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Efficiency of many small vs.  one large simulation

Smith [73] and Heggie [38] have noted that n simulations each with N/n particles is much less expensive than 1 simulation with N particles, and is also completely trivial to parallelize. Such sets of simulations can also give better statistics based on the larger sample size, as long as it is known how to scale the statistics from smaller simulations to larger ones. Unfortunately, this scaling is non-trivial because different processes scale differently with N, so it is possible that they interact differently in current simulations than they do in real clusters [38]. Again, we are led to the conclusion that increasing N is the most desirable way of increasing the reliability of N-body simulations.

Smith [73] continued his previous study ([74]) to ascertain the effects of different numbers of particles on statistical measurements. He measured density profiles and binary star formation rates for clusters with N=8,16,32,64 and found that, although the scaled statistics for N=8 differed substantially from those with higher N, the statistics for N=16 and higher agreed quite well. Furthermore, the number of binaries formed scaled as tex2html_wrap_inline2060 , consistent with a theoretical estimate of tex2html_wrap_inline2062 . He didn't measure information on escapers, since escapes happen sufficiently rarely that N=64 doesn't provide enough of a sample. He concluded that better statistics can be taken with many small simulations than with 1 large one.

Although this method is less effective at modelling some processes that really do need a large N, such as gravothermal effects, it may be reliable enough to study processes such as core collapse rates, escape rates, binary star formation rates, density profiles, and gradients of velocity dispersion with radius [38]. However, this does not mean that we can learn everything there is to learn about these statistics by running millions of simulations with N=64, because discreteness noise is still a factor. What these results say is that at any given time, if tex2html_wrap_inline2070 is the largest simulation one is currently capable of running, it may be more productive to run 100 simulations with tex2html_wrap_inline2072 than a single simulation with tex2html_wrap_inline2074 .


next up previous
Next: Exponential divergence in N-body Up: Statistics of collisional N-body Previous: Statistics of collisional N-body

Wayne Hayes
Fri Dec 27 17:41:39 EST 1996

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