Multiple multipole expansions for elastic scattering

Imhof, Matthias G.

doi:10.1121/1.417109

Cited by 29 publications

(14 citation statements)

References 16 publications

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“…Hafner 1990). The MMP method was later adapted to acoustic (Imhof 1995) and elastic (Imhof 1996;Imhof & Toksöz 2000) scattering problems in 2-D. Its extension to 3-D was obvious, but at that time still impractical due to inadequate computer resources. In the meantime, computer power has increased dramatically, which allows practical application of 3-D MMP methods for elastic scattering problems.…”

Section: Introductionmentioning

confidence: 99%

Computing the elastic scattering from inclusions using the multiple multipoles method in three dimensions

Imhof¹

2004

Geophysical Journal International

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S U M M A R YThe paper extends the multiple multipole method (MMP) to compute the multiple scattering effects from inclusions in a homogeneous full-space from two dimensions to three dimensions. MMP methods are based on a scattered wavefield model where the unknown weighting coefficients are determined from satisfying the boundary conditions at discrete matching points. The wavefield model is most commonly constructed from multiple spherical wavefunctions with different expansion centres, but any solution or approximation to the wave equation may also be used. Such an expansion is non-orthogonal and requires use of overdetermined matrix systems, but this system can be constructed rapidly because simple point matching without costly integration is sufficient. Furthermore, irregularities of the boundary are resolved locally from the nearest centre of expansion, which decouples different parts of the boundary, and thus, promotes rapid conversion with small numbers of expansion functions. The resulting algorithm is a very general tool to solve relatively large and complex 3-D scattering problems.

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Section: Introductionmentioning

confidence: 99%

Computing the elastic scattering from inclusions using the multiple multipoles method in three dimensions

Imhof¹

2004

Geophysical Journal International

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“…For an arbitrarily shaped dot geometry, we develop a multiple expansion technique to solve the Dirac-Weyl equation for spin-1 particles, incorporating the evanescent waves by generalizing the multiple multipole expansion method originally developed in optics [66][67][68][69][70]. Our method is computationally reliable and efficient, providing a powerful tool to detect and verify the existence of in-gap excitations/modes and study their robustness in the presence of geometric deformations.…”

Section: Appendix B: Multiple Multipoles Method: Calculation Of Eigenmentioning

confidence: 99%

Anomalous chiral edge states in spin-1 Dirac quantum dots

Lai

2020

Phys. Rev. Research

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We uncover an unexpected family of in-gap chiral edge states in noninverted spin-1 Dirac quantum dots. The system represents a topologically trivial confinement configuration where such edge states are not expected according to the conventional wisdom. In particular, for a massive type of confining potential, two distinct situations can arise: with or without mass sign change, corresponding to a quantum dot with or without band inversion, respectively. The former case is conventional, where topologically protected chiral edge modes can arise in the gap. For the latter, contrary to the belief that there should be no one-way current-carrying edge channels, we find the surprising emergence of such edge states and the spin-1 analog of Majorana modes. These states are strikingly robust and immune to backscattering. In the presence of a magnetic field, the edge states result in peculiar Fock-Darwin states originated from Landau-level confinement. The unexpected phenomenon is also validated in systems with bulk-topology regularization through (1) a properly regularized continuum model and (2) an experimentally accessible tight-binding dice lattice system.

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“…In fact, to our knowledge, there were no previous numerical methods for solving the generalized Dirac-Weyl equation for α-T 3 particles that are neither pseudospin-1/2 nor pseudospin-1. Taking advantage of a recently developed computational method [94] for pseudospin-1 particles based on the multiple multipole (MMP) method in optics [95][96][97][98][99], we have developed an efficient computational method [94] to solve the spinor wave functions associated with the scattering of α-T 3 particles from an arbitrary geometric domain (Appendix E). The basic idea is to place two sets of fictitious "poles," one inside the cavity and another outside, which are regarded as the sources for generating the scattering wave function.…”

Section: A Confinement In Deformed Cavities With Distinct Classical mentioning

confidence: 99%

Electrical confinement in a spectrum of two-dimensional Dirac materials with classically integrable, mixed, and chaotic dynamics

Han

Lai

2020

Phys. Rev. Research

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An emergent class of two-dimensional Dirac materials is α-T 3 lattices that can be realized by adding an atom at the center of each unit cell of a lattice with T 3 symmetry. The interaction strength α between this atom and any of its nearest neighbors is a parameter that can be continuously tuned between zero and one to generate a spectrum of materials. We investigate the fundamentally important and practically relevant issue of quasiparticle confinement for the entire spectrum of α-T 3 materials. Except for the two end points, i.e., α = 0, 1, which correspond to the graphene and pseudospin-1 lattices, respectively, the time-reversal symmetry is broken, leading to the removal of level degeneracy and facilitating confinement. Taking the approach of quantum scattering off an electrically generated potential cavity in the quantum-dot regime, we characterize confinement by identifying and examining the scattering resonances. We study a number of cavities with characteristically distinct classical dynamics: circular, annular, elliptical, and stadium cavities. For the circular and annular cavities with classically integrable and mixed dynamics, respectively, the scattering matrix can be analytically obtained, so the scattering cross sections and the Wigner-Smith time delay associated with the resonances can be calculated to quantify confinement. For the elliptical and stadium cavities with mixed and chaotic dynamics in the classical limit, respectively, the scattering-matrix approach is infeasible, so we adopt an efficient numerical method to calculate the scattering wave functions and experimentally accessible measures of confinement such as the magnetic moment. The main finding is that, for all the cases, the regime of small α values offers the best confinement possible among the spectrum of α-T 3 materials, which is general and holds regardless of the nature of the corresponding classical dynamics.

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Multiple multipole expansions for elastic scattering

Cited by 29 publications

References 16 publications

Computing the elastic scattering from inclusions using the multiple multipoles method in three dimensions

Computing the elastic scattering from inclusions using the multiple multipoles method in three dimensions

Anomalous chiral edge states in spin-1 Dirac quantum dots

Electrical confinement in a spectrum of two-dimensional Dirac materials with classically integrable, mixed, and chaotic dynamics

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