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}

The Monte Carlo method was developed by Metropolis and Ulam for their
work in fissionable material.\cite{metropolis:1949} The method is so
named, because it heavily uses random numbers in the solution of the
problem.


\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}
Revision:	953
Committed:	Sun Jan 18 03:07:59 2004 UTC (20 years, 7 months ago) by mmeineke
Content type:	application/x-tex
File size:	2416 byte(s)
Log Message:	did some work, started on the introduction chapter
#	User	Rev	Content
1	mmeineke	914
2
3			\chapter{\label{chapt:intro}Introduction and Theoretical Background}
4
5
6
7			\section{\label{introSec:theory}Theoretical Background}
8
9	mmeineke	953	The techniques used in the course of this research fall under the two
10			main classes of molecular simulation: Molecular Dynamics and Monte
11			Carlo. Molecular Dynamic simulations integrate the equations of motion
12			for a given system of particles, allowing the researher to gain
13			insight into the time dependent evolution of a system. Diffusion
14			phenomena are readily studied with this simulation technique, making
15			Molecular Dynamics the main simulation technique used in this
16			research. Other aspects of the research fall under the Monte Carlo
17			class of simulations. In Monte Carlo, the configuration space
18			available to the collection of particles is sampled stochastichally,
19			or randomly. Each configuration is chosen with a given probability
20			based on the Maxwell Boltzman distribution. These types of simulations
21			are best used to probe properties of a system that are only dependent
22			only on the state of the system. Structural information about a system
23			is most readily obtained through these types of methods.
24	mmeineke	914
25	mmeineke	953	Although the two techniques employed seem dissimilar, they are both
26			linked by the overarching principles of Statistical
27			Thermodynamics. Statistical Thermodynamics governs the behavior of
28			both classes of simulations and dictates what each method can and
29			cannot do. When investigating a system, one most first analyze what
30			thermodynamic properties of the system are being probed, then chose
31			which method best suits that objective.
32	mmeineke	914
33			\subsection{\label{introSec:statThermo}Statistical Thermodynamics}
34
35			ergodic hypothesis
36
37			enesemble averages
38
39			\subsection{\label{introSec:monteCarlo}Monte Carlo Simulations}
40
41	mmeineke	953	The Monte Carlo method was developed by Metropolis and Ulam for their
42			work in fissionable material.\cite{metropolis:1949} The method is so
43			named, because it heavily uses random numbers in the solution of the
44			problem.
45	mmeineke	914
46
47			\subsection{\label{introSec:md}Molecular Dynamics Simulations}
48
49			time averages
50
51			time integrating schemes
52
53			time reversible
54
55			symplectic methods
56
57			Extended ensembles (NVT NPT)
58
59			constrained dynamics
60
61			\section{\label{introSec:chapterLayout}Chapter Layout}
62
63			\subsection{\label{introSec:RSA}Random Sequential Adsorption}
64
65			\subsection{\label{introSec:OOPSE}The OOPSE Simulation Package}
66
67			\subsection{\label{introSec:bilayers}A Mesoscale Model for Phospholipid Bilayers}