[from Pawel] how to compute tau? Party on Sat.

I'm talking about the optical thicknaess calculation for a bunch of particles.
Suppose the disk is 2D, otherwise you'll have to generalize. Then each particle must deposit
its dtau (small contribution to tau).

we talked a lot about this with James amd he's your guru on that (right James?). ask him any questions. you first declare an array (2d: r,phi) that will hold dtau(r,phi)

we established that it is much better to use the so-called "scatter" approach than "gather" approach. in the first, you traverse the list of N particles, and donate their dtau's to the
appropriate grid locations (grid indexes are not stored but found each time you need them for a given particle, it should save time and space in ram). in the second approach, you'd traverse the
dtau grid and look for particles inside each grid cell (that's a lot of searching! ~N.)

we need exp(-tau) in the end, we can get it by integrating tau(r,phi) = integral_0^r dtau(r,phi)
= sum_along_r_from_the_innermost_to_the_particle's_cell of dtau(r,phi).

we've talked about a nice trick to avoid computing exponential functions later on.
suppose you have dtau(r) in an array and want exp(-tau). then you can get a very good approximation to f=exp(-tau) by
f = integral_0^tau (-f) dtau
why? because df(tau) = -f(tau) dtau is the differential equation with solution f=exp(-tau) .
you need to start with initial value f=1 at the inner radius and integrate outside.

what is dtau contributed by each particle? it's dA/(4pi r^2) where dA is its geom. cross section.
in general, we don't want to count particles, all we want is to arrive at tau(r,phi) which
in the initial axisymmetric state has tau(r=outer radius) = tau_infinity = 10 (or 3, or something you input). Therefore do an integration using dtau = C/r^2 where C=1 initially, and after getting
tau(outer) or exp(-tau(outer)) computed with the above algorithm, you recalculate C so in all the
later calls to the tau-computing procedure it gives the right outside exp(-tau_infinity) number.

* * *

We will meet on Friday downtown, meanwhile there seems to be enough work and enough computers already doing or starting to do cuda at UTSC to drop in there the rest of the week.

On Sat, as I mentioned, you are invited for a pool-side party (swimming encouraged,
take your swimming pants). bring a friend if you'd like.
I'll make some bbq, but if you want fancy salads maybe we can make it a potluck = byo.. party) hopefully the weather will cooperate so we can go flying for 20 min with each of you out of buttonville airport (north of 404 & 407). http://planets.utsc.utoronto.ca/~pawel/VANsRV.html

please let me know how many are coming and whether you have a car (it would be good to have
more than just my car for the buttonville trip).

finally, the coordinates (time will still be confirmed, we'll see if the Wx is ok the whole or just part of the day):

37 Fairhill Cres., toronto, 2pm, Sat 26 May. I can give you a 1-2km ride from from Underhill and Lawrence to my place, send me the details of how you're coming so we'll set some time to meet
at the gas station there. the bus that goes on Lawrence is called 54.