This work focuses on the modeling and numerical approximation of population balance models (PBMs) for simulating dispersed systems, especially the batch crystallization pro- cess. Apart from applying the existing numerical schemes, new numerical techniques are introduced for solving these models efficiently and accurately. The effects of nucleation, growth, aggregation, breakage, and fines dissolution phenomena on the crystal size distri- bution (CSD) are investigated. An alternative quadrature method of moments (QMOM) is introduced for solving the single-variate length-based PBM incorporating simultaneous nucleation, growth, aggregation and breakage phenomena. In the proposed QMOM, or- thogonal polynomials, formed by lower order moments, are used to find the quadrature points and weights. To ensure better accuracy of the scheme, a third order orthogonal polynomial, utilizing the first six moments, is selected to calculate the quadrature points (abscissas) and corresponding quadrature weights. Therefore, at least a six moment sys- tem is needed to solve. This choice of polynomial gives a three-point Gaussian quadrature rule which generally yields exact results for polynomials of degree five or less. A mathe- matical model is derived for simulating batch crystallization process incorporating crystals nucleation, size-dependent growth and dissolution of small nuclei below certain critical size in a recycling pipe. Moreover, a time delay in the dissolution unit is also incorporated in the model. The dissolution of small crystals (fines dissolution) is helpful to further improve the product CSD. It withdraws and dissolve excessive fines from the quiescent zone of crystallizer which are generated during periods of high supersaturation. This ef- fectively shifts the CSD towards right and often makes the distribution narrow. A new numerical scheme is introduced for simulating this model. The method of characteristics, the Duhamel’s principle, and the QMOM are employed together to devise the proposed numerical scheme. Several test problems are considered and the numerical results are val- idated against available analytical solutions and the finite volume scheme (FVS). It was found that the suggested numerical methods have capability to solve the given models efficiently and accurately.
صرع کے دوروں کا الزام مستشرقین اپنے مذموم عزائم کو برواکار لاتے ہوئے آپ ﷺ کو مصروع ثابت کرنے کے لیے چند واقعات کا سہارا لیتے ہیں جو ان کی ذہنی اختراع اور باطل تاویلات کا نتیجہ ہیں جبکہ ایسے واقعات دیگر مقدس ہستیوں کو بھی پیش آئے لیکن مستشرقین و منکرین سب کو چھوڑ کر صرف حضور ﷺ کے سر الزام دھرتے ہیں اور دوسری برگزیدہ شخصیات کا نام تک نہیں لیتے کیونکہ ایسا کرنے سے ان کی اپنی محبوب ہستیاں بھی زد میں آتی ہیں۔ وہ واقعات جن سے یہ مستشرقین آپ کو مصروع ہونے کی ناکام کوشش کرتے ہیں درج ذیل ہیں ۔ ۱۔اسپرنگر حضرت آمنہ کے فرشتوں کو دیکھنے کو مرگی سے تعبیر کیا اور یہی مرض حضور کو ورثہ میں ملا‘ کا الزام دھر دیا ۔ علامہ محمد احسان الحق سیلمانی لکھتے ہیں کہ حضرت آمنہ ؓ ، حضور ﷺ کی والدہ ماجدہ نے اپنے رویا میں فرشتوں کو دیکھا جو انہیں احمد ﷺ کی خوشخبری دینے اور آپ کا نام مبارک تجویز کرنے آئے تھے ۔‘‘ سپرنگر نے کہا کہ فرشتوں نے کیا بشارت دینی تھی ، حقیقت میں حضرت آمنہ کو ضعف دماغ اور صرع کی بیماری تھی ۔ حضرت آمنہ ؓ تو فرشتوں کو دیکھے اور یہی کہے کہ یہ فرشتے ہیں لیکن مستشرقین اسے صرع کہتے ہیں ، عجیب منطق ہے۔ جو ساتھی آپ کے ساتھ مدت العمر رہے انہوں نے کسی موقع پر بھی مصروع نہیں کہا ۔ یہ سب کچھ پیغمبر اسلام اور آپ کے گھرانہ کی شان گھٹاناچاہتے ہیں(۲) دوسرا واقعہ یہ ہے کہ آپ ﷺ اپنے بچپن میں اپنے رضاعی بہن بھائیوں کے ساتھ بکریاں چرانے گئے کہ آپ کا رضاعی بھائی اپنے والدین کے پاس دوڑتا ہوا آیا کہ دو سفید پوش مردوں نے میرے قریشی بھائی کا لٹا کر اس کا...
