Numerical simulations for the Toda lattices Hamiltonian system : Higher order symplectic illustrative perspective

In this paper we apply some higher order symplectic numerical methods to analyze the dynamics of 3-site Toda lattices (reduced to relative coordinates). We present benchmark numerical simulations that has been generated from the HOMsPY (Higher Order Methods in Python) library. These results provide detailed information of the underlying Hamiltonian system. These numerical simulations reinforce the claim that the symplectic numerical methods are highly accurate qualitatively and quantitatively when applied not only to Hamiltonian of the Toda lattices, but also to other physical models. Excepting exactly integrable models, these symplectic numerical schemes are superior, efficient, energy preserving and suitable for a long time integrations, unlike standard non-symplectic numerical methods which lacks preservation of energy (and other constants of motion, when such exist).publishedVersio

Numerical comparison of constant and variable fluid properties for MHD flow over a nonlinearly stretching sheet

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Exploiting Authentic Materials for Developing Writing Skills at Secondary Level

Writing is an extremely complex process; there are various ways, means and techniques involved in teaching writing. The present study intends to scrutinize the efficacy of authentic materials for enhancing writing skills of the second language assimilators at secondary level in Pakistan. Authentic materials are very interesting, absorbing and motivating. Change and variety is something very important for human development and upbringing. Authentic materials can serve this purpose very well. Moreover, authentic materials are diverse in nature and have a variety of things to offer. They have been popular for last decade or so and are a very impressive technique. There is a great variety of materials available in newspapers, broadcasts, magazines etc in the form of advertisements, cartoons, bulletins, horoscopes, weather reports etc. Exploited appropriately, they can be of great help to improve students writing skills. Authentic materials can even more be useful to those learners who intend to go to a foreign country for higher education. Such materials will acquaint them not only with the language but also with the culture and value system of the country concerned. Authentic materials, of course, hold great promise for those who are in the process of learning and improving writing skills. The use of authentic materials creates a lot of interest in the learners and they do not feel bored and tired. There comes a big part of charming and attractive outside world into the classroom. Authentic materials reduce the dullness of specially contrived text material. It makes significant contributions toward meeting the learning objective of a programme. Authentic materials are varied and very flexible in nature, which allow free play to the students and never restrict them at a place. Key words: Authentic materials, writing skills, second languag

Unsteady MHD Bionanofluid Flow in a Porous Medium with Thermal Radiation near a Stretching/Shrinking Sheet

This research aims at providing the theoretical effects of the unsteady MHD stagnation point flow of heat and mass transfer across a stretching and shrinking surface in a porous medium including internal heat generation/absorption, thermal radiation, and chemical reaction. The fundamental principles of the similarity transformations are applied to the governing partial differential equations (PDEs) that lead to ordinary differential equations (ODEs). The transformed ODEs are numerically solved by the shooting algorithm implemented in MATLAB, and verification is done from MATLAB built-in solver bvp4c. The numerical data produced for the skin friction coefficient, the local Nusselt number, and the local Sherwood number are compared with the available result and found to be in a close agreement. The impact of involved physical parameters on velocity, temperature, concentration, and density of motile microorganisms profiles is scrutinized through graphs. It is analyzed that the skin friction coefficient enhances with increasing values of an unsteady parameter A, magnetic parameter M, and porosity parameter Kp. In addition, we observe that the density of a motile microorganisms profile enhances larger values of the bioconvection Lewis number Lb and Peclet number Pe and decreases with the increasing values of an unsteady parameter A.publishedVersio

Pedagogical Practices of English Language Student Teachers during the Practicum in Pakistan

Along with the government documents, a number of authors have showed concern on the quality of teachers being produced by the teacher education institutions and have called for reforms in teacher education programmes and teacher preparation to improve quality of teaching in Pakistan. I conducted this study to analyze the pedagogical practices of a group of English language student teachers and support provided to them during the practicum in Pakistan. Another focus of analysis was conceptualization of teacher learning by the practicum triad. The study has fit well into the research agenda on teacher cognition and teacher education and contributes to improve the teacher preparation programmes through improvement of the practicum. Methodologically, the study was qualitative and used case study approach. I selected four student teachers, two supervising teachers, one course teacher, four cooperating teachers and the head of the department as participants in my study. The student teachers did six weeks practicum in public secondary schools. I generated data mainly through classroom observations of and interviews with the student teachers and other participants of the study. In addition, I also used documents such as lesson plans, reflective journals and the textbooks of English for grades 9 and 10. The purpose of these documents was to provide additional data needed for field notes and interviews. I analyzed data through thematic analysis and reported the findings individually for each student teacher. In relation to the existing literature, my study has suggested that the school and the contextual factors exert strong influence on the teaching practices of the student teachers. It has also suggested that in the contexts and situations where student teachers are not appropriately supervised and supported, their teaching practices would likely to be based on their previous learning experiences as learners of English, hence, it would minimize the impact of the teacher education programmes. In relation to conceptualization of teacher learning by the practicum triad, the study found contradictions about the notion of what constitutes teaching and learning to teach. The contradictions were held strongly by the student teachers, supervising teachers and the head of the department and no explicit and sustained effort was made by the teacher education programme to raise awareness of beliefs about learning through dialogue and reflection. My study is the first of its kind to provide evidence of what occurred during the practicum in my context. As the practicum is the only opportunity for the student teachers to enact their learning from the university based course work, any reforms in teacher preparation programmes without improving and re-organizing the practicum are less likely to succeed

