How to Write Fortran Code for a Complex Phase Speed

[logi]

Hi,

We assume
Max hBy(y) = α1 for y ε (a1, a2) and Min hBy(y) = α2 for y ε (a1, a2)
Where -∞ < α2 ≤ α1 < ∞, and the complex phase speed must lie in the region defined by

(CR + α1 )^2 + CI^2 ≤ µγ^2/k^2, if CR <- α1

CI^2 ≤ µγ^2/k^2, if -α1≤ CR ≤-α2,

(CR + α2 )^2 + CI^2 ≤ µγ^2/k^2, if CR >- α2

Where CI ≥ 0 and γ^2= max [hBy(y) h0y(y)] >0, h0y(y)= -8(y-a)/L^2
The region represents a rectangle of length α1 - α2 with a quarter circle on each end, with the height of the rectangle and the radius of the circles given by µ^(1/2)γ/k.

Could you please help me to write the Fortran code for this equations?

Thanks
Logi

 

[Borek]

You have already asked that question.

https://www.physicsforums.com/showthread.php?t=241115

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[quicknote]

Hello Logi,

Thank you for your question. Writing Fortran code for a complex phase speed can be challenging, but I can provide some guidance to help you get started. Here are some steps to follow:

1. Define the necessary variables: The first step is to define the variables that will be used in your code. In this case, you will need to define the variables CR, CI, α1, α2, µ, γ, k, a1, a2, L, and h0y(y). Make sure to specify the data types for each variable (e.g. integer, real, complex).

2. Define the conditions: Based on the given equations, there are three conditions that need to be checked in order to determine the complex phase speed. These conditions correspond to the three regions given in the question. You will need to use IF statements to check each condition and perform the necessary calculations.

3. Calculate the complex phase speed: Once the conditions have been checked, you can use the given equations to calculate the complex phase speed. This will involve using the variables defined in step 1 and the conditions determined in step 2. The final result will be a complex number, which you can store in a variable named "phase_speed" for example.

4. Output the result: Finally, you can use a PRINT statement to display the calculated complex phase speed to the user. This will allow them to see the result of the code and verify its accuracy.

Overall, the code will look something like this:

! Define variables
integer :: CR, CI, α1, α2, µ, γ, k, a1, a2, L
real :: h0y, phase_speed

! Prompt user for input values and assign them to variables

! Check conditions
if (CR < -α1) then
! Perform calculations for first region
phase_speed = (CR + α1)**2 + CI**2
else if (-α1 <= CR <= -α2) then
! Perform calculations for second region
phase_speed = CI**2
else if (CR > -α2) then
! Perform calculations for third region
phase_speed = (CR + α2)**2 + CI**2
end if

! Calculate the complex phase speed
phase_speed = µ**(1/2) * γ / k * phase_speed

! Output the result
print*, "The calculated