The research in topological materials and meta-materials has reached maturity and is gradually entering the phase of practical applications and devices. However, scaling down experimental demonstrations presents a major challenge. In this work, we study identical coupled mechanical resonators whose collective dynamics are fully determined by the pattern in which they are arranged. We call a pattern topological if boundary resonant modes fully fill all existing spectral gaps whenever the pattern is halved. This is a characteristic of the pattern and is entirely independent of the structure of the resonators and the details of the couplings. The existence of such patterns is proven using Ktheory and exemplified using a novel experimental platform based on magnetically coupled spinners. Topological meta-materials built on these principles can be easily engineered at any scale, providing a practical platform for applications and devices.

The emergence of a fractal energy spectrum is the quintessence of the interplay between two periodic parameters with incommensurate length scales. crystals can emulate such interplay and also exhibit a topological bulk-boundary correspondence, enabled by their nontrivial topology in virtual dimensions. Here we propose, fabricate and experimentally test a reconfigurable one-dimensional (1D) acoustic array, in which the resonant frequencies of each element can be independently fine-tuned by a piston. We map experimentally the full Hofstadter butterfly spectrum by measuring the acoustic density of states distributed over frequency while varying the long-range order of the array. Furthermore, by adiabatically changing the phason of the array, we map topologically protected fractal boundary states, which are shown to be pumped from one edge to the other. This reconfigurable crystal serves as a model for future extensions to electronics, photonics and mechanics, as well as to quasicrystalline systems in higher dimensions.

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Topological boundary and interface modes are generated in an acoustic waveguide by simple quasiperiodic patterning of the walls. The procedure opens many topological gaps in the resonant spectrum and qualitative as well as quantitative assessments of their topological character are supplied. In particular, computations of the bulk invariant for the continuum wave equation are performed. The experimental measurements reproduce the theoretical predictions with high fidelity. In particular, acoustic modes with high Q-factors localized in the middle of a breathable waveguide are engineered by a simple patterning of the walls.

A flow sensor has been fabricated and tested that is capable of measuring the slow flow characteristic of the cerebrospinal fluid in the range from less than 4 mL/h to above 100 mL/h. This sensor is suitable for long-term implantation because it uses a wireless external spectrometer to measure passive subcutaneous components. The sensors are pressure-sensitive capacitors, in the range of 5 pF with an air gap at atmospheric pressure. Each capacitor is in series with an inductor to provide a resonant frequency that varies with flow rate. At constant flow, the system is steady with drift <0.3 mL/h over a month. At variable flow rate, V̇, the resonant frequency, f0, which is in the 200–400 MHz range, follows a second order polynomial with respect to V̇. For this sensor system the uncertainty in measuring f0 is 30 kHz which corresponds to a sensitivity in measuring flow of ΔV̇= 0.6 mL/hr. Pressures up to 20 cm H2O relative to ambient pressure were also measured. An implantable twin capacitor system is proposed that can measure flow, which is fully compensated for all hydrostatic pressures. For twin capacitors, other sources of systematic variation within clinical range, such as temperature and ambient pressure, are smaller than our sensitivity and we delineate a calibration method that should maintain clinically useful accuracy over long times.