Editing Muon Decay Simulation (section)

==Results and Brief Discussion==

Our basic finding was that muon decay and lead thickness have a positively correlating relationship. Below are two plots illustrating our data and demonstrating that finding. The first was generated as a result of our first simulation where the energy distribution displayed above was used. The second was generated by another simulation where the energy distribution was ignored and all particles were given a single energy(4 GeV). Brief discussions of both results and an explanation of the inspiration for the second run accompany the results.

 [[File:Dist Results .gif]]
 In this plot the data points are represented by the red points, and the associated error bars are represented by the red bars attached to each points.

Clearly this data demonstrates a complex relationship between muon decay and thickness. It would appear that the data would be best fit by some combination of decaying exponential curves; however no fit was applied here because of its complex nature. The data does clearly demonstrate a positive relationship between muon decay and lead thickness.

As a result of compiling and view this data, we theorized that the complex nature of the relationship was caused at least in part by the fact that we used an energy distribution to choose a particles initial energy. To see if this conclusion was reasonable, we ran a second simulation not using the distribution, but instead setting the starting energy of each particle to four giga-electron-volts(4 GeV). The results of that simulation are demonstrated below. 

 [[File:Single Energy Results.gif]]
 In this plot the data points are represented by the red points, and the associated error bars are represented by the red bars attached to each points.

This data set shows a positive correlation between muon decay and lead thickness as well, however the relationship is not as complex as the one revealed by the first simulation. It appears that this data set would be easier to fit and would be an excellent continuation of this project: We were not able to fit this data by the time we stopped working on the project. Despite this fact, two significant conclusions can be drawn about the relationship between muon decay and lead thickness: First, the relationship is smooth and positive, and second, there is almost no decay when no lead is present and eventually as lead is added almost all particles will decay. The asymtotic behavior we predicted would seem to be supported, although with no proper fit this is just a general observation and has no evidential support. 

Considering our primary goal was to find if there was a relationship between lead thickness and muon decay, the project was a success despite not being able to generate any kind of model about that relationship. There is clearly a lot more research opportunity associated with this project to be worked on. Fitting the data already collected, collecting more and targeted data, and redesigning the simulation to allow for greater variable ranges are just a few ideas. With most of the code already produced a few simple adaptations could add significant depth to this project going forward.