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For those of you who remember my last thread here, I'm doing a high school graduation project about conformal mapping and the complex potential applied to fluid flow problems. The last time I asked for help you were incredibly helpful so I thought I'd share another issue with you.

I thought of trying to apply the complex potential method to one of the most basic problem I studied in wave theory: interference, for example from two point-like sources. This looks natural if I recall that for a single source at point a we have the complex potential

[tex]\frac{Q}{2\pi} \mathrm{Ln} (z-a)[/tex]

and superposition holds, so if we have two sources of equal strength at points d,-d (d is real), the overall potential should be

[tex]\frac{Q}{2\pi} (\mathrm{Ln} (z-d) + \mathrm{Ln} (z+d) )[/tex]

So I tried to work it out algebrically and found that the streamlines should be the curves that give rise so

[tex]x^2 - y^2 - \frac{2xy}{c} = d^2[/tex]

where c are the constants that represent the different streamlines. Since I don't recognize this algebric form of a curve, I just put it in Maxima and it gave me these graphs:

http://img383.imageshack.us/img383/5893/complex1qq5.png" [Broken]

(d=0)

http://img374.imageshack.us/img374/7287/complex2wx5.png" [Broken]

(d=0.1)

http://img376.imageshack.us/img376/4890/complex3xu8.png" [Broken]

(d=1)

Is that consistent with the "usual" interference analysis done in wave theory? And if so, how is it related to the classical picture, such as:

http://www.paulfriedlander.com/images/timetravel/interference%20-1.jpg" [Broken]

I realize that the streamlines are the maximum lines of the pictures above, but are they really the same as what I got?

Thanks a lot!

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# Another question about complex potential

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