The study of scattering by a high aspect ratio particle has important applications in sensing and plasmonic imaging. To illustrate the effect of particle’s narrowness (that can be related to parity properties) and the need for adapted methods (in the context of boundary integral methods), we consider the scattering by a penetrable, high aspect ratio ellipse. This problem highlights the main challenge and provides valuable insights to tackle general high aspect ratio particles. We find that boundary integral operators are nearly singular due to the collapsing geometry to a line segment. We show that these nearly singular behaviors lead to qualitatively different asymptotic behaviors for solutions with different parities. Without explicitly taking this into account, computed solutions incur large errors. We introduce the Quadrature by Parity Asymptotic eXpansions (QPAX) that effectively and efficiently addresses these issues. We demonstrate the effectiveness of QPAX through several numerical examples.
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Asymptotic analysis for sound-hard acoustic scattering by two closely-situated spheres
We consider acoustic binding of particles resulting from radiation forces created through multiple scattering. This problem has potential for
developing methods for assembling novel meta-materials. A key consideration in acoustic binding is when two or more particles are closely situated to one another and form a cluster. For that case, the near-field scattering by the particles becomes important. Here, we study multiple scattering by two closely-situated sound-hard spheres. Using boundary integral equation (BIE) methods, we find that a close evaluation problem arises leading to a nearly singular system of BIEs governing the surface fields. An asymptotic analysis of the problem reveals that this nearly singular behavior will lead to large error in the numerical solution unless it is explicitly addressed.
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- Award ID(s):
- 1819052
- NSF-PAR ID:
- 10357845
- Date Published:
- Journal Name:
- WAVES 2022
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Ultrasound directed self-assembly (DSA) utilizes the acoustic radiation force (ARF) associated with a standing ultrasound wave to organize particles dispersed in a fluid medium into specific patterns. The ARF is a superposition of the primary acoustic radiation force, which results from the incident standing ultrasound wave, and the acoustic interaction force, which originates from single and multiple scattering between neighboring particles. In contrast with most reports in the literature that neglect multiple scattering when calculating the ARF, we demonstrate that the deviation between considering single or multiple scattering may reach up to 100%, depending on the ultrasound DSA process parameters and material properties. We evaluate a theoretical case with three spherical particles in a viscous medium and derive operating maps that quantify the deviation between both scattering approaches as a function of the ultrasound DSA process parameters. Then, we study a realistic system with hundreds of particles dispersed in a viscous medium, and show that the deviation between the ARF resulting from single and multiple scattering increases with decreasing particle size and increasing medium viscosity, density ratio, compressibility ratio, and particle volume fraction. This work provides a quantitative basis for determining whether to consider single or multiple scattering in ultrasound DSA simulations.
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We develop a novel algorithm for large-scale holographic reconstruction of 3D particle fields. Our method is based on a multiple-scattering beam propagation method (BPM) combined with sparse regularization that enables recovering dense 3D particles of high refractive index contrast from a single hologram. We show that the BPM-computed hologram generates intensity statistics closely matching with the experimental measurements and provides up to 9× higher accuracy than the single-scattering model. To solve the inverse problem, we devise a computationally efficient algorithm, which reduces the computation time by two orders of magnitude as compared to the state-of-the-art multiple-scattering based technique. We demonstrate the superior reconstruction accuracy in both simulations and experiments under different scattering strengths. We show that the BPM reconstruction significantly outperforms the single-scattering method in particular for deep imaging depths and high particle densities.
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Optical cloaking refers to making an object invisible by preventing the light scattering in some directions as it hits the object. There is interest in cloaking devices in radar and other applications. Developing a model to accurately capture cloaking comes with numerical challenges, however. We must determine how light propagates through a medium composed by multiple, thin layers of materials with different electromagnetic properties. In this paper we consider a multi-layered scalar transmission problem in 2D and use boundary integral equation methods to compute the field. The Kress product quadrature rule is used to approximate singular integrals evaluated on boundaries, the Boundary Regularized Integral Equation Formulation (BRIEF) method [1] with Periodic Trapezoid Rule (PTR) is employed to treat nearly singular ones (off boundaries) appearing in the representation formula. Numerical results illustrate the efficiency of this approach, which may be applied to N arbitrary smooth layers.more » « less
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Consider the elastic scattering of a time-harmonic wave by multiple well-separated rigid particles with smooth boundaries in two dimensions. Instead of using the complex Green's tensor of the elastic wave equation, we utilize the Helmholtz decomposition to convert the boundary value problem of the elastic wave equation into a coupled boundary value problem of the Helmholtz equation. Based on single, double, and combined layer potentials with the simpler Green's function of the Helmholtz equation, we present three different boundary integral equations for the coupled boundary value problem. The well-posedness of the new integral equations is established. Computationally, a scattering matrix based method is proposed to evaluate the elastic wave for arbitrarily shaped particles. The method uses the local expansion for the incident wave and the multipole expansion for the scattered wave. The linear system of algebraic equations is solved by GMRES with fast multipole method (FMM) acceleration. Numerical results show that the method is fast and highly accurate for solving elastic scattering problems with multiple particles.more » « less
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Accepted Manuscript1.0
- Conference Paper:
- The DOI is not currently available.
