplectic methods

Extended ensembles (NVT NPT)

constrained dynamics

\section{\label{introSec:chapterLayout}Chapter Layout}

\subsection{\label{introSec:RSA}Random Sequential Adsorption}

\subsection{\label{introSec:OOPSE}The OOPSE Simulation Package}

\subsection{\label{introSec:bilayers}A Mesoscale Model for Phospholipid Bilayers}
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2
3			\chapter{\label{chapt:intro}Introduction and Theoretical Background}
4
5
6
7			\section{\label{introSec:theory}Theoretical Background}
8
9			The techniques used in the course of this research fall under the two main classes of
10			molecular simulation: Molecular Dynamics and Monte Carlo. Molecular Dynamic simulations
11			integrate the equations of motion for a given system of particles, allowing the researher
12			to gain insight into the time dependent evolution of a system. Diffusion phenomena are
13			readily studied with this simulation technique, making Molecular Dynamics the main simulation
14			technique used in this research. Other aspects of the research fall under the Monte Carlo
15			class of simulations. In Monte Carlo, the configuration space available to the collection
16			of particles is sampled stochastichally, or randomly. Each configuration is chosen with
17			a given probability based on the Maxwell Boltzman distribution. These types of simulations
18			are best used to probe properties of a system that are only dependent only on the state of
19			the system. Structural information about a system is most readily obtained through
20			these types of methods.
21
22			Although the two techniques employed seem dissimilar, they are both linked by the overarching
23			principles of Statistical Thermodynamics. Statistical Thermodynamics governs the behavior of
24			both classes of simulations and dictates what each method can and cannot do. When investigating
25			a system, one most first analyze what thermodynamic properties of the system are being probed,
26			then chose which method best suits that objective.
27
28			\subsection{\label{introSec:statThermo}Statistical Thermodynamics}
29
30			ergodic hypothesis
31
32			enesemble averages
33
34			\subsection{\label{introSec:monteCarlo}Monte Carlo Simulations}
35
36			Stochastic sampling
37
38			detatiled balance
39
40			metropilis monte carlo
41
42			\subsection{\label{introSec:md}Molecular Dynamics Simulations}
43
44			time averages
45
46			time integrating schemes
47
48			time reversible
49
50			symplectic methods
51
52			Extended ensembles (NVT NPT)
53
54			constrained dynamics
55
56			\section{\label{introSec:chapterLayout}Chapter Layout}
57
58			\subsection{\label{introSec:RSA}Random Sequential Adsorption}
59
60			\subsection{\label{introSec:OOPSE}The OOPSE Simulation Package}
61
62			\subsection{\label{introSec:bilayers}A Mesoscale Model for Phospholipid Bilayers}