Hearing the shape of a drum with several complex ears

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Hearing the shape of a drumwith several complex
ears

• Siqi Fu
• Rutgers-Camden
• September, 2004

Richard Feynman
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Hearing the length (1)

• U(x, t) displacement

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Hearing the length (2)
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Hearing the length (3)
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Hearing the drum
Drum D
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Hearing the area (1)
Hilbert and Weyl
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Hearing the area (2)
Approximate D from inside by squares
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Hearing the area (3)
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Hearing more
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Can one hear the shape of a drum?
Mark Kac
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One cannot hear the shape of a drum (1)
Gordon, Webb, Wolpert (1992) No!
Drums that sound alike
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One cannot hear the shape of a drum (2)
Simplification by Buser, Conway, et al.
Numerical computations by Sridhar, Driscoll, et
al.
Idea transplantation. Find a 1-1 correspondence
between eigenvalues and eigenfunctions of the
two domains.
Courtesy Toby Driscoll
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One cannot hear the shape of a drum (3)
First Four Eigen- values
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One cannot hear the shape of the drum (4)
Drums being plucked at the center combinations
of the first six modes
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Several complex ears (1)
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Several complex ears (2)