Abstract
Energy transport properties in heterogeneous materials have attracted scientific interest for more than half of a century, and they continue to offer fundamental and rich questions. One of the outstanding challenges is to extend Anderson theory for uncorrelated and fully disordered lattices in condensed-matter systems to physical settings in which additional effects compete with disorder. Here we present the first systematic experimental study of energy transport and localization properties in simultaneously disordered and nonlinear granular crystals. In line with prior theoretical studies, we observe in our experiments that disorder and nonlinearity—which individually favor energy localization—can effectively cancel each other out, resulting in the destruction of wave localization. We also show that the combined effect of disorder and nonlinearity can enable manipulation of energy transport speed in granular crystals. Specifically, we experimentally demonstrate superdiffusive transport. Furthermore, our numerical computations suggest that subdiffusive transport should be attainable by controlling the strength of the system’s external precompression force.
Highlights
Granular crystals composed of spherical particles are a popular vehicle for investigating various nonlinear wave features[15,16,17,18]
We observe exponential attenuation of the energy distribution for disordered chains when we apply strong precompression to obtain almost linear dynamics. This is reminiscent of Anderson localization. We show that this localized pattern oscillates persistently near the chain boundary
We follow the above procedures and conduct three tests. This amounts to 672 experimental realizations to construct the spatiotemporal dynamics of the granular chains for all of the cases that we study in the present article
Summary
We experimentally and numerically investigate energy transport in one-dimensional disordered granular crystals (i.e., granular chains) in a wide variety of regimes, extending from almost linear to strongly nonlinear ones. Two particles interact with each other nonlinearly via a Hertzian interaction[19]: the force–displacement relation in the contact interaction is governed by a 3/2 power law under compression and zero force under tension. In this class of models, one can tune the effective system nonlinearity very precisely by varying the ratio of excitation amplitude to static precompression[18]. A very recent study examined the relation between chaos and transport properties in granular chains[21]
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