Assignment #11 (Due Sunday, April 11)

 

1. Visit the site ‘http://web.mse.uiuc.edu/matse390/’and choose ‘Simulation Links’. You will find a listing of several applications and software. Choose ‘Buffon’s Needle Monte Carlo Simulation’. Run the applet. Monte Carlo integration algorithms use these ideas to estimate integrals (wavefunctions, energies etc.) for complex higher dimensional systems.

 

1. Repeat the experment on your own with a toothpick using 50-100 drops. Record your results and that from the web simulation.
2. Will increasing the spacing between the lines for a constant needle length decrease or increase the number of drops required to estimate pi accurately? Why?

 

2. Goto the ‘Travelling Salesman Problem’ link from the same page.

 

1. Run the simulation for 5, 10 and 20 points, adjusting the cooling rate and temperature to try and find the optimum distance.
2. Does it matter if the points are collinear?
3. Was the simulation most sensitive to cooling or temperature?