Boundary Integral Equation Formulations for Scattering of Elastic Waves in Three-Dimensional Half-Spaces

1988 ◽  
pp. 65-68
Author(s):  
I. R. Gonsalves ◽  
D. J. Shippy ◽  
F. J. Rizzo
Keyword(s):  
Integral Equation ◽  
Boundary Integral Equation ◽  
Elastic Waves ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Scattering Of Elastic Waves

Wave propagation through an interface between dissimilar media with a doubly periodic array of arbitrary shaped planar delaminations

2017 ◽  
Vol 24 (2) ◽  
pp. 483-498 ◽  
Author(s):  
Mikhail V Golub ◽  
Olga V Doroshenko
Keyword(s):  
Integral Equation ◽  
Wave Propagation ◽  
Elastic Waves ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Periodic Array ◽  
Integral Approach ◽  
Galerkin Scheme ◽  
Scattering Of Elastic Waves ◽  
Doubly Periodic Array

This paper considers the scattering of elastic waves by a doubly periodic array of three-dimensional planar delaminations at the interface between two dissimilar media. The delaminations are modelled in terms of the spring boundary conditions, which are employed to formulate a boundary integral equation. The problem is solved using the Bubnov–Galerkin scheme and the integral approach, taking into account geometrical periodicity. The effects of distribution and shape of periodic delaminations on wave transmission and diffraction are analysed. The specific phenomenon of pass-bands or an ‘opening’ interface for wave propagation by a periodic array of delaminations is revealed.

scholarly journals A boundary integral method with volume-changing objects for ultrasound-triggered margination of microbubbles

2017 ◽  
Vol 836 ◽  
pp. 952-997 ◽  
Author(s):  
Achim Guckenberger ◽  
Stephan Gekle
Keyword(s):  
Drug Delivery ◽  
Integral Equation ◽  
Boundary Integral Equation ◽  
Integral Method ◽  
Three Dimensional ◽  
Formal Proof ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Drug Uptake ◽  
Periodic Domains

A variety of numerical methods exist for the study of deformable particles in dense suspensions. None of the standard tools, however, currently include volume-changing objects such as oscillating microbubbles in three-dimensional periodic domains. In the first part of this work, we develop a novel method to include such entities based on the boundary integral method. We show that the well-known boundary integral equation must be amended with two additional terms containing the volume flux through the bubble surface. We rigorously prove the existence and uniqueness of the solution. Our proof contains as a subset the simpler boundary integral equation without volume-changing objects (such as red blood cell or capsule suspensions) which is widely used but for which a formal proof in periodic domains has not been published to date. In the second part, we apply our method to study microbubbles for targeted drug delivery. The ideal drug delivery agent should stay away from the biochemically active vessel walls during circulation. However, upon reaching its target it should attain a near-wall position for efficient drug uptake. Though seemingly contradictory, we show that lipid-coated microbubbles in conjunction with a localized ultrasound pulse possess precisely these two properties. This ultrasound-triggered margination is due to hydrodynamic interactions between the red blood cells and the oscillating lipid-coated microbubbles which alternate between a soft and a stiff state. We find that the effect is very robust, existing even if the duration in the stiff state is more than three times lower than the opposing time in the soft state.

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