Data-driven Identification of Parametric Governing Equations of Dynamical Systems Using the Signed Cumulative Distribution Transform.

This paper presents a novel data-driven approach to identify partial differential equation (PDE) parameters of a dynamical system. Specifically, we adopt a mathematical "transport" model for the solution of the dynamical system at specific spatial locations that allows us to accurately estimate the model parameters, including those associated with structural damage. This is accomplished by means of a newly-developed mathematical transform, the signed cumulative distribution transform (SCDT), which is shown to convert the general nonlinear parameter estimation problem into a simple linear regression.

Numerical study of acoustic focusing using a bianisotropic acoustic lens.

Materials with sub-wavelength asymmetry and long-range order have recently been shown to demonstrate acoustical properties analogous to electromagnetic bianisotropy. One characteristic of bianisotropic acoustic media is the existence of direction-dependent acoustic impedance. Therefore, the magnitude and phase of the acoustic fields transmitted through bianisotropic acoustic media are dependent on the direction of bianisotropic polarization.

Non-reciprocal wave propagation in mechanically-modulated continuous elastic metamaterials.

Acoustic and elastic metamaterials with time- and space-dependent effective material properties have recently received significant attention as a means to induce non-reciprocal wave propagation. Recent analytical models of spring-mass chains have shown that external application of a nonlinear mechanical deformation, when applied on time scales that are slow compared to the characteristic times of propagating linear elastic waves, may induce non-reciprocity via changes in the apparent elastic modulus for perturbations around that deformation. Unfortunately, it is rarely possible to derive analogous analytical models for continuous elastic metamaterials due to complex unit cell geometry.

Longitudinal eigenvibration of multilayer colloidal crystals and the effect of nanoscale contact bridges.

Longitudinal contact-based vibrations of colloidal crystals with a controlled layer thickness are studied. These crystals consist of 390 nm diameter polystyrene spheres arranged into close packed, ordered lattices with a thickness of one to twelve layers. Using laser ultrasonics, eigenmodes of the crystals that have out-of-plane motion are excited.