scholarly journals Fractal ladder models and power law wave equations

2009 ◽  
Vol 126 (4) ◽  
pp. 2072 ◽  
Author(s):  
James F. Kelly ◽  
Robert J. McGough
Keyword(s):  
Power Law ◽  
Wave Equations ◽  
Ladder Models

Fractal ladder models and power‐law wave equations.

2009 ◽  
Vol 125 (4) ◽  
pp. 2513-2513
Author(s):  
James F. Kelly ◽  
Robert J McGough
Keyword(s):  
Power Law ◽  
Wave Equations ◽  
Ladder Models

scholarly journals Fractional wave equations with attenuation

2013 ◽  
Vol 16 (1) ◽  
Author(s):  
Peter Straka ◽  
Mark Meerschaert ◽  
Robert McGough ◽  
Yuzhen Zhou
Keyword(s):  
Wave Equation ◽  
Power Law ◽  
Weak Solutions ◽  
Wave Equations ◽  
Inhomogeneous Media ◽  
Medical Ultrasound ◽  
Sound Waves ◽  
Fractional Wave Equations

AbstractFractional wave equations with attenuation have been proposed by Caputo [5], Szabo [28], Chen and Holm [7], and Kelly et al. [11]. These equations capture the power-law attenuation with frequency observed in many experimental settings when sound waves travel through inhomogeneous media. In particular, these models are useful for medical ultrasound. This paper develops stochastic solutions and weak solutions to the power law wave equation of Kelly et al. [11].

Dispersion of sausage waves in coronal waveguides with transverse density structuring

2019 ◽  
Vol 488 (1) ◽  
pp. 660-675 ◽  
Author(s):  
I Lopin ◽  
I Nagorny
Keyword(s):  
Density Distribution ◽  
Longitudinal Wave ◽  
Power Law ◽  
Wave Equations ◽  
Wave Dispersion ◽  
Dispersion Properties ◽  
Varying Coefficients ◽  
Uniform Region ◽  
Wave Numbers ◽  
Power Law Index

ABSTRACT We study dispersion properties of fast-sausage waves in a radially structured coronal magnetic tube with continuous radial density distribution. The models, containing either a non-uniform core or inhomogeneous external medium are considered. The dispersion relations are obtained for a power law density distribution in the corresponding non-uniform region, where the power-law index controls the steepness of the tube boundary. The governing wave equations with varying coefficients were solved with the Wentzel–Kramers–Brillouin (WKB) approximation. The model with the non-uniform core supports the existence of trapped and leaky sausage modes. The density non-uniformity in the core modifies the values of cut-off wave numbers kc. The smaller values of cut-offs, normalized to the effective tube radius r0, correspond to the smaller power index p. The wave dispersion (i.e. dVph/dk) decreases for smaller p. This occurs in the range of not too small longitudinal wave numbers k > kc. For the model, containing inhomogeneous environment the basic dispersion properties are generally identical to that for the monolithic tube model, studied in Lopin & Nagorny (2015b). The waves are trapped for all wave numbers, if the power-law index 0 < n < 2. There are both trapped and leaky regimes for n ≥ 2. The wave dispersion decreases for smaller n, in the range of the intermediate values of the longitudinal wave numbers k > kc. The seismological application of the obtained results is discussed.

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