Boundary scattering of phonons: specularity of a randomly rough surface in the small perturbation limit

Scattering of normally incident longitudinal and transverse acoustic waves by a randomly rough surface of an elastically isotropic solid is analyzed within the small perturbation approach. In the limiting case of a large correlation length $L$ compared with the acoustic wavelength, the specularity reduction is given by $4\eta^2k^2$, where $\eta$ is the RMS roughness and $k$ is the acoustic wavevector, which is in agreement with the well-known Kirchhoff approximation result often referred to as Ziman's equation [J. M. Ziman, Electrons and Phonons (Clarendon Press, Oxford, 1960)]. In the opposite limiting case of a small correlation length, the specularity reduction is found to be proportional to $\eta^2k^4L^2$, with the fourth power dependence on frequency as in Rayleigh scattering. Numerical calculations for a Gaussian autocorrelation function of surface roughness connect these limiting cases and reveal a maximum of diffuse scattering at an intermediate value of $L$. This maximum becomes increasingly pronounced for the incident longitudinal wave as the Poisson's ratio of the medium approaches 1/2 as a result of increased scattering into transverse and Rayleigh surface waves. The results indicate that thermal transport models using Ziman's formula are likely to overestimate the heat flux dissipation due to boundary scattering, whereas modeling interface roughness as atomic disorder is likely to underestimate scattering

Dynamics of a Monolayer of Microspheres on an Elastic Substrate

We present a model for wave propagation in a monolayer of spheres on an elastic substrate. The model, which considers sagittally polarized waves, includes: horizontal, vertical, and rotational degrees of freedom; normal and shear coupling between the spheres and substrate, as well as between adjacent spheres; and the effects of wave propagation in the elastic substrate. For a monolayer of interacting spheres, we find three contact resonances, whose frequencies are given by simple closed-form expressions. For a monolayer of isolated spheres, only two resonances are present. The contact resonances couple to surface acoustic waves in the substrate, leading to mode hybridization and "avoided crossing" phenomena. We present dispersion curves for a monolayer of silica microspheres on a silica substrate, assuming adhesive, Hertzian interactions, and compare calculations using an effective medium approximation to a discrete model of a monolayer on a rigid substrate. While the effective medium model does not account for discrete lattice effects at short wavelengths, we find that it is well suited for describing the interaction between the monolayer and substrate in the long wavelength limit. We suggest that a complete picture of the dynamics of a discrete monolayer adhered to an elastic substrate can be found using a combination of the results presented for the discrete and effective medium descriptions. This model is potentially scalable for use with both micro- and macroscale systems, and offers the prospect of experimentally extracting contact stiffnesses from measurements of acoustic dispersion

Hypertrophic Cardiomyopathy and Sports

Hypertrophic cardiomyopathy (HCM) is one of the most common causes of sudden cardiac death (SCD) in athletes. Knowledge of the problem is essential for detection of the disease. According to the current recommendations of the European Society of Cardiology (ESC), in individuals with established HCM disease, including those without phenotypic expression, participation in competitive sports is forbidden. The recommendations of the American College of Cardiology/American Heart Association (ACC/AHA) are more liberal, allowing participation in competitive sports in people with non-phenotypic manifestations of the disease and participation in low-intensity sports for patients with phenotypic manifestation. An individual approach will most likely be adopted in the future, mainly on the basis of precise risk stratification

Waveguiding by a locally resonant metasurface

Dispersion relations for acoustic and electromagnetic waves guided by resonant inclusions located at the surface of an elastic solid or an interface between two media are analyzed theoretically within the effective medium approximation. Oscillators on the surface of an elastic half-space are shown to give rise to a Love-type surface acoustic wave only existing below the oscillator frequency. A simple dispersion relation governing this system is shown to also hold for electromagnetic waves guided by Lorentz oscillators at an interface between two media with equal dielectric constants. Different kinds of behavior of the dispersion of the resonantly guided mode are identified, depending on whether the bulk wave in the absence of oscillators can propagate along the surface or interface.National Science Foundation (U.S.) (Grant CHE-1111557

What is the Brillouin Zone of an Anisotropic Photonic Crystal?

The concept of the Brillouin zone (BZ) in relation to a photonic crystal fabricated in an optically anisotropic material is explored both experimentally and theoretically. In experiment, we used femtosecond laser pulses to excite THz polaritons and image their propagation in lithium niobate and lithium tantalate photonic crystal (PhC) slabs. We directly measured the dispersion relation inside PhCs and observed that the lowest bandgap expected to form at the BZ boundary forms inside the BZ in the anisotropic lithium niobate PhC. Our analysis shows that in an anisotropic material the BZ - defined as the Wigner-Seitz cell in the reciprocal lattice - is no longer bounded by Bragg planes and thus does not conform to the original definition of the BZ by Brillouin. We construct an alternative Brillouin zone defined by Bragg planes and show its utility in identifying features of the dispersion bands. We show that for an anisotropic 2D PhC without dispersion, the Bragg plane BZ can be constructed by applying the Wigner-Seitz method to a stretched or compressed reciprocal lattice. We also show that in the presence of the dispersion in the underlying material or in a slab waveguide, the Bragg planes are generally represented by curved surfaces rather than planes. The concept of constructing a BZ with Bragg planes should prove useful in understanding the formation of dispersion bands in anisotropic PhCs and in selectively tailoring their optical properties.Comment: 9 pages, 6 figure

A Variational Approach to Extracting the Phonon Mean Free Path Distribution from the Spectral Boltzmann Transport Equation

The phonon Boltzmann transport equation (BTE) is a powerful tool for studying non-diffusive thermal transport. Here, we develop a new universal variational approach to solving the BTE that enables extraction of phonon mean free path (MFP) distributions from experiments exploring non-diffusive transport. By utilizing the known Fourier solution as a trial function, we present a direct approach to calculating the effective thermal conductivity from the BTE. We demonstrate this technique on the transient thermal grating (TTG) experiment, which is a useful tool for studying non-diffusive thermal transport and probing the mean free path (MFP) distribution of materials. We obtain a closed form expression for a suppression function that is materials dependent, successfully addressing the non-universality of the suppression function used in the past, while providing a general approach to studying thermal properties in the non-diffusive regime.Comment: 17 pages, 2 figure