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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.

Sound-waves. --- Vibration --- Waves --- Acoustics. --- Vibration. --- Diagnosis, Ultrasonic. --- Acoustics in engineering. --- Physical geography. --- Vibration, Dynamical Systems, Control. --- Mathematical Physics. --- Ultrasound. --- Engineering Acoustics. --- Geophysics/Geodesy. --- Geography --- Diagnosis, Ultrasonic --- Diagnostic sonography --- Diagnostic ultrasonics --- Diagnostic ultrasonography --- Diagnostic ultrasound --- Medical diagnostic ultrasonic imaging --- Medical ultrasonography --- Ultrasonic diagnosis --- Ultrasonic diagnostic imaging --- Ultrasonic imaging --- Ultrasonic waves --- Diagnostic imaging --- Ultrasonics in medicine --- Cycles --- Mechanics --- Sound --- Diagnostic use --- Dynamical systems. --- Dynamics. --- Mathematical physics. --- Radiology. --- Acoustical engineering. --- Geophysics. --- Geological physics --- Terrestrial physics --- Earth sciences --- Physics --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Statics --- Acoustic engineering --- Sonic engineering --- Sonics --- Sound engineering --- Sound-waves --- Engineering --- Radiological physics --- Radiation --- Physical mathematics --- Industrial applications --- Multibody systems. --- Mechanics, Applied. --- Ultrasonics. --- Multibody Systems and Mechanical Vibrations. --- Inaudible sound --- Supersonics --- Sound pressure --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Multi-body systems --- Systems, Multibody --- Sound.

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Deense letterkunde --- Littérature --- Littérature danoise --- 839.81 (Holm, S. 7.03 = 393)