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Random numbers in , adaptive integration and properties of lasers.

I finally got help in solving a problem I was having with generating random generators in C, using the standard function rand(). Apparently, srand48() also does the same job as rand() does and does it better even but I wanted to get my code working with rand() in the first place. Calling rand() returns a random large integer and I needed to convert it to a float between (0,1). RAND_MAX is defined as the largest random number that the system can generate. I knew that I had to divide the output of rand() by RAND_MAX and after a bit of juggling things around, I finally got it working. The relevant code is an implementation of the one I've written earlier in python ad fortran to estimate the value of pi using monte carlo integration. The numerical methods lab in the afternoon had us implementing an adaptive integration method that would choose step size depending on the error and increase or decrease it accordingly if our new estimate was correspondingly better or worse than the prior one. I hacked together an ugly code based on an ugly method to solve the problem, which I am not at all happy with. And I wasn't able to implement the solution told to us, nor was I able to implement how I understood the problem. And further, I would also like to implement this in fortran and python I need to get my ass moving if I want to clean shop by the weekend.

Finally, I made one more visualization on how the modes supported by a laser medium+cavity vary depending on the cavity length and on the properties of the medium. A crude hack that varies the center of the gain function, modeled as a gaussian, and the bandwidth of the gain function, while showing the cavity modes was put together, on an ipython notebook, using ipywidgets, matplotlib and numpy. I need to add a cavity length dependence on the mode spacing of the laser cavity and I need to get numbers for the gain function's center and bandwidth for a real system. Weekend ahoy!

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