A novel principle to localize the sensitivity of waveform tomography using wave interferences at the observation boundary

When using waveform tomography to perform high-resolution imaging of a medium, it is vital to calculate the sensitivity in order to describe how well a model fits a given set of data and how the sensitivity changes with the spatial distribution of the heterogeneities. The traditional principle behind calculating the sensitivity—for detecting small changes—suffers from an inherent limitation in case other structures, not of interest, are present along the wave propagation path. We propose a novel principle that leads to enhanced localization of the sensitivity of the waveform tomography, without having to know the intermediate structures. This new principle emerges from a boundary integral representation which utilizes wave interferences observed at multiple points. When tested on geophysical acoustic wave data, this new principle leads to much better sensitivity localization and detection of small changes in seismic velocities, which were otherwise impossible. Overcoming the insensitivity to a target area, it offers new possibilities for imaging and monitoring small changes in properties, which is critical in a wide range of disciplines and scales.

A boundary-integral representation for biphasic mixture theory, with application to the post-capillary glycocalyx

We describe a new boundary-integral representation for biphasic mixture theory, which allows us to efficiently solve certain elastohydrodynamic–mobility problems using boundary element methods. We apply this formulation to model the motion of a rigid particle through a microtube which has non-uniform wall shape, is filled with a viscous Newtonian fluid, and is lined with a thin poroelastic layer. This is relevant to scenarios such as the transport of small rigid cells (such as neutrophils) through microvessels that are lined with an endothelial glycocalyx layer (EGL). In this context, we examine the impact of geometry upon some recently reported phenomena, including the creation of viscous eddies, fluid flux into the EGL, as well as the role of the EGL in transmitting mechanical signals to the underlying endothelial cells.

COMPUTATIONAL HOMOGENIZATION OF POLYCRYSTALLINE MATERIALS WITH PORES: A THREE-DIMENSIONAL GRAIN BOUNDARY FORMULATION

In this study, the influence of porosity on the elastic effective properties of polycrystalline materials is investigated using a 3D grain boundary micro mechanical model. The volume fraction of pores, their size and distribution can be varied to better simulate the response of real porous materials. The formulation is built on a boundary integral representation of the elastic problem for the grains, which are modeled as 3D linearly elastic orthotropic domains with arbitrary spatial orientation. The artificial polycrystalline morphology is represented using 3D Voronoi Tessellations. The formulation is expressed in terms of intergranular fields, namely displacements and tractions that play an important role in polycrystalline micromechanics. The continuity of the aggregate is enforced through suitable intergranular conditions. The effective material properties are obtained through material homogenization, computing the volume averages of micro-strains and stresses and taking the ensemble average over a certain number of microstructural samples. The obtained results show the capability of the model to assess the macroscopic effects of porosity.

Shape and stability of axisymmetric levitated viscous drops

We consider levitation of an axisymmetric drop of molten glass above a spherical porous mould through which air is injected at a constant velocity. Owing to the viscosity contrast, the float height for a given shape is established on a much shorter time scale than the subsequent deformation of the drop under gravity, surface tension and the underlying lubrication pressure. Equilibrium shapes, in which an internal hydrostatic pressure is coupled to the external lubrication pressure through the total curvature and the Young–Laplace equation, are determined using a numerical continuation scheme. The set of solution branches is surprisingly complicated and shows a rich bifurcation structure in the parameter space (Bo=ρgV2/3/γ, Ca=μav/γ), where Bo is bond number and Ca is capillary number, ρ and V are the drop density and volume, γ the surface tension, μa the air viscosity and v the injection velocity. The linear stability of equilibria is determined using a boundary-integral representation for drop deformation that factors out the rapid vertical adjustment of the float height. The results give good agreement with time-dependent simulations. For sufficiently large Ca there are intervals of Bo for which there are no stable solutions and, as Ca increases, these intervals grow and merge. The region of stability decreases as the mould radius aM increases with an approximate scaling Ca~aM−5, which imposes practical limitations on the use of this geometry for the manufacture of lenses.

BEM Solutions of Frequency Domain Gradient Elastodynamic 3-D Porblems

A boundary element methodology is presented for the frequency domain elastodynamic analysis of three-dimensional solids characterized by a linear elastic material behavior coupled with microstructural effects taken into account with the aid of the simple gradient elastic theory of Aifantis. A variational statement is established to determine all possible classical and non-classical (due to gradient terms) boundary conditions of the general boundary value problem. The gradient frequency domain elastodynamic fundamental solution is explicitly derived and used to construct the boundary integral representation of the solution with the aid of a reciprocal integral identity. In addition to a boundary integral representation for the displacement, a boundary integral representation for its normal derivative is also necessary for the complete formulation of a well posed problem. All the kernels in the integral equations are explicitly provided. Surface quadratic quadrilateral boundary elements are employed and the discretization is restricted only to the boundary. The solution procedure is described in detail. A numerical example serves to illustrate the method and demonstrate its accuracy. The present version of the method does not provide explicit expressions for the computation of interior stresses.

Hydrodynamic Analysis of Floating Bodies in General Bathymetry

A hybrid technique, based on the coupled-mode theory developed by Athanassoulis & Belibassakis (1999) and extended to 3D by Belibassakis et al (2001) and Belibassakis & Athanassoulis (2004), which is free of any mild-slope assumption, is used, in conjunction with a boundary integral representation of the near field in the vicinity of the body, to treat the problem of hydrodynamic analysis of floating bodies in the presence of variable bathymetry. Numerical results are presented concerning floating bodies of simple geometry lying over sloping seabeds. With the aid of systematic comparisons, the effects of bottom slope on the hydrodynamic characteristics (hydrodynamic coefficients and responses) are illustrated and discussed.