TY - GEN

T1 - Spectral entropy in a fractional order model of anomalous diffusion

AU - Magin, Richard L.

AU - Ingo, Carson

PY - 2012

Y1 - 2012

N2 - Fractional order dynamic models of complex systems provide improved fits to experimental data with a reduced mean-squared error. The success of this approach, however, is dependent on the order of the derivatives included in the model. Fractional order models, for example, work better in describing the electrical and mechanical properties of multi-scale, heterogeneous materials than do integer order models. In order to estimate a measure of the expected improvement provided by fractional order models, we calculate the spectral entropy for anomalous diffusion as governed by the generalized diffusion equation in space and time. This fractional order representation of diffusion gives a minimum spectral entropy for Gaussian diffusion and predicts an increasing spectral entropy for non-Gaussian, or fractional, diffusion.

AB - Fractional order dynamic models of complex systems provide improved fits to experimental data with a reduced mean-squared error. The success of this approach, however, is dependent on the order of the derivatives included in the model. Fractional order models, for example, work better in describing the electrical and mechanical properties of multi-scale, heterogeneous materials than do integer order models. In order to estimate a measure of the expected improvement provided by fractional order models, we calculate the spectral entropy for anomalous diffusion as governed by the generalized diffusion equation in space and time. This fractional order representation of diffusion gives a minimum spectral entropy for Gaussian diffusion and predicts an increasing spectral entropy for non-Gaussian, or fractional, diffusion.

KW - anomalous diffusion

KW - complex systems

KW - entropy

KW - fractional derivative

KW - information theory

UR - http://www.scopus.com/inward/record.url?scp=84864211112&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84864211112&partnerID=8YFLogxK

U2 - 10.1109/CarpathianCC.2012.6228687

DO - 10.1109/CarpathianCC.2012.6228687

M3 - Conference contribution

AN - SCOPUS:84864211112

SN - 9781457718687

T3 - Proceedings of the 2012 13th International Carpathian Control Conference, ICCC 2012

SP - 458

EP - 463

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

T2 - 2012 13th International Carpathian Control Conference, ICCC 2012

Y2 - 28 May 2012 through 31 May 2012

ER -