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Scattering of Elastic Waves in a Quasi-One-Dimensional Cavity: Theory and Experiment

100%
Báez G., Cobián-Suárez M., Martínez-Argüello A., Martínez-Mares M., Méndez-Sánchez R.
Acta Physica Polonica A
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2013
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vol. 124
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issue 6
1069-1073
EN
We study the scattering of torsional waves through a quasi-one-dimensional cavity both from the experimental and theoretical points of view. The experiment consists of an elastic rod with square cross-section. In order to form a cavity, a notch at a certain distance of one end of the rod was grooved. To absorb the waves, at the other side of the rod, a wedge, covered by an absorbing foam, was machined. In the theoretical description, the scattering matrix S of the torsional waves was obtained. The distribution of S is given by Poisson's kernel. The theoretical predictions show an excellent agreement with the experimental results. This experiment corresponds, in quantum mechanics, to the scattering by a delta potential, in one dimension, located at a certain distance from an impenetrable wall.
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Anderson Localization Phenomenon in One-Dimensional Elastic Systems

86%
Méndez-Sánchez R., Gutiérrez L., Morales A., Flores J., Díaz-de-Anda A., Monsivais G.
Acta Physica Polonica A
|
2013
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vol. 124
|
issue 6
1063-1068
EN
The phenomenon of the Anderson localization of waves in elastic systems is studied. We analyze this phenomenon in two different sets of systems: disordered linear chains of harmonic oscillators and disordered rods which oscillate with torsional waves. The first set is analyzed numerically whereas the second one is studied both experimentally and theoretically. In particular, we discuss the localization properties of the waves as a function of the frequency. In doing that we have used the inverse participation ratio, which is related to the localization length. We find that the normal modes localize exponentially according to the Anderson theory. In the elastic systems, the localization length decreases with frequency. This behavior is in contrast with what happens in analogous quantum mechanical systems, for which the localization length grows with energy. This difference is explained by means of the properties of the reflection coefficient of a single scatterer in each case.
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