No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Fractal ladder models and power law wave equations
3.P. He, “Experimental verification of models for determining dispersion from attenuation,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 46, 706–714 (1999).
4.F. A. Duck, Physical Properties of Tissue, 1st ed. (Academic, London, 1990), pp. 99–124.
5.P. A. Narayana and J. Ophir, “On the frequency dependence of attenuation in normal and fatty liver,” IEEE Trans. Sonics Ultrason. SU-30, 379–383 (1983).
6.T. Lin, J. Ophir, and G. Potter, “Frequency-dependent ultrasonic differentiation of normal and diffusely diseased liver,” J. Acoust. Soc. Am. 82, 1131–1138 (1987).
7.P. M. Morse and K. U. Ingard, Theoretical Acoustics (Princeton University Pres, Princeton, NJ, 1968), pp. 270–300.
8.M. A. Biot, “Theory of propagation of elastic waves in fluid-saturated porous solid. I. Low-frequency range,” J. Acoust. Soc. Am. 28, 168–178 (1956).
9.A. I. Nachman, J. F. Smith, and R. C. Waag, “An equation for acoustic propagation in inhomogeneous media with relaxation losses,” J. Acoust. Soc. Am. 88, 1584–1595 (1990).
10.A. C. Kak and K. A. Dines, “Signal-processing of broad-band pulsed ultrasound—Measurement of attenuation of soft biological tissues,” IEEE Trans. Biomed. Eng. 25, 321–344 (1978).
12.T. L. Szabo, “The material impulse response for broadband pulses in lossy media,” in Proceedings of the IEEE Ultrasonics Symposium, Honolulu, HI (2003), pp. 748–751.
13.P. He, “Simulation of ultrasound pulse propagation in lossy media obeying a frequency power law,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 45, 114–125 (1998).
14.M. G. Wismer and R. Ludwig, “An explicit numerical time domain formulation to simulate pulsed pressure waves in viscous fluids exhibiting arbitrary frequency power law attenuation,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 42, 1040–1049 (1995).
15.R. S. C. Cobbold, N. V. Sushilov, and A. C. Weathermon, “Transient propagation in media with classical or power-law loss,” J. Acoust. Soc. Am. 116, 3294–3303 (2004).
16.S. Leeman, “Ultrasound pulse propagation in dispersive media,” Ultrasound Med. Biol. 25, 481–488 (1980).
18.T. L. Szabo, “Time-domain wave-equations for lossy media obeying a frequency power-law,” J. Acoust. Soc. Am. 96, 491–500 (1994).
20.W. Chen and S. Holm, “Fractional Laplacian time-space models for linear and nonlinear lossy media exhibiting arbitrary frequency power-law dependency,” J. Acoust. Soc. Am. 115, 1424–1430 (2004).
22.M. Caputo, “Linear models of dissipation whose is almost frequency independent II,” Geophys. J. R. Astron. Soc. 13, 529–539 (1967).
23.M. G. Wismer, “Finite element analysis of broadband acoustic pulses through inhomogeneous media with power law attenuation,” J. Acoust. Soc. Am. 120, 3493–3502 (2006).
24.M. Ochmann and S. Makarov, “Representation of the absorption of nonlinear waves by fractional derivatives,” J. Acoust. Soc. Am. 94, 3392–3399 (1993).
25.Z. E. A. Fellah and C. Depollier, “Transient acoustic wave propagation in rigid porous media: A time-domain approach,” J. Acoust. Soc. Am. 107, 683–688 (2000).
26.T. L. Szabo and J. Wu, “A model for longitudinal and shear wave propagation in viscoelastic media,” J. Acoust. Soc. Am. 107, 2437–2446 (2000).
29.W. G. Glöckle and T. F. Nonnenmacher, “Fox function representation of non-Debye relaxation processes,” J. Stat. Phys. 71, 741–756 (1993).
31.R. L. Bagley and P. J. Torvik, “A theoretical basis for the application of fractional calculus to viscoelasticity,” J. Rheol. 27, 201–210 (1983).
32.J. Wu and C. Layman, “Wave equations, dispersion relations, and van Hove singularities for applications of doublet mechanics to ultrasound propagation in bio- and nanomaterials,” J. Acoust. Soc. Am. 115, 893–900 (2004).
33.N. W. Tschoegl, The Phenomenological Theory of Linear Viscoelastic Behavior: An Introduction (Springer-Verlag, Berlin, 1989).
36.E. M. Darling, M. Topel, S. Zauscher, T. P. Vail, and F. Guilak, “Viscoelastic properties of human mesenchymally-derived stem cells and primary osteoblasts, chondrocytes, and adipocytes,” J. Biomech. 41, 454–464 (2008).
41.H. Schiessel and A. Blumen, “Mesoscopic pictures of the sol-gel transition: Ladder models and fractal networks,” Macromolecules 28, 4013–4019 (1995).
42.N. Heymans and J.-C. Bauwens, “Fractal rheological models and fractional differential equations for viscoelastic behavior,” Rheol. Acta 33, 210–219 (1994).
43.B. Alberts, A. Johnson, J. Lewis, M. Raff, K. Roberts, and P. Walter, Molecular Biology of the Cell, 4th ed. (Garland Science, New York, 2002).
44.B. Gross, “Ladder structures for representation of viscoelastic systems. II,” J. Polym. Sci. 20, 123–131 (1956).
46.P. E. Rouse, “A theory of linear viscoelastic properties of dilute solutions of coiling polymers,” J. Chem. Phys. 21, 1272–1280 (1953).
47.A. Kreis and A. C. Pipkin, “Viscoelastic pulse propagation and stable probability distributions,” Q. Appl. Math. 44, 353–360 (1986).
49.T. L. Szabo, “Causal theories and data for acoustic attenuation obeying a frequency power-law,” J. Acoust. Soc. Am. 97, 14–24 (1995).
50.J. F. Kelly, M. M. Meerschaert, and R. J. McGough, “Analytical time-domain Green’s functions for power-law media,” J. Acoust. Soc. Am. 124, 2861–2872 (2008).
51.L. E. Kinsler, A. R. Frey, A. B. Coppens, and J. V. Sanders, Fundamentals of Acoustics, 4th ed. (Wiley, New York, 2000), pp. 210–245.
52.K. R. Waters, M. S. Hughes, J. Mobley, G. H. Brandenburger, and J. G. Miller, “On the applicability of Kramers-Krönig relations for ultrasonic attenuation obeying a frequency power law,” J. Acoust. Soc. Am. 108, 556–563 (2000).
53.E. R. Weibel, “Fractal geometry: A design principle for living organisms,” Am. J. Physiol. Lung Cell. Mol. Physiol. 261, L361–L369 (1991).
54.J. W. Baish and R. K. Jain, “Fractals and cancer,” Cancer Res.60, 3683–3688 (2000).
56.S. Alexander and R. Orbach, “Density of states on fractals: Fractons,” J. Phys. (Paris) 43, L625–L631 (1982).
57.G. Wojcik, J. Mould, F. Lizzi, N. Abboud, M. Ostromogilsky, and D. Vaughn, “Nonlinear modeling of therapeutic ultrasound,” in Proceedings of the IEEE Ultrasonics Symposium, Cannes, France (1995), pp. 1617–1622.
58.A. A. Kilbas, H. M. Srivastava, and J. J. Truhillo, Theory and Applications of Fractional Differential Equations (Elsevier, Amsterdam, 2006).
Article metrics loading...
Full text loading...
Most read this month