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32
u22maxmaxu22():=
u12maxmaxu12():=
u22
i
u22
i
u22max
:=
u12
i
u12
i
u12max
:=
u13
i
U θ
i
ρ03,∆1,n1,
()
:= u23
i
U θ
i
ρ01,∆2,n2,
()
:=
u13maxmaxu13():= u23maxmaxu23():=
u13
i
u13
i
u13max
:= u23
i
u23
i
u23max
:=
u0
i
0.5:=
∆30.01:= n31:=
u31
i
U θ
i
ρ01,∆3,n3,
()
:= u33
i
U θ
i
ρ03,∆3,n3,
()
:=
u31maxmaxu31():= u33maxmaxu33():=
u31
i
u31
i
u31max
:=
u33
i
u33
i
u33max
:=
u32
i
U θ
i
ρ02,∆3,n3,
()
:=
u32maxmaxu32():=
u32
i
u32
i
u32max
:=
TOL0.001:=λ0.4:= k2
π
λ
⋅:= imax50:= i02imax⋅..:=
θ
i
iimax−()
imax
π
15
⋅:=
U θρ0,∆, n,
()
0
2π
φ
0
ρ0
ρ∆ 1 ∆−
()
1
ρ
ρ0
2
−
n
⋅+
ρ⋅ expi−k⋅sin θ
()
⋅ρ⋅ cos φ
()()
⌠
⌡
d
⌠
⌡
d
2
:=
∆11:= n11:=
ρ015λ⋅:=ρ0210 λ⋅:=ρ0325 λ⋅:=∆20.01:= n00:= n22:=
u21
i
U θ
i
ρ01,∆2,n0,
()
:=
u11
i
U θ
i
ρ01,∆1,n1,
()
:=
u21maxmaxu21():=
u11maxmaxu11():=
u21
i
u21
i
u21max
:=
u11
i
u11
i
u11max
:=
u22
i
U θ
i
ρ01,∆2,n1,
()
:=
u12
i
U θ
i
ρ02,∆1,n1,
()
:=
32
π
TOL := 0.001 λ := 0.4 k := 2 ⋅ imax := 50 i := 0 .. 2 ⋅imax
λ
( i − imax) π
θ i := ⋅
imax 15
2
⌠
2π
⌠
ρ0
2 n
ρ
U( θ , ρ0 , ∆ , n) :=
∆ + ( 1 − ∆ ) ⋅ 1 − ρ0 ⋅ρ exp( −i⋅k ⋅sin( θ) ⋅ρ cos ( φ ) ) dρ dφ
⌡0
⌡0
∆1 := 1 n1 := 1
ρ01 := 5 ⋅λ ρ02 := 10 ⋅λ ρ03 := 25 ⋅λ ∆2 := 0.01 n0 := 0 n2 := 2
u11i := U( θ i , ρ01 , ∆1 , n1) u21i := U( θ i , ρ01 , ∆2 , n0)
u11max := max(u11) u21max := max( u21)
u21i
u11i :=
u11i u21i :=
u11max u21max
u12i := U( θ i , ρ02 , ∆1 , n1) u22i := U( θ i , ρ01 , ∆2 , n1)
u12max := max(u12) u22max := max( u22)
u22i
u12i :=
u12i u22i :=
u12max u22max
u13i := U( θ i , ρ03 , ∆1 , n1) u23i := U( θ i , ρ01 , ∆2 , n2)
u13max := max(u13) u23max := max( u23)
u13i u23i
u13i := u23i :=
u13max u23max
u0i := 0.5
∆3 := 0.01 n3 := 1
u31i := U( θ i , ρ01 , ∆3 , n3) u33i := U( θ i , ρ03 , ∆3 , n3)
u31max := max(u31) u33max := max(u33)
u31i
u31i := u33i :=
u33i
u31max u33max
u32i := U( θ i , ρ02 , ∆3 , n3)
u32max := max(u32)
u32i
u32i :=
u32max
