Fractional models and power-law models


Journal Papers

  1. Xu Yang, Wei Cai, Yingjie Liang, Sverre Holm, A novel representation of time-varying viscosity with power-law and comparative study, Int. J. Non-Lin. Mech., March 2020
  2. H. Esmonde and S. Holm, Fractional Derivative Modelling of Adhesive Cure, Appl. Math. Mod., Jan 2020.
  3. S. Holm, Dispersion analysis for wave equations with fractional Laplacian loss operators, Invited paperFract. Calc. Appl. Anal., vol. 22, no 6., Dec 2019
  4. K. Parker, T. Szabo, S. Holm, "Towards a consensus on rheological models for elastography in soft tissues," Phys. Med. Biol., Oct. 2019.
  5. S. N. Chandrasekaran and S. Holm, "A multiple relaxation interpretation of the extended Biot model," Journ. Acoust. Soc. Am, July 2019.
  6. Wei Cai, Wen Chen, Jun Fang and Sverre Holm, A survey on fractional derivative modeling of power-law frequency-dependent viscous dissipative and scattering attenuation in acoustic wave propagation, Appl. Mech. Rev., 2018
  7. R. Sinkus, S. Lambert, K. Z. Abd-Elmoniem, C. Morse, T. Heller, C. Guenthner, A. M Ghanem, S. Holm, and A. M. Gharib, Rheological Determinants for Simultaneous Staging of Hepatic Fibrosis and Inflammation in Patients with Chronic Liver Disease, NMR in Biomedicine, 2018.
  8. S. Holm, "Spring-damper equivalents of the fractional, poroelastic, and poroviscoelastic models for elastography," NMR in Biomedicine, Nov 2017.
  9. S. Holm and M. B. Holm, "Restrictions on wave equations for passive media," Journ. Acoust. Soc. Am., 2017.
    • Erratum - missing convolution sign in Eqs. 2 and 3. 
  10. Wen Chen, Jun Fang, Guofei Pang, Sverre Holm, "Fractional biharmonic operator equation model for arbitrary frequency-dependent scattering attenuation in acoustic wave propagation," Journ. Acoust. Soc. Am., Jan 2017.
  11. V. Pandey, S. Holm, "Connecting the grain-shearing mechanism of wave propagation in marine sediments to fractional order wave equations," Dec. 2016, Journ. Acoust. Soc. Am.
  12. V. Pandey, S. Holm, "Linking the fractional derivative and the Lomnitz creep law to non-Newtonian time-varying viscosity", Physical Review E, Sept 2016. 
  13. V. Pandey, S. P. Näsholm, S. Holm, "Spatial dispersion of elastic waves in a bar characterized by tempered nonlocal elasticity," Fract. Calc. Appl. Anal. Vol. 19, No 2 (2016).
  14. W. Zhang and S. Holm, "Estimation of shear modulus in media with power law characteristics," Ultrasonics, Jan. 2016.
  15. S. A. Lambert, S. P. Näsholm, D. Nordsletten, C. Michler, L. Juge, J.-M. Serfaty, L. Bilston, B. Guzina, S. Holm, R. Sinkus, "Bridging three orders of magnitude: Multiple scattered waves sense fractal microscopic structures via dispersion," Physical Review Letters, Aug. 2015.
  16. S. Holm and S. P. Näsholm, "Comparison of fractional wave equations for power law attenuation in ultrasound and elastography," Ultrasound in Medicine and Biology, April 2014
  17. W. Zhang, X. Cai, S. Holm, "Time-fractional heat equations and negative absolute temperatures," Computers and Mathematics with Applications, pp 164–171, Jan 2014.
  18. S. Holm, S. P. Näsholm, F. Prieur, R. Sinkus, "Deriving fractional acoustic wave equations from mechanical and thermal constitutive equations," Computers & Mathematics with Applications, Sept. 2013.
  19. S. P. Näsholm and S. Holm, "On a Fractional Zener Elastic Wave Equation," Fract. Calc. Appl. Anal. Vol. 16, No 1 (2013).
  20. F. Prieur, G. Vilenskiy, S. Holm, "A more fundamental approach to the derivation of nonlinear acoustic wave equations with fractional loss operator," Journ. Acoust. Soc. Am., Oct. 2012.
  21. S. P. Näsholm and S. Holm, "Linking multiple relaxation, power-law attenuation, and fractional wave equations," Journ. Acoust. Soc. Am, Nov. 2011.
  22. S. Holm and S. P. Näsholm, "A causal and fractional all-frequency wave equation for lossy media," Journ. Acoust. Soc. Am, Oct. 2011.
  23. F. Prieur and S. Holm, "Nonlinear acoustic wave equations with fractional loss operators," Journ. Acoust. Soc. Am, Sept. 2011.
  24. S. Holm and R. Sinkus, ”A unifying fractional wave equation for compressional and shear waves,” Journ. Acoust. Soc. Am., vol 127, no 1, pp-542-548, 2010.
  25. W. Chen and S. Holm, "Fractional Laplacian time-space models for linear and nonlinear lossy media exhibiting arbitrary frequency dependency," J. Acoust. Soc. Amer., pp. 1424-1430, Apr. 2004.
  26. W.Chen and S. Holm, "Modified Szabo’s wave equation models for lossy media obeying frequency power law," J. Acoust. Soc. Amer., pp. 2570-2574, Nov. 2003.
Published May 26, 2020 10:55 AM - Last modified May 26, 2020 11:09 AM