Changes between Version 10 and Version 11 of SelfGravityDevel
- Timestamp:
- 01/22/12 17:33:02 (13 years ago)
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SelfGravityDevel
v10 v11 41 41 This can be discretized as 42 42 43 [[latex($\phi(l)= 4 \pi GM \Delta k^{D-2} \displaystyle \sum_{j=-N/2}^{N/2}{\frac{1}{j^2}e^{2\pi ijl/N}}=8 \pi GM (2 \pi/L)^{D-2}\displaystyle \sum_{j=1}^{N/2}{\frac{1}{j^2}\cos(2\pi jl/N)}$)]]43 [[latex($\phi(l)=\frac{4 \pi GM}{\Delta k^2} \displaystyle \sum_{j=-N/2}^{N/2}{\frac{1}{j^2}e^{2\pi ijl/N} \frac{\Delta k}{2\pi}}=\frac{4 \pi GM}{(2 \pi/L)^2}\left(\frac{2 \pi}{L}\right) \displaystyle \sum_{j=1}^{N/2}{\frac{1}{j^2}\cos(2\pi jl/N)}$)]] 44 44 45 This still requires summation over many wave numbers - although the higher wave numbers have less impact because of the [[latex($k^{-2}$)]] dependence. However in 2D this is lessened because there are more wave vectors in each anuli, and in 3D there is equal power in each shell. This then, becomes an order N^6 operation :| 46 47 Solutions: 48 * Don't ever use sink potential? 49 * Don't use sink potential to update gas potential 50 * Solve for gas potential after accretion? 51 *