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Waves with Power-Law Attenuation

Holm, Sverre.

Waves with Power-Law Attenuation

Record Type:	Electronic resources : Monograph/item
Title/Author:	Waves with Power-Law Attenuationby Sverre Holm.
Author:	Holm, Sverre.
Published:	Cham :Springer International Publishing :2019.
Description:	xxxvii, 312 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Sound-wavesAttenuation.
Online resource:	https://doi.org/10.1007/978-3-030-14927-7
ISBN:	9783030149277$q(electronic bk.)

Waves with Power-Law Attenuation
Holm, Sverre.

Waves with Power-Law Attenuation[electronic resource] /by Sverre Holm. - Cham :Springer International Publishing :2019. - xxxvii, 312 p. :ill., digital ;24 cm.

Preface -- Acknowledgements -- About the Author -- List of Symbols -- List of Figures -- List of Tables -- 1 Introduction -- Part I Acoustics and Linear Viscoelasticity -- 2 Classical Wave Equations -- 3 Models of Linear Viscoelasticity -- 4 Absorption Mechanisms and Physical Constraints -- Part II Modeling of Power-Law Media -- 5 Power-Law Wave Equations from Constitutive Equations -- 6 Phenomenological Power-Law Wave Equations -- 7 Justification for Power Laws and Fractional Models -- 8 Power Laws and Porous Media -- 9 Power Laws and Fractal Scattering Media -- Appendix A Mathematical Background -- Appendix B Wave and Heat Equations -- Index.

This book integrates concepts from physical acoustics with those from linear viscoelasticity and fractional linear viscoelasticity. Compressional waves and shear waves in applications such as medical ultrasound, elastography, and sediment acoustics often follow power law attenuation and dispersion laws that cannot be described with classical viscous and relaxation models. This is accompanied by temporal power laws rather than the temporal exponential responses of classical models. The book starts by reformulating the classical models of acoustics in terms of standard models from linear elasticity. Then, non-classical loss models that follow power laws and which are expressed via convolution models and fractional derivatives are covered in depth. In addition, parallels are drawn to electromagnetic waves in complex dielectric media. The book also contains historical vignettes and important side notes about the validity of central questions. While addressed primarily to physicists and engineers working in the field of acoustics, this expert monograph will also be of interest to mathematicians, mathematical physicists, and geophysicists. Couples fractional derivatives and power laws and gives their multiple relaxation process interpretation Investigates causes of power law attenuation and dispersion such as interaction with hierarchical models of polymer chains and non-Newtonian viscosity Shows how fractional and multiple relaxation models are inherent in the grain shearing and extended Biot descriptions of sediment acoustics Contains historical vignettes and side notes about the formulation of some of the concepts discussed.

ISBN: 9783030149277$q(electronic bk.)

Standard No.: 10.1007/978-3-030-14927-7doiSubjects--Topical Terms:

839302
Sound-waves
--Attenuation.

LC Class. No.: QC243 / .H65 2019

Dewey Class. No.: 534.2

Waves with Power-Law Attenuation
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245 1 0 $a Waves with Power-Law Attenuation $h [electronic resource] / $c by Sverre Holm.
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300 $a xxxvii, 312 p. : $b ill., digital ; $c 24 cm.
505 0 $a Preface -- Acknowledgements -- About the Author -- List of Symbols -- List of Figures -- List of Tables -- 1 Introduction -- Part I Acoustics and Linear Viscoelasticity -- 2 Classical Wave Equations -- 3 Models of Linear Viscoelasticity -- 4 Absorption Mechanisms and Physical Constraints -- Part II Modeling of Power-Law Media -- 5 Power-Law Wave Equations from Constitutive Equations -- 6 Phenomenological Power-Law Wave Equations -- 7 Justification for Power Laws and Fractional Models -- 8 Power Laws and Porous Media -- 9 Power Laws and Fractal Scattering Media -- Appendix A Mathematical Background -- Appendix B Wave and Heat Equations -- Index.
520 $a This book integrates concepts from physical acoustics with those from linear viscoelasticity and fractional linear viscoelasticity. Compressional waves and shear waves in applications such as medical ultrasound, elastography, and sediment acoustics often follow power law attenuation and dispersion laws that cannot be described with classical viscous and relaxation models. This is accompanied by temporal power laws rather than the temporal exponential responses of classical models. The book starts by reformulating the classical models of acoustics in terms of standard models from linear elasticity. Then, non-classical loss models that follow power laws and which are expressed via convolution models and fractional derivatives are covered in depth. In addition, parallels are drawn to electromagnetic waves in complex dielectric media. The book also contains historical vignettes and important side notes about the validity of central questions. While addressed primarily to physicists and engineers working in the field of acoustics, this expert monograph will also be of interest to mathematicians, mathematical physicists, and geophysicists. Couples fractional derivatives and power laws and gives their multiple relaxation process interpretation Investigates causes of power law attenuation and dispersion such as interaction with hierarchical models of polymer chains and non-Newtonian viscosity Shows how fractional and multiple relaxation models are inherent in the grain shearing and extended Biot descriptions of sediment acoustics Contains historical vignettes and side notes about the formulation of some of the concepts discussed.
650 0 $a Sound-waves $x Attenuation. $3 839302
650 1 4 $a Acoustics. $3 242702
650 2 4 $a Vibration, Dynamical Systems, Control. $3 274667
650 2 4 $a Mathematical Physics. $3 522725
650 2 4 $a Ultrasound. $3 274971
650 2 4 $a Engineering Acoustics. $3 357294
650 2 4 $a Geophysics/Geodesy. $3 274000
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773 0 $t Springer eBooks
856 4 0 $u https://doi.org/10.1007/978-3-030-14927-7
950 $a Physics and Astronomy (Springer-11651)