Résumé: We present a semi-analytical approach to compute quasi-guided elastic wave modes in horizontally layered structures radiating into unbounded fluid or solid media. This problem is of relevance, e.g., for the simulation of guided ultrasound in embedded plate structures or seismic waves in soil layers over an elastic half-space. We employ a semi-analytical formulation to describe the layers, thus discretizing the thickness direction by means of finite elements. For a free layer, this technique leads to a well-known quadratic eigenvalue problem for the mode shapes and corresponding horizontal wavenumbers. Incorporating the coupling conditions to account for the adjacent half-spaces gives rise to additional terms that are nonlinear in the wavenumber. We show that the resulting nonlinear eigenvalue problem can be cast in the form of a multiparameter eigenvalue problem whose solutions represent the wave numbers in the plate and in the half-spaces. The multiparameter eigenvalue problem is solved numerically using recently developed algorithms. Matlab implementations of the proposed methods are publicly available.

Résumé: Multiple scattering of waves presents challenges for imaging complex media but offers potential for their characterization. Its onset is actually governed by the scattering mean free path ℓs that provides crucial information on the medium microarchitecture. Here, we introduce a reflection matrix method designed to estimate this parameter from the time decay of the single scattering rate. Our method is first validated by an ultrasound experiment on a tissue-mimicking phantom before being applied in vivo to a human liver. This Letter opens important perspectives for quantitative imaging of heterogeneous media with waves, whether it be for nondestructive testing, biomedical, or geophysical applications.

Résumé: Shear stress plays a critical role in regulating physiological processes within microcirculatory systems. While particle imaging velocimetry is a standard technique for quantifying shear flow, uncertainty near boundaries and low resolution remain severe restrictions. Additionally, shear stress determination is particularly challenging in biofluids due to their significant non-Newtonian behaviors. The present study develops a shearmetry technique in physiological settings using a biomimetic fluid containing rare earth-doped luminescent nanorods acting in two roles. First, they are used as colloidal additives adjusting rheological properties in physiological media. Their anisotropic morphology and interparticle interaction synergistically induce a non-Newtonian shear-thinning effect emulating real biofluids. Second, they can probe shear stress due to the shear-induced alignment. The polarized luminescence of the nanorods allows for quantifying their orientational order parameter and thus correlated shear stress. Using scanning confocal microscopy, we demonstrate the tomographic mapping of the shear stress distribution in microfluidics. High shear stress is evident near the constriction and the cellular periphery, in which non-Newtonian effects can have a significant impact. This emerging shearmetry technique is promising for implementation in physiological and rheological environments of biofluids.