Bound states in coupled guides. I. Two dimensions

Linton, C. M.; Ratcliffe, Keith

doi:10.1063/1.1675931

Cited by 13 publications

(16 citation statements)

References 33 publications

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“…In quantum waveguides trapped modes are known as bound states, cf. Duclos & Exner (1995) or Linton & Ratcliffe (2004). Similar trapped modes are found in electromagnetic waves, cf.…”

Section: Introductionsupporting

confidence: 64%

Acoustic resonances and trapped modes in annular plate cascades

Koch¹

2009

J. Fluid Mech.

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As a stepping stone towards understanding acoustic resonances in axial flow compressors, acoustic resonances are computed numerically in fixed single and tandem plate cascades in an infinitely long annular duct. Applying perfectly matched layer absorbing boundary conditions in the form of the complex scaling method of atomic and molecular physics to approximate the radiation condition the resonance problem is transformed into an eigenvalue problem. Of particular interest are resonances with zero radiation damping (trapped modes) or very small radiation damping (nearly trapped modes). Such resonances can be excited by wakes from compressor cascades or struts. If the shedding frequency is sufficiently close to an acoustic resonant frequency, the latter may control the vortex shedding causing high-intensity tonal noise or occasionally even blade failure. All resonances are computed for zero mean flow approximating low-Mach-number flows. The influence of various cascade parameters on the resonant frequencies is studied and, whenever possible, our numerical results are compared with published experimental findings.

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“…In quantum waveguides trapped modes are known as bound states, cf. Duclos & Exner (1995) or Linton & Ratcliffe (2004). Similar trapped modes are found in electromagnetic waves, cf.…”

Section: Introductionsupporting

confidence: 64%

Acoustic resonances and trapped modes in annular plate cascades

Koch¹

2009

J. Fluid Mech.

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“…These single-resonance parametric BICs can also exist in non-periodic structures, as shown theoretically in acoustic and water waveguides with an obstacle [143][144][145][146][147][148] , in quantum waveguides with impurities [149][150][151] or bends 95,152,153 , for mechanically coupled beads 29,30 and mechanical resonators 154 , and in optics for a low-index waveguide on a high-index membrane 155 .…”

Section: Single Resonancementioning

confidence: 79%

Bound states in the continuum

et al. 2016

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Bound states in the continuum are waves that, defying conventional wisdom, remain localized even though they coexist with a continuous spectrum of radiating waves that can carry energy away. Their existence was first proposed in quantum mechanics and, being a general wave phenomenon, later identified in electromagnetic, acoustic, and water waves. They have been studied in a wide variety of material systems such as photonic crystals, optical waveguides and fibers, piezoelectric materials, quantum dots, graphene, and topological insulators. This Review describes recent developments in this field with an emphasis on the physical mechanisms that lead to these unusual states across the seemingly very different platforms. We discuss recent experimental realizations, existing applications, and directions for future work.

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“…Very similar problems occur in quantum waveguides, where the trapped modes are known as bound states, cf. Exner et al (1996) or Linton & Ratcliffe (2004) (see also Grikurov 2004).…”

Section: Introductionmentioning

confidence: 99%

Complex resonances and trapped modes in ducted domains

Duan¹,

Koch²,

Linton

et al. 2007

J. Fluid Mech.

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Due to radiation losses, resonances in open systems are generally complex valued. However, near symmetric, centred objects in ducted domains, or in periodic arrays, so-called trapped modes can exist below the cut-off frequency of the first non-trivial duct mode. These trapped modes have no radiation loss and correspond to real-valued resonances. Above the first cut-off frequency isolated trapped modes exist only for specific parameter combinations. These isolated trapped modes are termed embedded, because their corresponding eigenvalues are embedded in the continuous spectrum of an appropriate differential operator. Trapped modes are of considerable importance in applications because at these parameters the system can be excited easily by external forcing. In the present paper directly computed embedded trapped modes are compared with numerically obtained resonances for several model configurations. Acoustic resonances are also computed in two-dimensional models of a butterfly and ball-type valve as examples of more complicated geometries.

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Bound states in coupled guides. I. Two dimensions

Cited by 13 publications

References 33 publications

Acoustic resonances and trapped modes in annular plate cascades

Acoustic resonances and trapped modes in annular plate cascades

Bound states in the continuum

Complex resonances and trapped modes in ducted domains

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