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Patricia Alonso Ruiz


Can one separate the tones of a fractal membrane?

January 25, 2023
3:00 pm    PHG 648 (different room)


As a music chord is composed of different notes played unison, most signals that reach us (sounds, biomolecules, electromagnetic waves or stock prices) may be expressed as the sum of more basic components. In mathematical terms a signal is regarded as a function that may also be decomposed into more elementary ones which act as "building blocks". Each "block" is associated with a specific "tone" and each tone corresponds, mathematically speaking, to an eigenvalue.

On occasion one may be interested in highlighting or damping a specific tone, for instance to enhance a particular sound. How well such a tone can be isolated partly depends on the "distance" between the tones: The more separated they are, the easier it is to distinguish them.

This talk will focus on the standard eigenvalues of a fractal called the Sierpinski gasket, which can serve as a mathematical model for a highly porous membrane. We will discuss how the distance between these eigenvalues is related to the lowest eigenvalue, sometimes referred to as the "fundamental tone" and discover that it is actually possible to separate all tones.

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