Titlebook: Waves with Power-Law Attenuation; Sverre Holm Book 2019 Springer Nature Switzerland AG 2019 Power laws acoustics.Linear viscoelasticity.El

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Absorption Mechanisms and Physical Constraintsch smaller than the wavelength, often at the molecular level. This is especially so in the acoustics case. In Sect.?. specific examples of processes were given due to ., ., and . for seawater as well as . and . for air. This chapter begins with a more detailed account of these processes starting wit

嘲笑

Power-Law Wave Equations from Constitutive Equationsnd Zener models (.) and (.) as well as the relaxation responses of the Maxwell and Zener models ((.) and (.)). But in many complex media this model is too simple, and power laws are observed instead, which may both be in time-domain responses and in the frequency-domain. As the Fourier transform of

歡樂東方

Phenomenological Power-Law Wave Equationse consideration for time domain properties. First wave equations which are found by manipulating the common wave equations will be discussed. This is done by replacing ordinary derivatives in time or space with fractional ones. In some cases, this will give the same solutions as those found from fra

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Prophylaxis

Book 2019es 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 expone

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tenuation and dispersion such as interaction with hierarchic.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

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Spirometry

Absorption Mechanisms and Physical Constraintsere given due to ., ., and . for seawater as well as . and . for air. This chapter begins with a more detailed account of these processes starting with the simplest monatomic and polyatomic gases, simple and associated liquids, and finally chemical solutions.

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Power-Law Wave Equations from Constitutive Equations too simple, and power laws are observed instead, which may both be in time-domain responses and in the frequency-domain. As the Fourier transform of a temporal power law is itself a power law, these observations are equivalent. The first section therefore starts by reviewing empirical observations of power laws in the frequency and time domains.

dialect

Phenomenological Power-Law Wave Equationsdone by replacing ordinary derivatives in time or space with fractional ones. In some cases, this will give the same solutions as those found from fractional constitutive laws, and in other cases new equations will result.