Problem I

1) Use the following parameters for the simulation and plot k vs S to see how k evolves with S under different set of parameters. Depending on the parameter, each simulation could take 10 to 40 minutes.

2) Fix N at 100, S at 100000, T at 300, R at 7 and M at 1, simulate k using various time intervals between two swaps W (e.g. from 10 to 300). See how the temperature distribution and k changes with W. Explain your finding. Identify a minimum W to determine k under the parameters specified above.

3) In what circumstances will the temperature profile approach linear? Attemp 2) before answering 3)

4) Fix N at 300, S at 300000, T at 1200, R at 7 and M at 1, plot k vs W for W = 10 - 600. Compare the result with part 2).