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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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> |
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 |
| 14 |
> |
phenomena are readily studied with this simulation technique, making |
| 15 |
> |
Molecular Dynamics the main simulation technique used in this |
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> |
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 |
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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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|
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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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> |
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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\subsection{\label{introSec:monteCarlo}Monte Carlo Simulations} |
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< |
Stochastic sampling |
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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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detatiled balance |
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– |
metropilis monte carlo |
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– |
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\subsection{\label{introSec:md}Molecular Dynamics Simulations} |
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time averages |
