133 research outputs found

    Sonic crystal lenses that obey Lensmaker's formula

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    This paper presents a theoretical study of the phenomenon of acoustic imaging by sonic crystals, which are made of two-dimensional regular arrays of rigid cylinders placed in parallel in air. The scattering of acoustic waves is computed using the standard multiple scattering theory, and the band structures are computed by the plane-wave expansion method. It is shown that properly arranged arrays not only can behave as acoustic lenses, but also the focusing effect can be well described by Lensmaker's formula. Possible applications are also discussed.Comment: 4 pages, 5 figure

    Theoretical analysis of acoustic stop bands in two-dimensional periodic scattering arrays

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    This paper presents a theoretical analysis of the recently reported observation of acoustic stop bands in two-dimensional scattering arrays (Robertson and Rudy, J. Acoust. Soc. Am. {\bf 104}, 694, 1998). A self-consistent wave scattering theory, incorporating all orders of multiple scattering, is used to obtain the wave transmission. The band structures for the regular arrays of cylinders are computed using the plane wave expansion method. The theoretical results compare favorably with the experimental data.Comment: 18 pages, 4 page

    Acoustic Attenuation by Two-dimensional Arrays of Rigid Cylinders

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    In this Letter, we present a theoretical analysis of the acoustic transmission through two-dimensional arrays of straight rigid cylinders placed parallelly in the air. Both periodic and completely random arrangements of the cylinders are considered. The results for the sound attenuation through the periodic arrays are shown to be in a remarkable agreement with the reported experimental data. As the arrangement of the cylinders is randomized, the transmission is significantly reduced for a wider range of frequencies. For the periodic arrays, the acoustic band structures are computed by the plane-wave expansion method and are also shown to agree with previous results.Comment: 4 pages, 3 figure

    Propagation inhibition and wave localization in a 2D random liquid medium

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    Acoustic propagation and scattering in water containing many parallel air-filled cylinders is studied. Two situations are considered and compared: (1) wave propagating through the array of cylinders, imitating a traditional experimental setup, and (2) wave transmitted from a source located inside the ensemble. We show that waves can be blocked from propagation by disorders in the first scenario, but the inhibition does not necessarily imply wave localization. Furthermore, the results reveal the phenomenon of wave localization in a range of frequencies.Comment: Typos in Fiures are correcte

    Theoretical analysis of the focusing of acoustic waves by two-dimensional sonic crystals

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    Motivated by a recent experiment on acoustic lenses, we perform numerical calculations based on a multiple scattering technique to investigate the focusing of acoustic waves with sonic crystals formed by rigid cylinders in air. The focusing effects for crystals of various shapes are examined. The dependance of the focusing length on the filling factor is also studied. It is observed that both the shape and filling factor play a crucial role in controlling the focusing. Furthermore, the robustness of the focusing against disorders is studied. The results show that the sensitivity of the focusing behavior depends on the strength of positional disorders. The theoretical results compare favorably with the experimental observations, reported by Cervera, et al. (Phys. Rev. Lett. 88, 023902 (2002)).Comment: 8 figure

    Acoustic Response of a Layer of Spherical Inclusions with a Random or Periodic Arrangement

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    Starting with the classic work of Ying and Truell [1], the scattering of a plane elastic wave by an isolated elastic sphere embedded in an unbounded medium has been studied in great detail. Similarly, the propagation of an effective elastic wave in an elastic matrix containing a random or periodic distribution of inclusions has received considerable attention. By comparison, an intermediate level of microstructure — a single layer of inclusions in an elastic matrix — has received very little attention. Apart from the fact that this problem is worth studying in its own right because of its inherent value as a canonical problem in elastodynamics of materials with a microstructure, it has applications in geophysics and quantitative nondestructive evaluation

    Bandgaps in the propagation and scattering of surface water waves over cylindrical steps

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    Here we investigate the propagation and scattering of surface water waves by arrays of bottom-mounted cylindrical steps. Both periodic and random arrangements of the steps are considered. The wave transmission through the arrays is computed using the multiple scattering method based upon a recently derived formulation. For the periodic case, the results are compared to the band structure calculation. We demonstrate that complete band gaps can be obtained in such a system. Furthermore, we show that the randomization of the location of the steps can significantly reduce the transmission of water waves. Comparison with other systems is also discussed.Comment: 4 pages, 3 figure

    In the name of the stakeholder: An assessment of representation surpluses and deficits by nonprofit leaders

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    Nonprofit leaders face the challenge of making deci- sions within a complex environment of heterogeneous and often competing stakeholder claims. In such a set- ting, leaders not only make judgments about the power of their organization's stakeholders but they also make conscious choices about which stakeholders they per- sonally represent while making organizational decisions. This study uses insights from stakeholder theory and agency theory to investigate (1) how nonprofit leaders' perceptions of stakeholder power and stake- holder representation are interrelated across a wide range of stakeholder groups and organizations, and (2) how perceptions of power and representation differ between board members and executive managers. Drawing on data from 491 nonprofit leaders, we find evidence of stakeholder representation surpluses and deficits for several stakeholders, although perceptions of these deficits and surpluses differ considerably between board members and managers. Our study holds important implications for nonprofit governance, the practice of stakeholder analysis, and the use of stakeholder constructs in future empirical research
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