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In previous works, it was shown that the propagation of magnetic spin waves in thin films can be approximated by a nonlinear Schrodinger-type equation. The formulation begins with the magnetostatic equations (Gauss and Ampere’s laws of magnetism) and the Landau–Lifshitz equation. The solution of this system is a potential function whose dimensionless amplitude is the solution of a nonlinear Schrodinger. In the current work, we are demonstrating an efficient infinite series solution using the Christov functions. This is the first time the functions are used in problems involving complex arithmetics. The solutions of the time-independent and time-dependent problems are given in complex series form.

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.

A mathematical model is proposed to investigate the effect of microgravity on biofilm growth. We examine the case of biofilm suspended in a quiescent aqueous nutrient solution contained in a rectangular tank. The bacterial colony is assumed to follow logistic growth whereas nutrient absorption is assumed to follow Monod kinetics. The problem is modeled by a coupled system of nonlinear partial differential equations in two spatial dimensions solved using the Discontinuous Galerkin Finite Element method. Nutrient and biofilm concentrations are computed in microgravity and normal gravity conditions. A preliminary quantitative relationship between the biofilm concentration and the gravity field intensity is derived.

A nematic liquid crystal (N-LC) cell is used as a substrate to a microstrip patch antenna in order to control its resonant frequency through the use of a DC or low-frequency AC bias voltage. The dielectric tensor properties of the liquid crystal (LC) are dependent on the orientation of the LC molecules, called the directors. The directors' tilt angle is controlled by the amplitude of an externally applied electric field. A finite-difference (FD) scheme with relaxation is formulated in order to solve the highly nonlinear partial differential equation (PDE) that models the directors' tilt angle in the LC. The problem of solving for the directors' field is coupled to an electrostatic boundary value problem (BVP) in a nonhomogeneous anisotropic medium. The orientation of the directors determines the constitutive parameters of the material. The HFSS is then utilized to obtain the radiation characteristics of the antenna under various bias conditions. Comparisons with measurements are provided in order to validate the proposed numerical approach and illustrate the potential use of LC's as tunable materials in microwave and millimeter-wave frequencies.

A frequency-agile microstrip patch antenna printed on a biased nematic liquid crystal (N-LC) substrate is accurately modelled. The dielectric properties of the N-LC are controlled through the strength of the bias voltage. The model is based on the solution of Poisson's equation coupled to a nonlinear partial differential equation (PDE) describing the orientation of the directors in a non-homogeneous electric field. The coupled problem was solved using an iterative finite difference (FD) scheme. The obtained numerical results are compared and verified against measurements already published in the literature.

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 Freedericksz 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.

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.