I Using the ni Formula from a Paper with N=7: What do I Get?

  • I
  • Thread starter Thread starter rabbed
  • Start date Start date
  • Tags Tags
    Formula Paper
AI Thread Summary
The discussion centers on the application of the formula ni = (e^(B*(eH-ei))-1)*e^(-0.5772156649..) from a referenced paper to derive specific values for n0 through n7, given N=7. Users are attempting to confirm if substituting values into the formula yields the expected results of (3,2,1,1,0,0,0,0). There is confusion regarding the derivation and matching of these values with Boltzmann's combinatorial argument. The inability to access the original paper adds to the difficulty in understanding the formula's application. The conversation highlights the challenge of finding a suitable B to achieve the desired outcomes.
rabbed
Messages
241
Reaction score
3
Hi

How do I use this formula:
ni = (e^(B*(eH-ei))-1)*e^(-0.5772156649..)
from this paper?
https://ui.adsabs.harvard.edu/abs/2018DDA...49P...2C/abstract
According to this site, (n0,n1,n2,n3,n4,n5,n6,n7) = (3,2,1,1,0,0,0,0) for N=7:
https://bouman.chem.georgetown.edu/S02/lect21/lect21.htm
Does that mean I should get:
n0 = (e^(B*(7-0))-1)*e^(-0.5772156649..) = 3
n1 = (e^(B*(7-1))-1)*e^(-0.5772156649..) = 2
n2 = (e^(B*(7-2))-1)*e^(-0.5772156649..) = 1
n3 = (e^(B*(7-3))-1)*e^(-0.5772156649..) = 1
?
 
Physics news on Phys.org
cant open this paper. says: No Sources Found
 
Yes, I can't find the actual paper either but that abstract (as well as another abstract from him) makes the derivation clear:

digamma(ni+1) = a-b*ei

use approximation digamma(x+1) = ln(e^-m+x) where m = 0.5772156649

ln(e^-m+ni) = a-b*ei

e^-m+ni = e^(a-b*ei)

ni = e^(a-b*ei)-e^-m
ni = e^(a+m-m-b*ei)-e^-m
ni = e^(a+m-b*ei)*e^-m-e^-m
ni = (e^(a+m-b*ei)-1)*e^-m
ni = (e^(a*((A+m)/b-ei))-1)*e^-m

replace eH = (a+m)/b

ni = (e^(b*(eH-ei))-1)*e^-m

I just can't get the ni's to match Boltzmann's combinatorical argument.
Shouldn't it be possible to find a B such that (n0,n1,n2,n3,n4,n5,n6,n7) = (3,2,1,1,0,0,0,0) for N=7?
 
Thread 'Gauss' law seems to imply instantaneous electric field'
Imagine a charged sphere at the origin connected through an open switch to a vertical grounded wire. We wish to find an expression for the horizontal component of the electric field at a distance ##\mathbf{r}## from the sphere as it discharges. By using the Lorenz gauge condition: $$\nabla \cdot \mathbf{A} + \frac{1}{c^2}\frac{\partial \phi}{\partial t}=0\tag{1}$$ we find the following retarded solutions to the Maxwell equations If we assume that...
Maxwell’s equations imply the following wave equation for the electric field $$\nabla^2\mathbf{E}-\frac{1}{c^2}\frac{\partial^2\mathbf{E}}{\partial t^2} = \frac{1}{\varepsilon_0}\nabla\rho+\mu_0\frac{\partial\mathbf J}{\partial t}.\tag{1}$$ I wonder if eqn.##(1)## can be split into the following transverse part $$\nabla^2\mathbf{E}_T-\frac{1}{c^2}\frac{\partial^2\mathbf{E}_T}{\partial t^2} = \mu_0\frac{\partial\mathbf{J}_T}{\partial t}\tag{2}$$ and longitudinal part...
Back
Top