#### Initial definitions

Initial definitions

The integrand

In[]:=

f=ρ/(1+ρ^2)^(5/2)

Out[]=

ρ

5/2

(1+)

2

ρ

Avoid error messages associated with the upper limit in the numerically evaluated integral

In[]:=

g[lower_,upper_?NumberQ]:=NIntegrate[f,{ρ,lower,upper}]

List of radii

In[]:=

r={0}

Out[]=

{0}

List of sector counts

In[]:=

s={8,16,24,24,24,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,32,32,16}

Out[]=

{8,16,24,24,24,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,32,32,16}

#### Ring radii and thicknesses

Ring radii and thicknesses

In[]:=

Do[AppendTo[r,x/.FindRoot[g[r[[i]],x]==.001/(3/s[[i]]),{x,r[[i]]+.1}]],{i,Length[s]}]

In[]:=

r

Out[]=

{0,0.0732744,0.127777,0.182585,0.226003,0.263816,0.330484,0.390801,0.448067,0.504125,0.560247,0.617473,0.676782,0.739211,0.805962,0.87854,0.958952,1.05003,1.15606,1.28396,1.44608,1.66772,2.01358,2.41493,3.31945,4.89898}

In[]:=

t=Table[r[[i+1]]-r[[i]],{i,1,Length[s]}]

Out[]=

{0.0732744,0.0545026,0.0548075,0.0434184,0.0378135,0.0666672,0.0603169,0.0572662,0.0560581,0.0561221,0.0572261,0.0593093,0.0624287,0.0667509,0.0725782,0.0804115,0.0910824,0.106026,0.127898,0.162126,0.221638,0.345857,0.401353,0.904518,1.57953}