Timeline for low-discrepancy sequences for sampling of distributions
Current License: CC BY-SA 2.5
7 events
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| Feb 10, 2011 at 9:09 | comment | added | Radfahrer | I want to calculate the beam width as standard deviation of the particles. This of course depends on the initial distributions. To get good results I need more particles. In the link they have those nice histograms for only 200 particles that represent the Gaussian distribution really good, and a plot with random numbers, which is not very good. This nice histogram is created with a low-discrepancy sequence. I simulate single electron beams. I just use more particles for sampling the initial distributions to get meaningful statistics for the beam width. | |
| Feb 10, 2011 at 8:39 | comment | added | Tim van Beek | @Radfahrer: THe reference you linked to is about a simulation of macroparticles in prescribed external electromagnetic fields and boundary conditions, in order to run simulations of new accelerator designs - you'll always have to simulate a certain amount of macroparticles to get representative results, mainly depending on the projected beams intensity - no matter what kind of random number generator you use to generate your initial distribution. Just try one from the standard sources, like "numerical recipes". | |
| Feb 10, 2011 at 8:12 | comment | added | Tim van Beek | @Radfahrer: A particle has 6 coordinates which are random variables and have a joint distribution function, ergo you have a 6-dim-distribution function - what you are saying is that some of these random variables are independent and the 6-dim distribution factors into the product of a two dim in xy coordinates and a one-dim in the z-coordinate etc. My main problem now is to understand, when you say "I would need to simulate more particles, to reduce the error", the error of what? I'll look at the reference you linked to... | |
| Feb 9, 2011 at 15:26 | comment | added | Radfahrer | i am trying to archive something similar like this: google.de/… in chapter 2.6 Initial particle distribution (page 48). I know the use the Hammersley sequence, but don't know how | |
| Feb 9, 2011 at 15:15 | comment | added | Radfahrer | sorry I didn't formulate the question right. I don't have a single 6 dimensional distribution function. What I want is to have a product of different distribution functions. So for example a Gauss distribution in xy plane and a linear distribution in the z direction. So i need to create different distributions. The particles are advanced by classical mechanics. I could use plain random numbers, but I would need to simulate more particles, to reduce the error. So if I understand it correctly I can use low-discrepancy sequences to sample my different distributions. | |
| Feb 9, 2011 at 14:34 | history | edited | Tim van Beek | CC BY-SA 2.5 |
added 123 characters in body
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| Feb 9, 2011 at 14:28 | history | answered | Tim van Beek | CC BY-SA 2.5 |