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\chapter{\label{chapt:intro}Introduction and Theoretical Background} |
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\section{\label{introSec:theory}Theoretical Background} |
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The techniques used in the course of this research fall under the two |
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main classes of molecular simulation: Molecular Dynamics and Monte |
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Carlo. Molecular Dynamic simulations integrate the equations of motion |
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for a given system of particles, allowing the researher to gain |
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insight into the time dependent evolution of a system. Diffusion |
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phenomena are readily studied with this simulation technique, making |
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Molecular Dynamics the main simulation technique used in this |
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research. Other aspects of the research fall under the Monte Carlo |
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class of simulations. In Monte Carlo, the configuration space |
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available to the collection of particles is sampled stochastichally, |
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or randomly. Each configuration is chosen with a given probability |
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based on the Maxwell Boltzman distribution. These types of simulations |
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are best used to probe properties of a system that are only dependent |
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only on the state of the system. Structural information about a system |
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is most readily obtained through these types of methods. |
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Although the two techniques employed seem dissimilar, they are both |
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linked by the overarching principles of Statistical |
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Thermodynamics. Statistical Thermodynamics governs the behavior of |
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both classes of simulations and dictates what each method can and |
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cannot do. When investigating a system, one most first analyze what |
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thermodynamic properties of the system are being probed, then chose |
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which method best suits that objective. |
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\subsection{\label{introSec:statThermo}Statistical Thermodynamics} |
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ergodic hypothesis |
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enesemble averages |
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\subsection{\label{introSec:monteCarlo}Monte Carlo Simulations} |
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The Monte Carlo method was developed by Metropolis and Ulam for their |
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work in fissionable material.\cite{metropolis:1949} The method is so |
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named, because it heavily uses random numbers in the solution of the |
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problem. |
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\subsection{\label{introSec:md}Molecular Dynamics Simulations} |
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time averages |
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time integrating schemes |
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time reversible |
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symplectic methods |
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Extended ensembles (NVT NPT) |
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constrained dynamics |
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\section{\label{introSec:chapterLayout}Chapter Layout} |
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\subsection{\label{introSec:RSA}Random Sequential Adsorption} |
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\subsection{\label{introSec:OOPSE}The OOPSE Simulation Package} |
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\subsection{\label{introSec:bilayers}A Mesoscale Model for Phospholipid Bilayers} |
