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Density in equilibrium distribution function

Posted by hammedhammed  
Density in equilibrium distribution function
November 22, 2016 03:46PM
Hi,
In the common Equilibrium distribution Function, we do not see the term rho (density). But in dimensionless form of the distribution function (sometimes referred as the normalized Maxwell’s distribution function) it comes up.

Common form= (4*pi*c^2)((m/2kT*pi)^3/2)(exp(-m.c^2/2kT*pi))

Normalized form= (rho/(2*pi/3))(exp(-3(c-u)^2/2))

(U=c-u, c=micro speed, u=fluid bulk speed)

Note that there are other types of normalized form. Does anybody know the mathematical procedure? I greatly appreciate it...
Re: Density in equilibrium distribution function
May 13, 2017 01:08AM
Hello Hammed. All it depend what you want to represent whit this term. Generally this term is used for density but in Shallow Water model is used for the water deep. In Donald A. Mcquarrie. Statistical Mechanics. 2 nd edition, 2007 can you see something like that. Regards
Re: Density in equilibrium distribution function
May 13, 2017 04:02AM
Dear Jairus
thank you for the note. I would take a look at that book.
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