The Kirchhoff approximation is widely used to describe the scatter of elastodynamic waves. It simulates the scattered field as the convolution of the free-space Green’s tensor with the geometrical elastodynamics approximation to the total field on the scatterer surface and, therefore, cannot be used to describe nongeometrical phenomena, such as head waves. The aim of this paper is to demonstrate that an alternative approximation, the convolution of the far-field asymptotics of the Lamb’s Green’s tensor with incident surface tractions, has no such limitation. This is done by simulating the scatter of a critical Gaussian beam of transverse motions from an infinite plane. The results are of interest in ultrasonic nondestructive testing.

Mollusc seashells grow through the local deposition and calcification of material at the shell opening by a soft and thin organ called the mantle. Through this process, a huge variety of shell structures are formed. Previous models have shown that these structural patterns can largely be understood by examining the mechanical interaction between the deformable mantle and the rigid shell aperture to which it adheres. In this paper we extend this modelling framework in two distinct directions. For one, we incorporate a mechanical feedback in the growth of the mollusc. Second, we develop an initial framework to couple the two primary and orthogonal modes of pattern formation in shells, which are termed antimarginal and commarginal ornamentation. In both cases we examine the change in shell morphology that occurs due to the different mechanical influences and evaluate the hypotheses in light of the fossil record.

Many biological settings involve complex fluids that have non-Newtonian mechanical responses that arise from suspended microstructures. In contrast, Newtonian fluids are liquids or mixtures of a simple molecular structure that exhibit a linear relationship between the shear stress and the rate of deformation. In modeling complex fluids, the extra stress from the non-Newtonian contribution must be included in the governing equations.

In this study we compare Lagrangian mesh and Oldroyd-B formulations of fluid-structure interaction in an immersed boundary framework. The start-up phase of planar Poiseuille flow between two parallel plates is used as a test case for the fluid models. For Newtonian and Oldroyd-B fluids there exist analytical solutions which are used in the comparison of simulation and theoretical results. The Lagrangian mesh results are compared with Oldroyd-B using comparable parameters. A regridding algorithm is introduced for the Lagrangian mesh model. We show that the Lagrangian mesh model simulations with regridding produce results in close agreement with the Oldfoyd-B model.