Marios A. Christou

Numerical solutions of boundary value problems for variable coefficient generalized KdV equations using Lie symmetries

Abstract The exhaustive group classification of a class of variable coefficient generalized KdV equations is presented, which completes and enhances results existing in the literature. Lie symmetries are used for solving an initial and boundary value problem for certain subclasses of the above class. Namely, the found Lie symmetries are applied in order to reduce the initial and boundary value problem for the generalized KdV equations (which are PDEs) to an initial value problem for nonlinear third-order ODEs. The latter problem is solved numerically using the finite difference method. Numerical solutions are computed and the vast parameter space is studied.

Full-Wave Scattering From a Grooved Cylinder-Tipped Conducting Wedge

The problem of full-wave electromagnetic scattering from a cylinder-tipped conducting wedge with either a sectoral or annular groove is formulated using the mode-matching technique. The mode expansion of the sector involves ratios of Bessel functions with large order as the order is inversely proportional to the inner angle of the sector. An asymptotic expansion of Bessel functions with large orders is introduced in order to overcome the numerical difficulty involved using a regular series expansion. Numerical results indicate good agreement with data obtained using the finite element method (FEM).

Kawahara solitons in Boussinesq equations using a robust Christov-Galerkin spectral method

We develop a robust Christov-Galerkin spectral technique for computing interacting localized wave solutions of and fourth and sixth-order generalized wave equations. To this end, a special complete orthonormal system of functions in L^2(-~,~) is used whose rate of convergence is shown to be exponential for the cases under consideration. For the time-stepping, an implicit algorithm is chosen which makes use of the banded structure of the matrices representing the different spatial derivatives. As featuring examples, the head-on collision of solitary waves is investigated for a sixth-order generalized Boussinesq equation and a fourth-order Boussinesq type equation with a linear term. Its solutions comprise monotone shapes (sech-es) and damped oscillatory shapes (Kawahara solitons). The numerical results are validated against published data in the literature using the method of variational imbedding.

A Mode-Matching Approach to Electromagnetic Wave Propagation in Nematic Liquid Crystals

In this paper, we present a computationally efficient and highly accurate numerical method for the analysis of electromagnetic wave propagation in nematic liquid crystal (N-LC) cells. An iterative procedure is employed where the mode-matching technique (MMT) is used to solve the time-harmonic Maxwell equations inside the N-LC cell, whereas a finite-difference method (FDM) with relaxation is utilized to treat the nonlinear stationary Ginzburg-Landau equation for the director field. The angular distortion of the directors in the N-LC cell depends on the applied electric field which, in turn, affects the anisotropic dielectric properties of the medium. Numerical results are obtained for various values of the governing parameters. These simulations provide further insight into the Fréedericksz transition with special emphasis on resonances, bi-stability, hysteresis, phase shift between ordinary and extraordinary waves (birefringence), and soft anchoring effects. Obtained results are compared and validated against measurements and data published in the literature.

Interaction of solitons in a Boussinesq equation with dissipation

We investigate numerically an equation of Boussinesq type with square and cubic nonlinearity. In the model equation, dissipation is added and we investigate the physical properties of the modified problem. The technique applied here is the Christov spectral method in L 2(−∞, ∞). In previous works of the author, it was found that this technique was effective, accurate and computationally efficient for problems of this kind. Localized solutions are obtained numerically for the case of the moving frame which are used as initial conditions for the time-dependent problem. We investigate the propagation, head-on and overcome interaction of solitons. The issue of the phase shift is introduced and is been evaluated numerically.

DESIGN OF WIDEBAND, CIRCULARLY POLARIZED PATCH ANTENNAS FOR RFID APPLICATIONS IN THE FCC/ETSI UHF BANDS

Abstract—The primary objective of this paper is to design a high-gain, circularly polarized patch antenna suitable for Radio Frequency Identification (RFID) readers that operate in the FCC and ETSI bands (865–928MHz). These designs will be used in a healthcare application to provide tag identification for thousands of medicines stored on shelves inside a pharmaceutical warehouse. Consequently, it is important that these antennas provide sufficient electromagnetic coverage and polarization diversity in order to boost tag readability and minimize item identification errors. The proposed RFID reader antenna design begins with a single patch with truncated corners on air substrate in order to help us understand the effect of various geometrical parameters on critical antenna figures of merit. A stub is introduced in order to improve the impedance matching characteristics of the antenna. The wideband characteristic of the design, for both impedance matching and axial ratio, is achieved by a second truncated-corner patch antenna positioned on top of the first one. An optimum design is achieved by changing the heights of the main and parasitic patches, the size of the truncated corners, and the probe position. The final antenna designs are verified by comparing measurement and simulation results.

Far-Field Scattering From an Electrically Small Circular Aperture in a Conducting Screen

Analytical expressions for the electromagnetic scattering in the far-field zone of an electrically small circular aperture in an infinite conducting screen with zero thickness were derived based on a quasi-static model of the aperture. The governing modal distributions of the surface magnetic current density in the aperture are directly related to the radius of the aperture, the angle of incidence and the polarization of the incident plane wave. The problem was formulated using the equivalence principle and the definition of the electric vector potential. The corresponding scattered fields were expressed in terms of surface integrals over the area of the aperture. These integrals were evaluated analytically after introducing the far-field approximation for amplitude and phase terms. The results are valid for any observation point in the lower half plane of the conducting screen. Results based on the obtained analytical expressions are compared and validated against numerical results based on the exact field expressions in the form of surface integrals over the circular aperture. The comparisons illustrate both the validity and accuracy of the analytical field expressions derived.

Soft Polarization Diffraction Coefficient for a Conducting Cylinder-Tipped Wedge

TM, electromagnetic scattering from a perfectly conducting wedge with a cylindrical tip is formulated using a mode-matching technique. The eigenmode expansion is then written in a convenient form, where the total field is expressed as a superposition of a wedge-diffraction term based on the uniform theory of diffraction, a geometrical optics term, and a Correction Field term due to the presence of the cylindrical tip. The obtained diffraction coefficient can be easily incorporated into existing ray-tracing, high-frequency codes for the prediction of scattered fields from electrically large structures. The underlined formulation and obtained expressions are verified by comparing numerical results with the finite element method.

Closed-Form Expressions for the On-Axis Scattered Fields by a Subwavelength Circular Aperture in an Infinite Conducting Plane

Closed-form analytical expressions for the on-axis scattered fields by a subwavelength circular aperture in an infinite perfectly conducting plane were derived using a vector potential formulation and the equivalence principle. The final expressions are valid for the near-field, intermediate-field, and far-field zones. The underlined formulation is based on the equivalent quasi-static magnetic current distributions in the aperture, which were derived by Bethe and Bouwkamp in the mid 40’s and early 50’s. The resulting scattered-field integrals, which involve the free-space Green’s function, were evaluated analytically after introducing Taylor series expansion and using transformations. The final closed-form expressions of the scattered fields are given in terms of a recursion formula. Obtained results based on these closed-form expressions are in excellent agreement with data generated by a numerical integration scheme.

The Christov-Galerkin spectral method in complex arithmetics

We apply the Christov-Galerkin spectral method for the numerical investigation of the interaction of solitons in the Cubic Nonlinear Schrodinger Equation. The issues of convergence are addressed and an algorithm is devised for the application of the method. Results are obtained for the interaction of solitons with different phase velocities and different carrier frequencies. The interactions are shown to be elastic, save for the phase shifts. The latter are extracted from the numerical solution and discussed.