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    Rights statement: This is the author’s version of a work that was accepted for publication in Wave Motion. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Wave Motion, 77, 2017 DOI: 10.1016/j.wavemoti.2017.11.002

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Generalized transformation design: Metrics, speeds, and diffusion

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Generalized transformation design: Metrics, speeds, and diffusion. / Kinsler, Paul; McCall, Martin W.
In: Wave Motion, Vol. 77, 03.2018, p. 91-106.

Research output: Contribution to Journal/MagazineJournal articlepeer-review

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Kinsler P, McCall MW. Generalized transformation design: Metrics, speeds, and diffusion. Wave Motion. 2018 Mar;77:91-106. Epub 2017 Nov 11. doi: 10.1016/j.wavemoti.2017.11.002

Author

Kinsler, Paul ; McCall, Martin W. / Generalized transformation design : Metrics, speeds, and diffusion. In: Wave Motion. 2018 ; Vol. 77. pp. 91-106.

Bibtex

@article{02916b5d34f347dcb8e9f83b31b5a07e,
title = "Generalized transformation design: Metrics, speeds, and diffusion",
abstract = "We show that a unified and maximally generalized approach to spatial transformation design is possible, one that encompasses all second order waves, rays, and diffusion processes in anisotropic media. Until the final step, it is unnecessary to specify the physical process for which a specific transformation design is to be implemented. The principal approximation is the neglect of wave impedance, an attribute that plays no role in ray propagation, and is therefore irrelevant for pure ray devices; another constraint is that for waves the spatial variation in material parameters needs to be sufficiently small compared with the wavelength. The key link between our general formulation and a specific implementation is how the spatial metric relates to the speed of disturbance in a given medium, whether it is electromagnetic, acoustic, or diffusive. Notably, we show that our generalised ray theory, in allowing for anisotropic indexes (speeds), generates the same predictions as does a wave theory, and the results are closely related to those for diffusion processes.",
keywords = "Propagation, Transformation, Metric, Speed, Diffusion, Ray",
author = "Paul Kinsler and McCall, {Martin W.}",
note = "This is the author{\textquoteright}s version of a work that was accepted for publication in Wave Motion. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Wave Motion, 77, 2017 DOI: 10.1016/j.wavemoti.2017.11.002",
year = "2018",
month = mar,
doi = "10.1016/j.wavemoti.2017.11.002",
language = "English",
volume = "77",
pages = "91--106",
journal = "Wave Motion",
issn = "0165-2125",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Generalized transformation design

T2 - Metrics, speeds, and diffusion

AU - Kinsler, Paul

AU - McCall, Martin W.

N1 - This is the author’s version of a work that was accepted for publication in Wave Motion. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Wave Motion, 77, 2017 DOI: 10.1016/j.wavemoti.2017.11.002

PY - 2018/3

Y1 - 2018/3

N2 - We show that a unified and maximally generalized approach to spatial transformation design is possible, one that encompasses all second order waves, rays, and diffusion processes in anisotropic media. Until the final step, it is unnecessary to specify the physical process for which a specific transformation design is to be implemented. The principal approximation is the neglect of wave impedance, an attribute that plays no role in ray propagation, and is therefore irrelevant for pure ray devices; another constraint is that for waves the spatial variation in material parameters needs to be sufficiently small compared with the wavelength. The key link between our general formulation and a specific implementation is how the spatial metric relates to the speed of disturbance in a given medium, whether it is electromagnetic, acoustic, or diffusive. Notably, we show that our generalised ray theory, in allowing for anisotropic indexes (speeds), generates the same predictions as does a wave theory, and the results are closely related to those for diffusion processes.

AB - We show that a unified and maximally generalized approach to spatial transformation design is possible, one that encompasses all second order waves, rays, and diffusion processes in anisotropic media. Until the final step, it is unnecessary to specify the physical process for which a specific transformation design is to be implemented. The principal approximation is the neglect of wave impedance, an attribute that plays no role in ray propagation, and is therefore irrelevant for pure ray devices; another constraint is that for waves the spatial variation in material parameters needs to be sufficiently small compared with the wavelength. The key link between our general formulation and a specific implementation is how the spatial metric relates to the speed of disturbance in a given medium, whether it is electromagnetic, acoustic, or diffusive. Notably, we show that our generalised ray theory, in allowing for anisotropic indexes (speeds), generates the same predictions as does a wave theory, and the results are closely related to those for diffusion processes.

KW - Propagation

KW - Transformation

KW - Metric

KW - Speed

KW - Diffusion

KW - Ray

U2 - 10.1016/j.wavemoti.2017.11.002

DO - 10.1016/j.wavemoti.2017.11.002

M3 - Journal article

VL - 77

SP - 91

EP - 106

JO - Wave Motion

JF - Wave Motion

SN - 0165-2125

ER -