علی اکبر ناطق۔۔۔سوانح و تخلیقات
علی اکبر ناطق پاکستانی ناول نگار ،افسانہ نگار، شاعر اور نقاد ہیں۔عصری اردو ادب میں ’علی اکبر ناطق‘‘ ان شخصیات میں نمایاں مقام رکھتے ہیں جو پچھلی دہائی میں اردو ادب کے افق پر ابھر کر سامنے آئی ہیں۔ادب کی بہت ساری جہتوں میں مصنف مذکور نے اپنی قسمت آزمائی ہے اور وہ اس میں کامیاب دکھائی دیتے ہیں۔شاعری ،ناول نگاری،افسانہ نگاری اور تنقید مصنف کے اہم میدان ہیں شاعری میں ان کی پانچ کتابیں ہیں’’سبز بستیوں کے غزال ‘‘غزلیات کا مجموعہ جبکہ’’ بے یقین بستیوں میں‘‘،’’یاقوت کے ورق ‘‘،’’سر منڈل کا راجہ ‘‘،’’ریشم بننا کھیل نہیں‘‘ ان منظومات کے مجموعے ہیں۔حال ہی میں انہوں نے اپنے ادبی سفر میں ایک اور کتاب کا اضافہ کیا ہے جس کا نام’’سفیر لیلی‘‘ہے ،اس میں نظمیں اور غزلیں دونو ں شامل ہیں’’ریشم بننا کھیل نہیں‘‘ کتاب میں مصنف مذکور نے اپنی تینوں کتابوں (نظموں) کے مجموعے کو ایک ہی جلد میں شائع کروایا ہے جو سانجھ پبلی کیشنز سے 2019 ء میں شائع ہوئی۔تینوں مجموعوں کے دیباچے بھی اس کتاب میں ایک ساتھ شائع کیے گئے ہیں اس کے علاوہ دو افسانوی مجموعے اور ناول نگاری میں ناطق کے ناول’’نولکھی کوٹھی ‘‘اور ’’کماری والا‘‘ ادبی دنیا میں اپنا مقامپیدا کر چکے ہیں۔محمد حسین آزاد کا مرقع لکھنے کے ساتھ ساتھ تنقید پر بھی ایک کتاب ’’ہئیت شعر ‘‘شائع ہو چکی ہے ۔مصنف کی کچھ کتابیں ابھی غیر مطبوعہ ہیں۔ہر وہ مصنف جو ادب کی مختلف اصناف پر کام کر چکا ہو اور صفِ اول کا ادیب جانا جائے تو اس کی ادبی جہات کا مطالعہ اپنی جگہ نہایت اہمیت کا حامل ہے۔
To develop in children a broad range of skills, including the problem solving, interpersonal and communication skills that are essential for successful living in a rapidly changing society. The curriculum encourages student initiative by providing children with materials, equipment, and time to pursue activities they choose. At the same time, it provides teachers with a framework for guiding children’s independent activities toward sequenced learning goals. There are seven specific types of learning styles. Visual learners prefer to learn mathematics through pictures, diagrams etc. A well-balanced intelligent child is able to develop all the types of learning styles. The students have to understand and accept their type of learning style earlier so that learning becomes easier and less stressful in the future. But it is important to train and practice the other types of learning styles so that the children can utilize them as effectively as possible. The teacher plays a key role in instructional activities by selecting appropriate, developmentally sequenced material and by encouraging children to adopt an active problem-solving approach to learning. This teacher-student interaction teachers helping students achieve developmentally sequenced goals while also encouraging them to set many of their own goals uniquely distinguishes the High/Scope Curriculum from direct-instruction and child-centered curricula (high/Scope Educational Research Foundation, 1989). Teachers keep notes about significant behaviors, changes, statements, and things that help them better understand a child’s way of thinking and learning. Teachers use two mechanisms to help them collect data: the key experiences note form and a portfolio. The High/Scope Child Observation Record is also used to assess children’s development. According to Ronald Barnett, learning may or may not take place when a subject is taught. While discussing this point he has presented two contrasting images of quality. They are institutional performance and student experience, student learning or student achievement. The teacher in his opinion is central to higher education. Teaching may be able to improve the quality of student’s learning but the teacher should remind himself that it may also impair the quality of student’s learning. This is partly because student’s learning strategies vary under two polarities, one between deep and surface understanding and the other between holistic and atomistic understanding of their learning experiences. He goes on to add that for a student, learning has three distinct aspects: learning style, motivation and curriculum demands. Therefore teachers have to pursue, beyond teaching strategies to enable their students to attain certain specific skills.
Numerical Solution of Incompressible Viscous Flow Problems Using High-order Schemes Numerical solution of the Navier-Stokes equations that describe incompressible viscous fluids has been a very active research field due to the rapid development of computational techniques and availability of high speed computers. It has motivated a very large number of researchers whose work provide an invaluable source of solution methods and test problems. Numerous computational methods have been developed and are in used today for steady and time-accurate computation of these equations. The motivation of this thesis is also a desire to develop an efficient, accurate and simple method for the numerical solution of incompressible viscous flow problems in primitive variables. For this purpose, a numerical method based on high-order compact finite difference schemes is developed in conjunction with the well-known artificial compressibility approach for solving incompressible Navier-Stokes equations. By adding pseudo time derivative terms to each equation, the coupled system becomes hyperbolic in time and the artificial compressibility method becomes applicable. We have also focused on the extension of the method for simulating two-phase flow by coupling phase-field model to the incompressible Navier-Stokes solver. This research work is divided into three steps in which each step focuses on an aspect of the development of a numerical method. In the first step, a third-order upwind compact finite difference scheme based on the fluxdifference splitting is developed and implemented with the implicit Beam-Warming approximate factorization scheme for solving the incompressible Navier-Stokes equations. The upwind compact scheme for the convective terms is preferred because of its high resolving efficiency with less numerical dissipation and truncation errors. The numerical scheme is applied to compute the flow inside the two sided lid driven cavity flow and compared with the finite difference alternating direction implicit scheme. In the second step, we implemented higher-order central compact finite difference scheme along with filtering procedure for steady and unsteady incompressible Navier- Stokes equations. The central compact scheme is also implemented under the framework of the artificial compressibility method in which convective terms of the governing x equations are approximated by using the high-order central compact schemes with filtering procedure and the viscous terms are discretized with a sixth-order central compact finite difference scheme. Dual-time stepping technique is employed for unsteady solutions at each physical time step. Computational efficiency and accuracy of the method is compared with upwind compact schemes by computing several benchmark flow problems. In the third step, the central compact scheme is applied successfully to incompressible two-phase flows both in two and three space dimensions. For this purpose, the modified Allen-Cahn type phase-field model is coupled with the incompressible Navier-Stokes equations. In the phase-field formulation, the classical infinitely thin boundary of separation between two immiscible fluids is replaced by a transition region of small but finite width, across which the composition of the one or two fluids changes continuously. The effectiveness of the method is demonstrated by computing several benchmark twophase incompressible flow problems. Finally, advantages and difficulties in solving incompressible viscous flow problems are discussed and future directions of the effort are proposed.