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What is the parametric equation guiding the geometry of a ferrofluid under a magnetic field? See also this Wikipedia page.

From previous research, Maxwell's Equations and Navier-Stokes Equations were previously used but I am not sure how they are being combined to create this stunning geometry.

If the 3d model is too complex, is there a 2D pointed parabola with a curved crest equation which we might use?

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migrated from math.stackexchange.com Oct 14 '12 at 19:57


You won't need the full Navier-Stokes equations since the problem is static. Neither will you need the full Maxwell equations. That should simplify the problem a lot. You'll also need equations describing the interaction between the ferrofluid and the field. –  Raskolnikov Oct 14 '12 at 19:01

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You assume a magnetic field as static? Magnetic fields may represent and even present at level 1X as standing wave functions, which has led classical physical sciences to regard them as static. However, basic researches have shown magnetic fields to be "consistently dynamic" and "coherently interactive" (distributable both algebraically and geometrically like fluids); magnetic fields "work" either with external impingement or without.

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