Read While You Wait - Get immediate ebook access, if available*, when you order a print book

Waves with Power-Law Attenuation

Authors: Holm, Sverre

Free Preview
  • 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
see more benefits

Buy this book

eBook $119.00
price for USA in USD
  • ISBN 978-3-030-14927-7
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $159.99
price for USA in USD
  • ISBN 978-3-030-14926-0
  • Free shipping for individuals worldwide. COVID-19 shipping restrictions apply.
  • Immediate ebook access, if available*, with your print order
  • Usually ready to be dispatched within 3 to 5 business days.
About this book

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.

About the authors

Sverre Holm was born in Oslo, Norway, in 1954. He received M.S. and Ph.D. degrees in electrical engineering from the Norwegian Institute of Technology (NTNU), Trondheim in 1978 and 1982, respectively.

He has academic experience from NTNU and Yarmouk University in Jordan (1984-86). Since 1995 he has been a professor of signal processing and acoustic imaging at the University of Oslo. In 2002 he was elected a member of the Norwegian Academy of Technological Sciences.

His industry experience includes GE Vingmed Ultrasound (1990-94), working on digital ultrasound imaging, and Sonitor Technologies (2000-05), where he developed ultrasonic indoor positioning. He is currently involved with several startups in the Oslo area working in the areas of acoustics and ultrasonics.

Dr. Holm has authored or co-authored around 220 publications and holds 12 patents. He has spent sabbaticals at GE Global Research, NY (1998), Institut Langevin, ESPCI, Paris (2008-09), and King’s College London (2014). His research interests include medical ultrasound imaging, elastography, modeling of waves in complex media, and ultrasonic positioning.

Reviews

“The book is interesting if you want to enter the field of fractional rheology. This is an actual topic of research that may be quite promising and this book is a helpful tool to take a first step in the subject. In my opinion it is well written and it is highly readable with technical details under control. I have highly appreciated the idea of integrating several ideas from physical acoustics with those from linear viscoelasticity.” (Giuseppe Saccomandi, Mathematical Reviews, November, 2019)

Table of contents (9 chapters)

Table of contents (9 chapters)

Buy this book

eBook $119.00
price for USA in USD
  • ISBN 978-3-030-14927-7
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $159.99
price for USA in USD
  • ISBN 978-3-030-14926-0
  • Free shipping for individuals worldwide. COVID-19 shipping restrictions apply.
  • Immediate ebook access, if available*, with your print order
  • Usually ready to be dispatched within 3 to 5 business days.
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Waves with Power-Law Attenuation
Authors
Copyright
2019
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-14927-7
DOI
10.1007/978-3-030-14927-7
Hardcover ISBN
978-3-030-14926-0
Edition Number
1
Number of Pages
XXXVII, 312
Number of Illustrations
60 b/w illustrations, 82 illustrations in colour
Topics

*immediately available upon purchase as print book shipments may be delayed due to the COVID-19 crisis. ebook access is temporary and does not include ownership of the ebook. Only valid for books with an ebook version. Springer Reference Works and instructor copies are not included.