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scratch4

v39	v40
33	33	[[latex($\sum \Delta E_i*dV_i=E ~~~~~~(1)$)]]
34	34
35		where [[latex($E$)]] is the accretion energy ~~from~~ the time step, [[latex($\Delta E_i$)]] is the differential amount of E to be distributed in the ith cell, and [[latex($dV_i$)]] is the volume of the ith cell. As of now, the units don't balance in this equation. We then need to find a normalization constant that has units of 1/volume, which we will do next.
	35	where [[latex($E$)]] is the accretion energy over the time step, [[latex($\Delta E_i$)]] is the differential amount of E to be distributed in the ith cell, and [[latex($dV_i$)]] is the volume of the ith cell. As of now, the units don't balance in this equation. We then need to find a normalization constant that has units of 1/volume, which we will do next.
36	36
37	37	We want the amount of E in each cell to drop off smoothly with radius away from the sink. For this we choose a decaying exponential. Let,