A Simplified Finite Difference Method (SFDM) Solution via Tridiagonal Matrix Algorithm for MHD Radiating Nanofluid Flow over a Slippery Sheet Submerged in a Permeable Medium

In this paper, we turn our attention to the mathematical model to simulate steady, hydromagnetic, and radiating nanofluid flow past an exponentially stretching sheet. A numerical modeling technique, simplified finite difference method (SFDM), has been applied to the flow model that is based on partial differential equations (PDEs) which is converted to nonlinear ordinary differential equations (ODEs) by using similarity variables. For the resultant algebraic system, the SFDM uses the tridiagonal matrix algorithm (TDMA) in computing the solution. The effectiveness of numerical scheme is verified by comparing it with solution from the literature. However, where reference solution is not available, one can compare its numerical results with the results of MATLAB built-in package bvp4c. The velocity, temperature, and concentration profiles are graphed for a variety of parameters, i.e., Prandtl number, Grashof number, thermal radiation parameter, Darcy number, Eckert number, Lewis number, and Brownian and thermophoresis parameters. The significant effects of the associated emerging thermophysical parameters, i.e., skin friction coefficient, local Nusselt number, and local Sherwood numbers are analyzed and discussed in detail. Numerical results are compared from the available literature and found a close agreement with each other. It is found that the Eckert number upsurges the velocity curve. However, the dimensionless temperature declines with the Grashof number. It is also shown that the SFDM gives good results when compared with the results obtained from bvp4c and results from the literature.publishedVersio

The impact of variable fluid properties on hydromagnetic boundary layer and heat transfer flows over an exponentially stretching sheet

This paper put forward an analysis of variable fluid properties and their impact on hydromagnetic boundary and thermal layers in a quiescent fluid which is developed due to the exponentially stretching sheet. The viscous incompressible fluid has been set into motion due to aforementioned sheet. We assume that the viscosity and the thermal conductivity of the Newtonian fluid are temperature dependent. The governing boundary layer equations containing continuity, momentum and energy equations are coupled and nonlinear in nature, thereby, cannot be solvable easily by using analytical methods. Since the general boundary layer equations admits a similarity solutions, thus a generalized Howarth-Dorodnitsyn transformations have been exploited for the set-up of a coupled nonlinear ODEs. These transformed ODEs are solved numerically by a shooting method and is verified from MATLAB built-in collocation solver bvp4c for different parameters appearing in the work. We show results graphically and in a tabulated form for a constant and a variable fluid properties. We find that the temperature dependent variable viscosity and a thermal conductivity influence a velocity and a temperature profiles. We show that the thermal boundary layer decreases for constant variable fluid properties and increases for variable fluid propertiesThe impact of variable fluid properties on hydromagnetic boundary layer and heat transfer flows over an exponentially stretching sheetpublishedVersio

Insight into the dynamics of electro-magneto-hydrodynamic fluid flow past a sheet using the Galerkin finite element method: Effects of variable magnetic and electric fields

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U.S. Interests in South Asia and Its Impacts on Regional Stability

United States has a significant involvement in the regional affairs of South Asia since 1947 and this region remained an area of interest and priority near West due to its momentous geostrategic and geopolitical importance. United States has forged effective bilateral bonds with countries across South Asia, however, its policy has regularly concentrated on the immediate over the enduring. United States policy toward the region had seen many ups and downs and had segments of successes and missed opportunities. The U.S. has to adopt a renewed policy towards South Asian states if it needs to forge interactions with this region built on mutual interests and trust, although preserving an enduring strategic approach towards Asia, so that both the U.S. and the South Asian countries will be better prepared to deal future uncertainties