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Quark Pressure
Name: Charles
Status: other
Age: 20s
Location: N/A
Country: N/A
Date: 1999
Question:
I was wondering if anybody could help me here: I don't
suppose anyone knows the degeneracy pressure of quarks? I'm trying to run
a comparison on degeneracy pressures of Fermions in general and I don't
have the materials handy for either calculating any given pressure
(adiabatic in particular) associated with a particular Fermion nor a
table of such (which would be of much greater value and use).
Specifically, my question/request is: I'm looking for a comparison of the
reaction to large scale (~3*10^30 through ~2*10^32 particles) confinement
of quarks (preferably of each type) vs. neutrons and electrons, but any
information will be better than none. Thanks! :-)
There's a second part to this which might not seem related, but it does
have bearing. However, it's fairly long, but here goes:
Question:
When one calculates n! is there a method to do so quickly and
exactly without crunching all intermediate n-x factors? For example, when
summing all numbers 1+2+3+...n one can either add all numbers from 1 to n
or one can apply a simple formula ((n+1)*(n/2)) to find the answer
without too much effort; can/has this be done for n!?
Specific examples: 10+9+8+7+6+5+4+3+2+1=(100+1)(100/2)=101*50=5050
10*9*8*7*6*5*4*3*2*1= (no exact shortcut) =3628800
I've run across the Stirling approximation formulae, but they're just
insufficiently approximate (predictably enough). Granted the inaccuracy
drops off to infinitesimally small amounts by ratio of the whole correct
answer to the whole incorrect answer (say, 1% or 2% for n~100), but when
comparing the logarithms, there's still an inaccuracy of several percent
for extremely large numbers (1% or 2% of
Replies:
What the heck is degeneracy pressure? Do you mean the Fermi
pressure? As I understand it, quarks don't interact that strongly
when they are close, so you might as well try the grand canonical
Fermi-Dirac partition function, and use a particle-in-the-box model to
model the energy spectrum. It's a rough pass, anyway.
You can improve on Stirling's approximation systematically by using
the Euler-Mclaurin series for conversion of a sum to an integral.
Finally, if you are looking for the log of factorials, you are
wanting approximations to a gamma function. Have a squint at
Abramowitz and Stegun (their book on special functions).
Grayce
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