Related papers: Fractional Derivative Modification of a Drude Mode…
Propagation, transmission and reflection properties of linearly polarized plane waves and arbitrarily short electromagnetic pulses in one-dimensional dispersionless dielectric media possessing an arbitrary space-time dependence of the…
First, we make a revision of the up-to-date Passive Scalar Fields properties: also, the refractive index is among them. Afterwards, we formulated the properties that make the family of `isotropic' fractional Brownian motion (with parameter…
In the present work, we investigate the potential of fractional derivatives to model atmospheric dispersion of pollutants. We propose simple fractional differential equation models for the steady state spatial distribution of concentration…
In this work we use tempered fractional advection-diffusion equations to model the dispersive transport in disordered materials. A numerical method is derived to approximate the solution of such differential models and we prove that it is…
This paper develops a fractional stochastic partial differential equation (SPDE) to model the evolution of a random tangent vector field on the unit sphere. The SPDE is governed by a fractional diffusion operator to model the L\'{e}vy-type…
The Drude-Smith model successfully describes the frequency and phase-resolved electrical conductivity data for a surprisingly broad range of systems, especially in the terahertz region. Still, its interpretation is unclear since its…
A fractional derivative is a temporally nonlocal operation which is computationally intensive due to inclusion of the accumulated contribution of function values at past times. In order to lessen the computational load while maintaining the…
Accurate spectrum prediction is crucial for dynamic spectrum access (DSA) and resource allocation. However, due to the unique characteristics of spectrum data, existing methods based on the time or frequency domain often struggle to…
We consider a semi-infinite dielectric with multiple spatially dispersive resonances in the susceptibility. The effect of the boundary is described by an arbitrary reflection coefficient for polarization waves in the material at the…
In this note we analyse the propagation of a small density perturbation in a one-dimensional compressible fluid by means of fractional calculus modelling, replacing thus the ordinary time derivative with the Caputo fractional derivative in…
A parallel dispersive finite-difference time-domain (FDTD) method for the modeling of three-dimensional (3-D) electromagnetic cloaking structures is presented in this paper. The permittivity and permeability of the cloak are mapped to the…
We investigate in this chapter the mathematical models for electromagnetic wave propagation in dispersive isotropic passive linear media for which the dielectric permittivity $\varepsilon$ and magnetic permeability $\mu$ depend on the…
Tracer diffusion and hydrodynamic dispersion in two-dimensional fractures with self-affine roughness is studied by analytic and numerical methods. Numerical simulations were performed via the lattice-Boltzmann approach, using a new boundary…
This study explores the use of fractional calculus as a possible tool to model wave propagation in complex, heterogeneous media. We illustrate the methodology by focusing on elastic wave propagation in a one-dimensional periodic rod. The…
This paper is devoted to a numerical analysis of a fractional viscoelastic wave propagation model that generalizes the fractional Maxwell model and the fractional Zener model. First, we convert the model problem into a velocity type…
We present and review several models of fractional viscous stresses from the literature, which generalise classical viscosity theories to fractional orders by replacing total strain derivatives in time with fractional time derivatives. We…
With the discovery of new superconductors there was a running to find the justifications for the new properties found in these materials. In order to describe these new effects some theories were adapted and some others have been tried. In…
This study makes the first attempt to use the 2/3-order fractional Laplacian modeling of enhanced diffusing movements of random turbulent particle resulting from nonlinear inertial interactions. A combined effect of the inertial…
Fractional diffusion has become a fundamental tool for the modeling of multiscale and heterogeneous phenomena. However, due to its nonlocal nature, its accurate numerical approximation is delicate. We survey our research program on the…
Wave turbulence in a thin elastic plate is experimentally investigated. By using a Fourier transform profilometry technique, the deformation field of the plate surface is measured simultaneously in time and space. This enables us to compute…