# Special Issue \"Numerical and Analytical Methods in Electromagnetics\"
###### Abstract  
We present a new method for the calculation of the physical properties of  
detection method among researchers in the field. [PERSON]'s equations are transformed via the relationship between the diffusion field and fictitious wave field. The fractional order Cole-Cole model is introduced into the fictitious wave field and the final solution is obtained by using the finite difference time domain (FDTD) method. Finally, an integral transformation is applied to obtain the calculation results in the actual diffusion field form. Moreover, electromagnetic properties of composites filled with carbon nano tubes (CNTs) are modeled by [PERSON] et al. in [3]. The total conductivity of the composite is governed by the inter-tube tunneling equation. In this framework, the direction for the conductivity computation is selected and the nanotubes near the initial and final boarders are collected. The Dijkstra algorithm is used to trace the paths of minimal resistance between the initial and final tubes, and, finally, conductivity is computed in a highly accurate way. Electromagnetic wave amplification by non-linear wave mixing is targeted in [4] by [PERSON] and [PERSON]. Suitable numerical analysis is performed that provides evidence for the high-gain amplification of a low-power stimulus wave, via intense pump waves of ultra-short duration, inside a several-micrometers-long micro-resonator, by maximizing the electric energy density of the pump wave in the resonator. In order to perform the optimization of the stimulus wave magnitude at a given wave frequency, an efficient optimization procedure, namely the quasi-Newton Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm is implemented. Although analytical solutions are rare in real-world problems, efficient approximations are still applicable to important devices. Such a case is a birdcage radio frequency coil used in nuclear magnetic resonance (NMR) imaging applications, as demonstrated in [5] by [PERSON] et al. A novel analytical solution for the characteristic properties of the coil is derived via equivalent circuit modeling and T-matrix theory, facilitating and efficient design strategy. Scattering analysis is another important aspect of applied electromagnetics which is in need of powerful mathematical tools. In [6], [PERSON] et al. describe how the method of auxiliary sources (MAS) can be optimized for cylindrical scattering geometries containing curvilinear wedges. Instead of retaining a conformal auxiliary surface, which is customary in MAS, auxiliary sources are locally positioned close to the wedge tips with variable density. Numerical results clearly show the reduction of the calculation error and the improvement in the accuracy of the radar cross section. An enjoyable application of numerical techniques to robotic system design is described in [7]: a coil gun found in soccer ball launchers is analyzed and designed by [PERSON] et al. A coupled electromagnetic, electrical and mechanical model is used to simulate the performance of reluctance coil guns. Four different mechatronic coupled models thereof are proposed, and for each one of these the electromagnetic behavior is investigated on the basis of a finite element (FEM) software tool, whereas commercial software was used for modeling the electrical and mechanical parts. Comparison of simplified analytical models based on the principles of superposition and reflections and the finite element method (FEM) was performed by [PERSON] and [PERSON] in [8], where the modeling of electric power lines is facilitated. The target of the analysis is an actual high-voltage AC, double-circuit 400 kV overhead power transmission line that runs from the city of Elk, Poland, to the city of Alytus, Lithuania. Integral equation methods could by no means be absent from this Special Issue. Indeed, an integral formulation was used in [9] by [PERSON] and [PERSON] to model thin surfaces coupled with an external circuit.