# Can you hear the fractal dimension of a drum

@article{Arrighetti2005CanYH, title={Can you hear the fractal dimension of a drum}, author={W. Arrighetti and G. Gerosa}, journal={arXiv: Spectral Theory}, year={2005} }

Electromagnetics and Acoustics on a bounded domain are governed by the Helmholtz's equation; when such a domain is a [pre-]fractal described by means of a `just-touching' Iterated Function System (IFS) spectral decomposition of the Helmholtz's operator is self-similar as well. Renormalization of the Green's function proves this feature and isolates a subclass of eigenmodes, called ``diaperiodic'', whose waveforms and eigenvalues can be recursively computed applying the IFS to the initiator's… Expand

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A lumped-parameter impedor-oriented and a 2-port-network-oriented circuit models for the Sierpinski gasket prefractal antenna are presented. With the former, the voltage and current patterns give a… Expand

Hearing the Drum of the Rhythm

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The title of the workshop is a twist on a question posed by mathematician Mark Kac in a 1966 paper, “Can One Hear the Shape of a Drum?” In the “Hearing the Drum of the Rhythm” workshop, the… Expand

Can you hear the shape of a drum ? Space , number , symmetry and equity – Pathways to African American STEM Leadership

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African Americans earned 21(1.2%) of 1,653 PhDs granted in mathematics in 2011. The mathematical sciences understand the world by performing formal symbolic reasoning and computation on abstract… Expand

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