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Unformatted text preview: PHYS 333 Winter 2009 Assignment 1 1. In Chapter 1 of Schroeders book, he talks about raindrops falling on a roof. He uses this example to introduce the thermodynamic limit when fluctuations are extremely small. Divide up the roof into NB equal parts ( NB = 100 would be suitable) Generate a random number between 0 and 1, and use it to allocate a raindrop randomly to one of the parts. Repeat N times Repeat again for larger values of N ( N = 1000000 would be a suitable upper limit) (a) For each value of N , compute the average number of raindrops per part of the roof, N Av and the standard deviation ( N Av ) of this number. (b) Plot the standard deviation against N Av to discover the functional dependence ( N Av ). What is this? Here is the graph that I generated. The line, on this log-log plot, has a slope of 1/2, and corresponds to = N av . 10 +1 10 +2 10 +3 10 +4 10 +5 10 +6 10 +7 10.0 100.0 1000. 20. 200. 2000. 5. 50. 500. average number of raindrops standard deviation (c) Optional. If you have the math knowledge, show how this dependence comes about....
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This note was uploaded on 04/11/2010 for the course PHYS 333 taught by Professor Harris during the Winter '09 term at McGill.
- Winter '09