Unconventional acoustic wave propagation transitions induced by resonant scatterers in the high-density limit.

Experiments on ultrasound propagation through a gel doped with resonant encapsulated microbubbles provided evidence for a discontinuous transition between wave propagation regimes at a critical excitation frequency. Such behavior is unlike that observed for soft materials doped with non-resonant air or through liquid foams, and disagrees with a simple mixture model for the effective sound speed. Here, we study the discontinuous transition by measuring the transition as a function of encapsulated microbubble volume fraction. The results show the transition always occurs in the strong-scattering limit (l/λ < 1, l and λ are the mean free path and wavelength, respectively), that at the critical frequency the effective phase velocity changes discontinuously to a constant value with increasing microbubble volume fraction, and the measured critical frequency shows a power law dependence on microbubble volume fraction. The results cannot be explained by multiple scattering theory, viscous effects, mode decoupling, or a critical density of states. It is hypothesized the transition depends upon the microbubble on-resonance effective properties, and we discuss the results within the context of percolation theory. The results shed light on the discontinuous transition's physics, and suggest soft materials can be engineered in this manner to achieve a broad range of physical properties with potential application in ultrasonic actuators and switches.

Generating functional for Green's functions of fluid-loaded structures.

A key step in applying the auxiliary superfield method to complex systems is the representation of the Green's function of the system as derivatives of a generating functional. This representation is known to be valid for Hermitian systems, but this precludes the application of the method to systems with fluid loading or damping. Here, it is demonstrated that the known representation continues to be valid for fluid-loaded and damped systems. Thus, the auxiliary superfield method may be applied to such systems.

Auxiliary superfield method for statistical predictions of complex, structural acoustics systems: Saddle point approximation for the mean field.

The auxiliary superfield approach is proposed as a method to obtain statistical predictions of the acoustic response of complex elastic structures. The potential advantage of the method is the full retention of interference and resonance effects associated with the degrees of freedom being averaged over. It is not known whether this approach leads to tractable problems for structural acoustics systems, however. We have applied the method to the idealized case of an infinite, thin plate with attached oscillators to obtain the mean Green's function. The oscillators are assumed to have an uncorrelated, Gaussian distributed mass and stiffness distribution representing a simple form of complex internal structure. Using the auxiliary superfield approach, the mean Green's functions are expressed exactly as a functional integral. For relatively small disorder, the integral may be estimated by a saddle point approximation which leads to coupled integral equations for effective mass and stiffness matrices that can be solved numerically for a given spatial distribution of the disorder. With the solutions for these matrices, one obtains a self-consistently determined, generalized fuzzy structure model. We give analytical solutions for the simple case of a uniform spatial distribution. The results are promising for the application of the method to more challenging geometries.

Acoustic cavities in 2D heterostructures.

Two-dimensional (2D) materials offer unique opportunities in engineering the ultrafast spatiotemporal response of composite nanomechanical structures. In this work, we report on high frequency, high quality factor (Q) 2D acoustic cavities operating in the 50-600 GHz frequency (f) range with f × Q up to 1 × 1014. Monolayer steps and material interfaces expand cavity functionality, as demonstrated by building adjacent cavities that are isolated or strongly-coupled, as well as a frequency comb generator in MoS2/h-BN systems. Energy dissipation measurements in 2D cavities are compared with attenuation derived from phonon-phonon scattering rates calculated using a fully microscopic ab initio approach. Phonon lifetime calculations extended to low frequencies (<1 THz) and combined with sound propagation analysis in ultrathin plates provide a framework for designing acoustic cavities that approach their fundamental performance limit. These results provide a pathway for developing platforms employing phonon-based signal processing and for exploring the quantum nature of phonons.

Critical Role of a Nanometer-Scale Microballoon Shell on Bulk Acoustic Properties of Doped Soft Matter.

A material's acoustic properties depend critically upon porosity. Doping a soft material with gas-filled microballoons permits a controlled variation of the porosity through a scalable fabrication process while generating well-tailored spherical cavities that are impermeable to liquids. However, evidence is lacking of how the nanometer-scale polymeric shell contributes to the overall effective material properties in the regime where the wavelength is comparable to the sample thickness. Here, we measure ultrasound transmission through a microballoon-doped soft material as a function of microballoon and impurity concentration, sample thickness, and frequency. The measured longitudinal wave speeds are an order of magnitude larger than those in similar systems where no shell is present, while the transverse wave speed is found to linearly increase with microballoon concentration, also in contrast to systems with no shell. Furthermore, we find the results are independent of the soft material's elastic moduli as well as a lesser contribution of the microballoon shell on material attenuation. The results are validated with a multiple scattering model and suggest the shell contributes significantly to the material's bulk acoustic properties despite its thickness being 4 orders of magnitude smaller than the acoustic wavelength. Our results demonstrate how a nanometer-scale interface between a gas cavity and a soft polymer can be used in the submicrometer design of acoustic materials, and are important for observations of such phenomena as strong interference effects in soft matter.

The effect of dissipation on the resistive admittance of an elastic medium.

The effect of dissipation on the real part of the admittance of an elastic half-space is typically thought to be unimportant if the loss factor ζ of the elastic medium is small. However, dissipation induces losses in the near field of the source and, provided the size of the source is small enough, this phenomenon can be more important than elastic wave radiation. Such losses give rise to a fundamental limit in the quality factor of an oscillator attached to a substrate. Near field losses associated with strains in the elastic substrate can actually be larger than intrinsic losses in the oscillator itself if the internal friction of the substrate is larger than the internal friction of the oscillator. For a uniform stress applied to a disk of radius a, a monopole source, such phenomena become significant for k(L)a<ζ, while for higher order multipole sources of order l, near field losses are important for (k(L)a)(l+1)<ζ, a far less restrictive constraint.

Ultrathin single crystal diamond nanomechanical dome resonators.

We present the first nanomechanical resonators microfabricated in single-crystal diamond. Shell-type resonators only 70 nm thick, the thinnest single crystal diamond structures produced to date, demonstrate a high-quality factor (Q ≈ 1000 at room temperature, Q ≈ 20 000 at 10 K) at radio frequencies (50-600 MHz). Quality factor dependence on temperature and frequency suggests an extrinsic origin to the dominant dissipation mechanism and methods to further enhance resonator performance.