1,721,276 research outputs found
Fractional Derivative Based FDTD Modeling of Transient Wave Propagation in Havriliak-Negami Media
No full textIn this paper, an accurate finite-difference time-domain (FDTD) scheme for modeling time-domain wave propagation in arbitrary dispersive biological media is proposed. The main drawback occurring in the conventional FDTD implementation for such materials is the approximation of the fractional derivatives appearing in the relevent time-domain permittivity model. To overcome this problem, we propose a novel FDTD scheme based on the direct solution of the time-domain Maxwell equations by using the Riemann-Liouville operator for fractional differentiation. The feasibility of the proposed method is demonstrated by simulating the transient wave propagation in general bulk and slab dispersive materials with dielectric spectrum described by Cole-Cole, Cole-Davidson, and Havriliak-Negami formulas. In particular, the comparison between the numerical results and those evaluated by using an analytical method based on the Fourier transformation and the matrix formulation for lossy layered media demonstrates the accuracy of the proposed FDTD scheme in a broadband frequency range
Fractional Bernoulli and Euler Numbers and Related Fractional Polynomials—A Symmetry in Number Theory
No full textA novel ultrawideband FDTD numerical modeling of ground penetrating radar on arbitrary dispersive soils
No full textA novel two-dimensional (2-D) finite-difference timedomain algorithm for modeling ultrawideband pulse propagation in arbitrary dispersive soils is presented. The soil dispersion is modeled by general power law series representation, accounting for multiple higher order dispersive relaxation processes and ohmic losses, and incorporated into the FDTD scheme by using the fractional derivative operators. The dispersive soil parameters are obtained by fitting the reported experimental data. Moreover, dedicated uniaxial perfectly matched layer for matching dispersive media are derived and implemented in combination with the basic time-marching scheme. Examples are given to verify the numerical solution and demonstrate its applications. The proposed technique features a significantly enhanced accuracy in the solution of complex electromagnetic propagation problems typically encountered in geoscience applications
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