In[]:=
g=.​​w=1​​d=0.5​​
Out[]=
1
Out[]=
0.5
In[]:=
a[x_,g_]=ArcCos
1
4
1-d

1-d
+
1+d
+
1-d
-
1+d
Cos[g*x]+
1
4
1+d

1-d
+
1+d
+-
1-d
+
1+d
Cos[g*x]​​b[t_,g_]=Sqrt-
1
8
-1+
1-
2
d
(2
2
g
+
2
w
-
2
w
Cos[2g*t])​​c[y_,g_]:=NIntegrate[b[t,g],{t,0,y}]​​Plot3D[t*a[t,g]/c[t,g],{t,0,10},{g,1,2},AxesLabel{τ,g,Indexed[τ,QSL]^WY}]​​Plot[x/Sqrt[2]*a[x]/c[x],{x,0,10}]
Out[]=
ArcCos[0.176777(1.93185-0.517638Cos[gx])+0.306186(1.93185+0.517638Cos[gx])]
Out[]=
0.12941
1+2
2
g
-Cos[2gt]
Out[]=
Out[]=
2
4
6
8
10
-1.0
-0.5
0.5
1.0
In[]:=
Plot[c[x],{x,0,10}]
Out[]=
2
4
6
8
10
-1.0
-0.5
0.5
1.0
In[]:=
e[t_,g_]=ArcCos
1
2
2
1+
2
d
Cos[gt]-
2
d
(1+Cos[gt])(2-
2
d
+
2
d
Cos[gt])
+
1+
2
d
Cos[gt]+
2
d
(1+Cos[gt])(2-
2
d
+
2
d
Cos[gt])
​​f[t_,g_]=Sqrt[-1/2w(-2+d^2+d^2Cos[2*g*t])+d*g^2*Sin[g*t]*Sin[t*w]]​​h[y_,g_]:=NIntegrate[f[t,g],{t,0,y}]​​Plot[x*e[x]/h[x],{x,0,10}]​​Plot3D[x*e[x,g]/h[x,g],{x,0,10},{g,1,2},AxesLabel{τ,g,Indexed[τ,QSL]^MT}]
Out[]=
ArcCos
1
2
2
1+0.25Cos[gt]-0.5
(1.75+0.25Cos[gt])(1+Cos[gt])
+
1+0.25Cos[gt]+0.5
(1.75+0.25Cos[gt])(1+Cos[gt])

Out[]=
1
2
(1.75-0.25Cos[2gt])+0.5
2
g
Sin[t]Sin[gt]
Out[]=
2
4
6
8
10
-1.0
-0.5
0.5
1.0
Out[]=
In[]:=
Plot[e[x],{x,0,10}]
Out[]=
2
4
6
8
10
-1.0
-0.5
0.5
1.0
In[]:=
j[t_,g_]=ArcCos
1
2
2
1+
2
d
Cos[gt]-
2
d
(1+Cos[gt])(2-
2
d
+
2
d
Cos[gt])
+
1+
2
d
Cos[gt]+
2
d
(1+Cos[gt])(2-
2
d
+
2
d
Cos[gt])
​​k[x_,g_]=-d*w/2-1/2Sqrt[g^2+w^2]​​Plot[-j[x,g]/k[x,g],{x,0,10}]​​Plot3D[-j[x,g]/k[x,g],{x,0,10},{g,1,2},AxesLabel{τ,g,Indexed[τ,QSL]^ML}]​​
Out[]=
ArcCos
1
2
2
1+0.25Cos[gt]-0.5
(1.75+0.25Cos[gt])(1+Cos[gt])
+
1+0.25Cos[gt]+0.5
(1.75+0.25Cos[gt])(1+Cos[gt])

Out[]=
-0.25-
1+
2
g
2
Out[]=
2
4
6
8
10
-1.0
-0.5
0.5
1.0
Out[]=