Urdu Dissertations of Islamic Studies on Semitic Religions (MPhil, PhD) in Pakistani Universities: An Index and Bibliometric Review Study of religions or Comparative Religions is a globally significance subject. Pakistan is also resourceful in this field. In many universities, there are special departments on this valuable subject. It is taught as compulsory course at BS & MA level in the departments of Isalmic studies in all universities. In many universities it’s also taught at MPhil and PhD level, some of them have produced hundreds of MS and PhDs dissertations on this subject. Due to its importance, it was a dire need to review and compile the titles of theses and dissertations, which are produced from the universities on the subject. In this study, efforts are made to review and compile a comprehensive index of such theses at MPhil and PhD level from Pakistani universities with statistical analysis. Due to its huge amount, the data is divided into two major types, Semitic and non-Semitic religions. The current study covers only Semitic/ Revealed and related topics. The word Semitic refers to the race of the son of Prophet Noah (A.S) or the areas where this race was spread and grew. Semitic Religions consists of; Judaism, Christianity and Islam. In this study, Biblometric approach is adopted with mix method approach. Total 393 theses of Islamic Studies on Semitic Religions are compiled and statistically evaluated in this paper. The study concludes that a good deal of literature and dissertations are available in Pakistani universities on Comparative Religions and Interfaith Studies. It is recommended that contents of theses should be analyzed for improvement of the Study of Religions in Pakistan
Protective coatings are used for external and internal corrosion protection of gas/oil storage, transmission and distribution. The key factors for corrosion protection are adhesion of the coating to the steel surface, and resistance of the coating to permeation of water, oxygen and/or ions. External three layer polyethylene/hotmelt/Fusion Bonded Epoxy (FBE) coating is being used for corrosion protection of gas/oil pipelines buried under soil. FBE, being in direct contact with steel surface, has immense bearing on corrosion protection and hence service lifetime of the pipeline. The corrosion protection properties of the two FBE materials have been assessed on the basis of inherent chlorine contamination, reaction kinetics, dimensional stability after cure, water absorption etc. Analytical techniques such as Thermal Analysis (TA), surface characterization techniques like Fourier Transform Infrared Spectroscopy (FTIR), Time of Flight Secondary Ion Mass Spectrometry (TOFSIMS) and electrochemical techniques like Electrochemical Impedance Spectroscopy (EIS) have proved to be extremely helpful not only for performance evaluation of coating materials but characterization of the coating-substrate interface as well. ToFSIMS has been extremely useful in elucidating the detrimental effect of contamination such as oil, grease, fats etc at the FBE–substrate interface on the coating disbondment. The characterization of the interface has helped to predict service lifetime of a 3 LPE coating. Our analytical results have been validated by field tests. The most important factor influencing the service lifetime of a coating is the steel surface preparation by minimizing residual contamination. Clean interface should contribute towards alleviating the need for Cathodic Protection (CP) application and hence reducing maintenance costs. The ionic chlorine contamination is one of the most important critical interfacial characteristics of epoxy coating adhesion on steel surfaces. Incomplete cross- linking of the resin has turned out to be one of the contributory factors towards coating disbondment on steel pipeline buried under irrigated pathways. The strength of coating adhesion has been found out to be damaged by molecular moisture which diffused from the soil and surrounding atmosphere through the free volume in polyethylene and hotmelt. Quality of wash water for steel substrate turned out to be one of the characteristics for better performance of epoxy coatings on steel substrates. Furthermore the results confirmed that special attention must be accorded to periodic removal of settled water from fuel storage tanks at regular intervals.