Spectral entropy in a fractional order model of anomalous diffusion

Proceedings of the 2012 13th International Carpathian Control Conference, ICCC 2012

Volumn , Issue , 2012, Pages 458-463

  Magin, Richard L ^a   Ingo, Carson ^a  

^a University of Illinois at Chicago   (United States)

Author keywords

anomalous diffusion; complex systems; entropy; fractional derivative; information theory

Indexed keywords

ANOMALOUS DIFFUSION; ELECTRICAL AND MECHANICAL PROPERTIES; EXPECTED IMPROVEMENTS; EXPERIMENTAL DATA; FRACTIONAL DERIVATIVES; FRACTIONAL ORDER; FRACTIONAL ORDER MODELS; GAUSSIAN DIFFUSION; GENERALIZED DIFFUSION EQUATION; HETEROGENEOUS MATERIALS; INTEGER ORDER; MEAN SQUARED ERROR; MULTISCALES; NON-GAUSSIAN; SPACE AND TIME; SPECTRAL ENTROPY;

ENTROPY; INFORMATION THEORY; LARGE SCALE SYSTEMS; MECHANICAL PROPERTIES; PARTIAL DIFFERENTIAL EQUATIONS;

DIFFUSION;

EID: 84864211112     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/CarpathianCC.2012.6228687     Document Type: Conference Paper

References (25)

1. West, B.J., M. Bologna, and P. Grigolini (2003). Physics of Fractal Operators. Springer, New York.
2. Zaslavsky, G.M. (2005). Hamiltonian Chaos & Fractional Dynamics. Oxford Univ. Press, Oxford, UK.
3. Caponetto, R., G. Dongola, L. Fortuna and I. Petras (2010). Fractional Order Systems: Modeling and Control Applications. World Scientific, Singapore
4. Klages, R., G. Radons, and I.M. Sokolov, (2008). Anomalous Transport: Foundations and Applications. Wiley-VDH, Weinheim, FRG.
5. Magin, R.L. (2006). Fractional Calculus in Bioengineering. Begell House, Connecticut.
6. Ortigueira, M.D. (2011). Fractional Calculus for Scientists and Engineers. Springer, New York.
7. Bruce, E.N. (2001). Biomedical Signal Processing and Signal Modeling. John Wiley, New York.
8. Keener, J., and J. Sneyd (2004). Mathematical Physiology. Springer, New York.
9. Shelhamer, M. (2007). Nonlinear Dynamics in Physiology: A State Space Approach. World Scientific, Singapore.
10. Grimnes, S. and O.G. Martinsen (2000). Bioimpedance and Bioelectricity Basics. Academic Press, San Diego.
11. Hilfer, R., editor, (2000). Applications of Fractional Calculus in Physics. World Scientific, Singapore.
12. Lakes, R.S. (1999). Viscoelastic Solids. CRC Press, Boca Raton, Florida.
13. Mandelbrot, B.B. (1977). The Fractal Geometry of Nature. W.H, Freeman, New York.
14. Bar-Yam, Y. (1997). Dynamics of Complex Systems. Perseus Books, Reading, Massachusetts.
15. Gleick, J. (2011). The Information. Pantheon, New York, New York.
16. Beck, C. (2009): Generalised information and entropy measures in physics, Contemporary Physics, 50:4, 495-510.
17. Viertio-Oja H, Maja V, Sarkela M, et al. (2004). Description of the Entropy algorithm as applied in the Datex-Ohmeda S/5 Entropy Module. Acta Anesthesiol Scand, 48, 154-61.
18. Liang, Z-P. (2000). Principles of Magnetic Resonance Imaging: A Signal Processing Approach, IEEE Press, New York.
19. Kimmich, R. (1997). NMR Tomography, Diffusometry, Reloxometry. Springer, Heidelberg, FRG.
20. Epstein, C.L. (2003). Introduction to the Mathematics of Medical Imaging. Pearson, Upper Saddle River, NJ.
21. Metzler, R. and J. Klafter (2000). The random walk's guide to anomalous diffusion: A fractional dynamics approach. Physics Reports, 339, 1-77.
22. Carpinteri, A. and F. Mainardi, editors, (1997). Fractals and Fractional Calculus in Continuum Mechanics CISM Courses and Lectures No. 378. Springer-Wien, New York.
23. Podlubny, I. (1999). Fractional Differential Equations. Academic Press, New York.
24. Samko, S.G., A.A. Kilbas and O.I. Marichev (1993). Fractional Integrals and Derivatives: Theory and Applications. Gordon and Breach, Switzerland.
25. Podlubny, I. (2009). The Mittag-Leffler function. http://www.mathworks. com/matlabcentral/fileexchange/8738.