[ExI] If you follow the developments with Tabby's star . .

Anders anders at aleph.se
Mon Sep 19 10:27:19 UTC 2016

Hmm, it sounds like a radiosity/radiometry problem. "Given a frustrum 
with incident energy I1 on the top, perfectly reflecting walls, and a 
bottom at 3K, give the equilibrium temperature distribution."

(much recent work has happened in computer graphics rather than in heat 

So we need to subdivide the walls into small patches, calculate form 
factors, and solve a big linear equation system. Seems totally doable, 
except that being lazy I wish there was a Matlab toolbox for it (HOT is 
just for thermodynamics). I see there are python libraries for it.

On 2016-09-18 16:51, spike wrote:
> -----Original Message-----
> From: extropy-chat [mailto:extropy-chat-bounces at lists.extropy.org] On Behalf
> Of Keith Henson
> Sent: Sunday, September 18, 2016 8:08 AM
> To: ExI chat list <extropy-chat at lists.extropy.org>
> Subject: Re: [ExI] If you follow the developments with Tabby's star . .
> On Sat, Sep 17, 2016 at 12:49 PM, Anders <anders at aleph.se> wrote:
>>> ... Let's see if I get the basic argument: you have a shell of radius R.
>> The luminosity L is absorbed, and in the standard model assumed to all...
>>> ...extra IR now is radiated all over the place. So this gives L/(32 pi^2
>> R^4 )extra input of heating per square meter. That doesn't *seem* too
> bad...
>> ...If it is really a shell, then radiation to the inside will be in net
> equilibrium.  Only the outside will radiate the energy from the star...So if
> we continue to find no excess IR from this star, it's supportive of certain
> classes of space industrial objects that radiate heat directionally...Keith
> _______________________________________________
> Anders and Keith, there is an approach I have been struggling with, which
> uses Bessel functions, but I need some adult supervision if someone here can
> offer it, or knows someone who can, specifically someone with access to idle
> graduate students armed with Matlab and such.
> Assume a sunlike star and assume away all planets and debris (I am not a
> mathematician, but I sometimes act like one when it is time to assume away
> planets and debris.)
> OK now assume a 1 square meter reference plane perpendicular to a line from
> the center of the square meter thru the center of the star.  Out at 1 AU,
> there are nearly half a mole such meter squares, so it shouldn't be hard to
> imagine picking one.
> OK now imagine a kind of truncated square based pyramid (frustum) opening
> outward from there, such that the included angle formed by lines to the
> center of the star remains constant.  Imagine the pyramid going out 5 AU so
> that the frustum base is 5 meters on a side.
> We now need only calculate the heat load on that small end square meter base
> (which is about 1400 W) and the heat emission at the 25 m^2 big end out into
> 3K space.  The heat load thru the sides of the frustum is irrelevant, since
> the heat going in vs the heat going out is identical along the entire face
> always and forever amen.  That simplifies the model to heat in at the small
> end, and heat load out the big end, ja?  Are we ready to Bessel?
> OK, with that model, and some clever Matlab coding (I no longer have access
> to Matlab, oy) we should be able to create thermal distributions along the
> length of that frustum.
> I did that using uniform distributions and discovered that my Bessel
> functions predict we overheat inboard if we extract too much energy from
> that mass distribution (of MBrain nodes) within the Frustum.
> If the mass distribution of MBrain nodes within the frustum is sufficiently
> low, most of the energy passes thru, and the temperature distribution stays
> good.  But if the mass distribution is high, the inboard part overheats.  At
> some point, there is a uniform mass distribution along the length of the
> frustum in which the peak temperature is a nice balmy 300K.  I propose we
> call this mass distribution the Bradbury density.  Or we could call it the
> Bradbury300 density, so we can calculate a new density for Bradbury350 and
> so on.
> The Bradbury density assumes no directional reflection, so all the energy
> has to come in the 1 meter square reference plane at 1 AU and be emitted
> from the 5 meter square 5 AU plane.
> We could of course use other numbers.  I propose a name for peak
> temperatures designated as inner diameter in AU, dash, outer diameter in AU,
> Bradbury, peak temperature in Kelvin.
> The above thought experiment assumes no low-entropy reflection and the peak
> temperature would be called:
> 1-5Bradbury300.
> I propose this name because had Robert lived, he would have embraced this
> notion, assuming I invested several hours arguing with him over it (he
> didn't do MBrain thermal models much and didn't cotton to them, but he liked
> my doing them.)
> spike
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Dr Anders Sandberg
Future of Humanity Institute
Oxford Martin School
Oxford University

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