Teachers’ Real and Perceived of ICTs Supported-Situation for Mathematics Teaching and Learning

Purpose of this research was to gain information related to the real and perceived ICT Infrastructures, Facilities, and Resources in Bojonegara Sub District, Indonesia. This article emphasize the publication of this information because it is needed for implementation of technology-based mathematics teaching and learning. The method used was survey. Instruments of survey were questionnaires, unstructured interview guideline, and handycam. During the survey, total of 220 questionnaire packages were distributed to teachers, however only 119 (response rate 54.1%) of them were filled and returned. A total of 12 teachers were interviewed, with five of these interviews were video recorded. Several head masters welcomed and allowed researcher to visit their schools and make documentation of ICT Infrastructures, facilities, and resources, while the others did not allow the researcher to do that. Based on survey, many important findings have been discovered. It is suggested that the Teachers-Centered Learning with Technology is the most appropriate method of technology-based learning to be implemented

Two-color, nonlocal vector solitary waves with angular momentum in nematic liquid crystals

The propagation and interaction of two solitary waves with angular momentum in bulk nematic liquid crystals, termed nematicons, have been studied in the nonlocal limit. These two spinning solitary waves are based on two different wavelengths of light and so are referred to as two-color nematicons. Under suitable boundary conditions, the two nematicons can form a bound state in which they spin about each other. This bound state is found to be stable to the emission of diffractive radiation as the nematicons evolve. In addition this bound state shows walk-off due to dispersion. Using an approximate method based on the use of suitable trial functions in an averaged Lagrangian of the two-color nematicon equations, modulation equations for the evolution of the individual nematicons are derived. These modulation equations are extended to include the diffractive radiation shed as the nematicons evolve. Excellent agreement is found between solutions of the modulation equations and full numerical solutions of the nematicon equations. The shed diffractive radiation is found to play a much lesser role in the nonlocal limit than in the local limit

Refraction of nonlinear beams by localized refractive index changes in nematic liquid crystals

The propagation of solitary waves in nematic liquid crystals in the presence of localized nonuniformities is studied. These nonuniformities can be caused by external electric fields, other light beams, or any other mechanism which results in a modified director orientation in a localized region of the liquid-crystal cell. The net effect is that the solitary wave undergoes refraction and trajectory bending. A general modulation theory for this refraction is developed, and particular cases of circular, elliptical, and rectangular perturbations are considered. The results are found to be in excellent agreement with numerical solutions

Propagation of optical spatial solitary waves in bias-free nematic-liquid-crystal cells

The propagation of a bulk optical solitary wave in a rectangular cell filled with a nematic liquid crystal—a nematicon—is mathematically modelled. In order to overcome the Freédricksz threshold the cell walls are rubbed to pretilt the nematic. A modulation theory, based on a Lagrangian formulation, is developed for the (2+1)-dimensional propagation of the solitary wave beam down the cell. This modulation theory is based on two different formulations of the director distribution. The relative advantages and disadvantages of these two methods are discussed. A previously unexplored method based on images is found to possess significant advantages. Excellent agreement with full numerical solutions of the nematicon equations is found for both methods. Finally, the implications of the results obtained for some widely used approximations to the nematicon equations are discussed, particularly their use in comparisons with experimental results

Soliton Steering by Longitudinal Modulation of the Nonlinearity in Waveguide Arrays

We show how discrete solitary waves in one and two-dimensional waveguide arrays can be steered across the lattice via the introduction of a longitudinal periodic modulation of the nonlinear response. Through parametric energy transfer from the modulation to the solitary wave, the latter can increase its width and overcome the Peierls-Nabarro potential to propagate freely

Elliptical optical solitary waves in a finite nematic liquid crystal cell

2015 Elsevier B.V. The addition of orbital angular momentum has been previously shown to stabilise beams of elliptic cross-section. In this article the evolution of such elliptical beams is explored through the use of an approximate methodology based on modulation theory. An approximate method is used as the equations that govern the optical system have no known exact solitary wave solution. This study brings to light two distinct phases in the evolution of a beam carrying orbital angular momentum. The two phases are determined by the shedding of radiation in the form of mass loss and angular momentum loss. The first phase is dominated by the shedding of angular momentum loss through spiral waves. The second phase is dominated by diffractive radiation loss which drives the elliptical solitary wave to a steady state. In addition to modulation theory, the chirp variational method is also used to study this evolution. Due to the significant role radiation loss plays in the evolution of an elliptical solitary wave, an attempt is made to couple radiation loss to the chirp variational method. This attempt furthers understanding as to why radiation loss cannot be coupled to the chirp method. The basic reason for this is that there is no consistent manner to match the chirp trial function to the generated radiating waves which is uniformly valid in time. Finally, full numerical solutions of the governing equations are compared with solutions obtained using the various variational approximations, with the best agreement achieved with modulation theory due to its ability to include both mass and angular momentum losses to shed diffractive radiation

Soliton evolution and radiation loss for the sine-Gordon equation

An approximate method for describing the evolution of solitonlike initial conditions to solitons for the sine-Gordon equation is developed. This method is based on using a solitonlike pulse with variable parameters in an averaged Lagrangian for the sine-Gordon equation. This averaged Lagrangian is then used to determine ordinary differential equations governing the evolution of the pulse parameters. The pulse evolves to a steady soliton by shedding dispersive radiation. The effect of this radiation is determined by examining the linearized sine-Gordon equation and loss terms are added to the variational equations derived from the averaged Lagrangian by using the momentum and energy conservation equations for the sine-Gordon equation. Solutions of the resulting approximate equations, which include loss, are found to be in good agreement with full numerical solutions of the sine-Gordon equation