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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 main classes of |
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molecular simulation: Molecular Dynamics and Monte Carlo. Molecular Dynamic simulations |
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integrate the equations of motion for a given system of particles, allowing the researher |
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to gain insight into the time dependent evolution of a system. Diffusion phenomena are |
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readily studied with this simulation technique, making Molecular Dynamics the main simulation |
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technique used in this research. Other aspects of the research fall under the Monte Carlo |
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class of simulations. In Monte Carlo, the configuration space available to the collection |
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of particles is sampled stochastichally, or randomly. Each configuration is chosen with |
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a given probability 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 only on the state of |
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the system. Structural information about a system is most readily obtained through |
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these types of methods. |
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Although the two techniques employed seem dissimilar, they are both linked by the overarching |
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principles of Statistical Thermodynamics. Statistical Thermodynamics governs the behavior of |
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both classes of simulations and dictates what each method can and cannot do. When investigating |
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a system, one most first analyze what thermodynamic properties of the system are being probed, |
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then chose 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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Stochastic sampling |
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detatiled balance |
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metropilis monte carlo |
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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} |
