Comment on "hydrodynamics of fractal continuum flow" and "map of fluid flow in fractal porous medium into fractal continuum flow"

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 88, Issue 5, 2013, Pages

  Li, Jun ^a   Ostoja Starzewski, Martin ^b  

^a California Institute of Technology   (United States)

^b UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CAUCHY STRESS TENSORS; CONTINUUM HYDRODYNAMICS; CONTINUUM MECHANICS MODELS; DERIVATIVE OPERATORS; FRACTAL POROUS MEDIUM; INITIAL CONFIGURATION; ITS APPLICATIONS; VOLUMETRIC COEFFICIENTS;

CONTINUUM MECHANICS; FLOW OF FLUIDS; HYDRODYNAMICS; POROUS MATERIALS;

FRACTALS;

EID: 84889254399     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.88.057001     Document Type: Review

References (23)

1. A. S. Balankin and B. E. Elizarraraz, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.85.025302 85, 025302 (R) (2012).
2. A. S. Balankin and B. E. Elizarraraz, Phys. Rev. E 10.1103/PhysRevE.85. 056314 85, 056314 (2012).
3. J. Li and M. Ostoja-Starzewski, Proc. R. Soc. A 1364-5021 10.1098/rspa.2009.0101 465, 2521 (2009);
4. J. Li and M. Ostoja-Starzewski, Proc. R. Soc. A 1364-5021 10.1098/rspa.2010.0491 467, 1214 (2010).
5. P. N. Demmie and M. Ostoja-Starzewski, J. Elasticity JELSAY 0374-3535 10.1007/s10659-011-9333-6 104, 187 (2011).
6. J. Li and M. Ostoja-Starzewski, Int. J. Eng. Sci. IJESAN 0020-7225 10.1016/j.ijengsci.2011.03.010 49, 1302 (2011).
7. V. E. Tarasov, Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media (Springer, Berlin, 2010).
8. G. Jumarie, Appl. Math. Lett. AMLEEL 0893-9659 10.1016/j.aml.2004.05.014 18, 739 (2005). (Pubitemid 40612588)
9. G. Jumarie, Appl. Math. Lett. AMLEEL 0893-9659 10.1016/j.aml.2008.06.003 22, 378 (2008).
10. W. Chen, Chaos, Solitons Fractals CSFOEH 0960-0779 10.1016/j.chaos.2005. 08.199 28, 923 (2006). (Pubitemid 41607590)
11. A. S. Balankin, B. Mena, J. Patiño, and D. Morales, Phys. Lett. A PYLAAG 0375-9601 10.1016/j.physleta.2013.01.030 377, 783 (2013).
12. A. S. Balankin, Phys. Lett. A PYLAAG 0375-9601 10.1016/j.physleta.2013. 04.040 377, 1606 (2013).
13. R. R. Nigmatullin, Theoret. Math. Phys. TMPHAH 0040-5779 10.1007/BF01036529 90, 242 (1992).
14. R. S. Rutman, Theoret. Math. Phys. TMPHAH 0040-5779 10.1007/BF01018580 100, 1154 (1994).
15. I. Podlubny, V. Despotovic, T. Skovranek, and B. H. McNaughton, J. Online Math. Its Appl. 7, 1664 (2007).
16. V. E. Tarasov, Int. J. Mod. Phys. B IJPBEV 0217-9792 10.1142/ S0217979213300053 27, 1330005 (2013).
17. K. Falconer, Fractal Geometry: Mathematical Foundations and Applications (Wiley, Chichester, 2003).
18. G. Christakos, D. T. Hristopulos, and P. Bogaert, Adv. Water Resour. AWREDI 0309-1708 10.1016/S0309-1708(00)00020-8 23, 799 (2000). (Pubitemid 30398111)
19. M. Ostoja-Starzewski, J. Li, H. Joumaa, and P. N. Demmie, Z. Angew. Math. Mech. 10.1002/zamm.201200164 93, 1 (2013).
20. A. C. Eringen, Microcontinuum Field Theories I: Foundations and Solids (Springer, Berlin, 1999).
21. P. M. Buechner and R. S. Lakes, Biomech. Model. Mechanobiol. 1617-7959 10.1007/s10237-002-0026-8 1, 295 (2003).
22. L. Pothuaud, C. L. Benhamou, P. Porion, E. Lespessailles, R. Harba and P. Levitz, J. Bone Miner. Res. JBMREJ 0884-0431 10.1359/jbmr.2000.15.4.691 15, 691 (2000).
23. H. Joumaa, M. Ostoja-Starzewski and P. N. Demmie, Math. Mech. Solids, doi: 10.1177/1081286512454557 (2012).