Department of Energy Argonne National Laboratory Office of Science NEWTON's Homepage NEWTON's Homepage
NEWTON, Ask A Scientist!
NEWTON Home Page NEWTON Teachers Visit Our Archives Ask A Question How To Ask A Question Question of the Week Our Expert Scientists Volunteer at NEWTON! Frequently Asked Questions Referencing NEWTON About NEWTON About Ask A Scientist Education At Argonne 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



Click here to return to the Physics Archives

NEWTON is an electronic community for Science, Math, and Computer Science K-12 Educators, sponsored and operated by Argonne National Laboratory's Educational Programs, Andrew Skipor, Ph.D., Head of Educational Programs.

For assistance with NEWTON contact a System Operator (help@newton.dep.anl.gov), or at Argonne's Educational Programs

NEWTON AND ASK A SCIENTIST
Educational Programs
Building 360
9700 S. Cass Ave.
Argonne, Illinois
60439-4845, USA
Update: June 2012
Weclome To Newton

Argonne National Laboratory