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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.

Liquid crystal compounds are increasingly used as tunable materials for a plethora of microwave and millimeter-wave devices such as phase shifters and printed antennas. Modeling of liquid crystals mandate the solution of the directors’ field under an externally biased electric field which is governed by the Oseen-Frank free-energy functional. Minimization of this functional results in a nonlinear partial differential equation which is often simplified by applying the one-constant approximation, where the splay and bend elastic constants are set equal to each other. The effects of this approximation on the radiation characteristics of a microstrip patch antenna built on top of a liquid-crystal substrate are not well-studied. In this work, we adopt this approximation, along with neglecting the off-diagonal entries of the corresponding dielectric tensor, and compare the results with the original model. The reduced model results in a more computationally efficient algorithm for the characterization of liquid crystal materials; however, there are substantial discrepancies in the simulated antenna figures of merit for intermediate bias voltages.

Tunable devices and materials have always been extremely important for a variety of applications in the optical as well as the µ-wave and mm-wave bands. With the arrival of 5G communications networks and the ubiquitous use of wireless gadgets and applications ranging from smartphones to the implementation of the Internet of Things (IoT), the need for compact, versatile, and lightweight devices is imperative. Liquid Crystals (LCs) are anisotropic and tunable, and these properties make them an attractive proposition for use in portable devices and communication hubs. In this paper, three such LC-based devices operating in the 5GHz I 30GHz (5G) bands are presented: A frequency-agile patch antenna, a variable phase shifter, and a beam­ steerable leaky wave antenna. In all cases, tunability is achieved via the application of a low-strength external bias electric field. This affects the dielectric properties of the crystal by re-orienting its molecules, the macroscopic orientation of which is denoted by a unit vector called the director. The dielectric properties of the LC-cell are characterized by its relative permittivity tensor, which is a function of the directors' orientation. The latter is determined at every point of the cell by solving a coupled system of partial differential equations (PDEs) numerically. The obtained relative permittivity tensor is input into a high-frequency full­ wave electromagnetic simulator based on the finite-element method (FEM). Finally, the simulation results are analyzed and the performance and capabilities of the applications are discussed.

In this Letter, an investigation is performed on the utilization of nematic liquid crystal (NLC) cells in the design of leaky-wave antennas (LWAs) for millimeter-wave (mm-wave) radiation in order to dynamically control its beam scanning capability at a single frequency. A NLC compound is sandwiched between two single-sided copper-plated substrates allowing a traveling wave to be guided through a substrate-integrated waveguide. The tuning capabilities of the structure, based on the use of K15 or GT7-29001 as the middle layer, were evaluated for different biasing conditions demonstrating the associated dynamic scanning of the main beam. A quasi-periodic LWA was designed to operate in the 5G mm-wave band, thus supporting a fast-wave propagation with tunable phase constant and dynamic beam steering at a single frequency. The simulated results clearly illustrate a dynamic beam scanning range of 45° through the use of an external bias voltage ranging between 0 and 40 V. These results are quite promising creating a fertile ground for the utilization of NLCs in the design and fabrication of LWAs for 5G wireless communication networks.

A robust two-dimensional (2D) formulation for the electrical characterization of nematic liquid crystals (N-LCs) under low-frequency (LF) AC biasing conditions is proposed. The finite-difference (FD) method is first implemented to solve Poisson's equation in the domain of interest in order to obtain the governing LF electric field, which affects the local dielectric properties of the anisotropic material. Then, the nonlinear Euler–Lagrange partial differential equation (PDE), governing the orientation of the directors, is solved using one of three FD schemes with relaxation proposed in this paper. Once the N-LC layer is characterized, the average refractive index as a function of the x -coordinate is calculated assuming a normally incident monochromatic laser beam. The results are compared with published data in the literature obtained using a finite element method (FEM). Solution of the PDE governing the orientation of the directors in a non-uniform 2D electric field is obtained using either strong anchoring or soft anchoring. An investigation of the effects of boundary conditions on the average refractive index is presented.

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.

A Nematic Liquid Crystal (N-LC) compound may be injected into a cavity beneath a printed patch antenna to act as a tunable material whose dielectric properties are controlled by an externally applied electric field. The strength and direction of the applied low-frequency field affects the orientation of the LC molecules known as directors. The orientation of the directors determines the dielectric tensor entries of the LC compound which, in general, is anisotropic and lossy. The directors' tilt angle is governed by a Partial Differential Equation (PDE) which is obtained through minimization of the Oseen-Frank free-energy functional and solved using a Finite-Difference (FD) scheme. The profile of the directors' tilt angle underneath the patch follows a flattened sinusoidal shape along the normal-to-the-patch direction. In previous work by the authors, this non-uniform dielectric profile was averaged out, thus treating the LC substrate as a homogeneous but lossy material. In this paper, we are investigating the accuracy of this model as compared to a more realistic representation of the sinusoidal dielectric profile using multiple homogeneous layers. In addition, we are proposing ways to improve the existing design of the tunable LC patch antenna in order to obtain enhanced radiation characteristics such as gain and radiation efficiency.

In this work, we develop a High-Order Symmetric Interior Penalty (SIP) Discontinuous Galerkin (DG) Finite Element Method (FEM) to investigate convective flows in a rectangular cavity subject to both vertical and horizontal temperature gradients. The whole cavity is subject to gravity modulation (g-jitter), simulating a microgravity environment. The sensitivity of the bifurcation problem makes the use of a high-order accurate and efficient technique essential. Our method is validated by solving the plane-parallel flow problem and the results were found to be in good agreement with published results. The numerical method was designed to be easily extendable to even more complex flows.