We examine theoretically and experimentally the localized electrical modes existing in a biinductive electrical lattice containing a bulk or a surface capacitive impurity. By means of the formalism of lattice Green's functions, we are able to obtain closed-form expressions for the frequencies of the impurity (bound-state) eigenmodes and for their associated spatial profiles. This affords us a systematic understanding of how these mode properties change as a function of the system parameters. We test these analytical results against experimental measurements, in both the bulk and surface cases, and find very good agreement. Lastly, we turn to a series of quench experiments, where either a parameter of the lattice or the lattice geometry itself is rapidly switched between two values or configurations. In all cases, we are able to naturally explain the results of such quench experiments from the larger analytical picture that emerges as a result of the detailed characterization of the impurity-mode solution branches.
We investigate acoustic levitation in a vertical standing wave in an attempt to understand the basic physical mechanism responsible for this phenomenon. We find that a description in terms of a simple pressure force leads to the prediction of stable equilibria that occur slightly below the anti-nodes of the standing pressure wave. We then demonstrate that such a prediction is at odds with experimental data, which show that levitating particles come to rest slightly below the nodes of the standing pressure wave. Finally, we outline a theoretical approach based on fluid dynamics that correctly predicts the locations of the levitating particles, which leads to a simple qualitative description for this fascinating phenomenon.
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