§ Develop the Monte Carlo Potts model to investigate microstructural evolution of polycrystalline materials. The emphasis is on coarsening of two-phase systems. In particular, the model is applied to investigate the microstructural evolution in a two-phase system in which both phase grow simultaneously. It is shown that a two-phase system with initially small grains eventually reaches an asymptotic regime in which grain growth in both phases is coupled due to Zener pinning and obeys a power-law scaling relationship. This conclusion is valid in a broad parameter range and is in agreement with theoretical predictions and laboratory experiments.

§ The Monte Carlo Potts model is shown to be successful in simulating the degeneration of lamellar structures formed upon eutectoid phase transformations. The Monte Carlo Potts model is developed to study microstructural evolution in three-phase polycrystalline materials. The Monte Carlo Potts model is developed to simulate grain growth in liquid phase sintered materials. The geometric metrics such as grain size distribution is considered; in addition, the topological metrics such as number of grain sides is considered. The Monte Carlo Potts model is developed to simulate grain size distributions in two-phase polycrystalline materials. Further, the Monte Carlo Potts model is adapted to simulate Ostwald ripening controlled by long-range diffusion in two- phase polycrystalline materials.

§ The Monte Carlo Potts model will be developed to study microstructural evolution in two-phase polycrystalline materials subjected to mechanical stress. The Monte Carlo Potts model will be developed to study invar alloys. The Monte Carlo Potts model will be developed to study Ostwald ripening in two-phase polycrystalline materials.§ Investigate thermal-stress effect on the optical performance of nonlinear symmetrical sensor. The dispersion equation and thermal-stress sensitivity are analytically derived and plotted numerically. It is shown that thermal sensitivity of sensor can be controlled by tuning the core size, by changing loading materials, and by carefully selecting the materials.

§ Explore propagation of light through the proposed structure of the optical waveguide. Different factor has been taken into account to study waveguide structure. As an example, the behavior of electromagnetic field in a medium possessing a dielectric constant which is sinusoidal stratified along one coordinate sandwiched between a nonlinear cladding and a linear dielectric substrate. A first area of application is concerned with TE wave propagation through a compressible medium which is influenced by acoustic or other mechanical wave. As an example, the results are applicable to acoustically modulated plasma media in range of frequencies above plasma frequency. A second area of application regards the stratified medium as a first step in analysis of a sinusoidal modulated dielectric slab antenna. The power has been calculated by using Mathieu equation and using perturbation methods (Whittaker’s Method, and Multiple Scale Method). A simple numerical method has also been applied based on Mathieu function approach. Numerical results have been presented, we found that the approximate techniques are much easier and faster, and the considered wave guide structure represents a band reject filter.§ Present the application of MTMs in the structure of the optical waveguides to realize integrated non reciprocal devices like isolators. The role of the MTMs parameters on the guided dispersion characteristic of the waveguide isolator is investigated by introducing several sets of negative permittivity and permeability with their products kept the same.

- Polarization rotation is studied in optical fibers where the frame of reference in which polarization rotation in twisted optical fibers is described to be compatible with the modeling of fiber sensor applications. A formulation of the polarization evolution in a twisted optical and birefringent fiber, which is based on a laboratory coordinate system, is introduced. Coupled mode theory using the fundamental modes of a single mode fiber as a basis is used. The results are also experimentally verified.
- Nonlinear Transmission lines (NTL) have attracted attention for microwave application such as filter, amplifier, signal reshaping, and ADC. A nonlinear transmission is loaded with resonant tunneling diode to be suitable for microwave A/D conversion. Theoretical derivations of the coupled equations, which represent the NLT system using simple circuits’ theory, are performed. Then numerical calculations are performed using OrCad programs.
- Nonlinear transmission lines (NLTL) that consist of coplanar waveguide periodically loaded with resonant tunnel diode are capable of shaping signal waveforms during transmission. Such system is the basis of very interesting microwave signal generation circuits and it has many applications in electronics. Pspice is used to model analog to digital converter by generating short electrical pulses on a nonlinear transmission line. Nonlinear transmission line is realized as electrical lattice with
*N*electrical cells coupled by inductor and resistor in series. Each cell consists of a resonant tunnel diode in parallel with both resistor and capacitor. Attenuation represented by the resistor is cancelled by nonlinear effect.

§ Use MatLab simulation to study the effect of the various parameters on solar photovoltaic (PV) performance. § Introducing a new photonic structure, which is composed of alternating lamellae of MTMs and Dielectric to extend the applications of photonic crystals (PCs).§ Use computing approach based on data mining techniques to study one of the business fields to produce a business technique that helps in extraction the association rules for the incubated startup companies.** **