Extending Maxwell's equations for dielectric materials using analytical principles from viscoelasticity based on the fractional calculus




Wharmby, Andrew William

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Existing fractional calculus models having a non-empirical basis used to describe constitutive relationships between stress and strain in viscoelastic materials are modified to employ all orders of fractional derivatives between zero and one. Parallels between viscoelastic and dielectric theory are drawn so that these modified fractional calculus based models for viscoelastic materials may be used to describe relationships between electric flux density and electric field intensity in dielectric materials. The resulting fractional calculus based dielectric relaxation model is tested using existing complex permittivity data in the radio-frequency bandwidth of a wide variety of homogeneous materials. The consequences that the application of this newly developed fractional calculus based dielectric relaxation model has on Maxwell's equations are also examined through the effects of dielectric dissipation and dispersion.


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Dielectric Relaxation, Dispersion, Fractional Calculus, Generalized Derivatives, Permittivity, Viscoelasticity



Biomedical Engineering