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Mathematical Modeling of Lopsided Structures in Self-Gravitating Systems

Thesis Info

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Author

Khalid, Muhammad

Program

PhD

Institute

Federal Urdu University of Arts, Science and Technology

City

Karachi

Province

Sindh

Country

Pakistan

Thesis Completing Year

2013

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/handle/123456789/962

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726620299

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In recent years, an exceptional progress has exposed a great deal of information about the formation and evolution of large-scale struc- tures in this stunning star-spangled Universe. But, with more infor- mation comes many thought-provoking questions for theorists. The images obtained by the Hubble Space Telescope (HST ) has revealed that basic large-scale structures are shaped at the non-stationary non- linear stage of their evolution; therefore modern extragalactic astron- omy is compelled to study early non-linear stages of evolution of self- gravitational systems. A great role is played by global pulsations in different stages of the formation of galaxies. Incidentally though, reliable mechanisms of development of their sub-structures, as well as possible various non- linear effects are not yet fully revealed. Similarly, the physics of the formation of large-scale structures in the non-stationary universe is not completely available. Many authors have put forward various specific models of the system that gravitate. Binney and Tremaine (1987) have obtained a large number of results. The basis of the most of these results are on the linearisation of the Euler-Poison and Vlasov Poison systems around a stationary solution. Kalnajs (1972) has covered milestones in station- ary models of self-gravitating systems. Although the stationary mod- els of gravitating systems are abundance in the research, the presence of non-stationary models is very conspicuous among various models for study of dynamical development of large-scale structures. There- fore it seemed necessary to develop a new non-linear model which is viinon-stationary in nature and discuss its stability, so that our model will be more accurate. Gravitational instability with respect to lopsided oscillation mode is examined in this dissertation. A phase model of non-stationary self- gravitating disks with isotropic and anisotropic diagrams has been constructed. We used well-known generalization of the Bisnovatyi- Kogan-Zel’dovich model is used in order to find out the formation criteria of galaxies whose nucleus is away from their center (lopsided galaxies). Non-stationary dispersion relations are obtained for both isotropic and anisotropic models of lopsided mode. ) calculations ( The 2T show the relationship between initial virial ratio |U and degree of | ◦ rotation Ω. A comparative analysis of increment (growth rate) of lop- sided mode with other oscillatory modes is made and concluded that lopsided mode has a clear lead over other oscillatory modes. A radial instability always occurs if total kinetic energy is no more than 12.4% of the initial potential energy, in non-stationary isotropic model for lopsided mode. Also, it has been shown that instability is aperiodic when Ω = 0 and oscillatory when Ω ̸ = 0. This ratio of total kinetic energy and total potential energy becomes 30.6% for an anisotropic model of lopsided structure. In this thesis, a multi-parameter composite model by the method of linear superposition has also been constructed and analyzed the stabil- ity of lopsided mode for this model. This new composite model inves- tigates intermediate stages between isotropic and anisotropic models. In the end, the application of lopsidedness in our solar system is dis- cussed. Here, we suggested that G. Darwin’s theory of origin of moon would be acceptable if he had calculated his model in the background of non-stationary and non-equilibrium theory. It has been shown that if Nuritdinov’s non-stationary spherical model is applied on the earth- moon system and calculated that at the initial moment of collapse, the kinetic energy will be lesser than 22.3% of the potential energy viiiwhere instability occurred and the earth became lopsided and then split into two parts and hence the moon came into existence.
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اردو کے اہم مدونین (مولوی عبدالحق)

اردو کے اہم مدونین (بابائے اردومولوی عبدالحق)
حالات زندگی:
مولوی عبدا لحق برِ صغیر پاک ہند کے عظیم اردو مفکر، محقق، ماہر لسانیات، معلم، بانی انجمن ترقی اردو اور اردو کالج کے بانی تھے، ا?پ کو بابائے اردو کے لقب سے یاد کیا جاتا ہے۔آپ کی تاریخ پیدائش کے حوالے سے کافی اختلاف پایا جاتا ہے ،لیکن بقول ممتاز حسین مولوی عبدالحق 20 اپریل،1870ء کوبرطانوی ہندوستان کے ضلع میرٹھ کے ہاپوڑ کے قریب سراوہ نامی ایک گاؤں میں پیدا ہوئے۔مولوی صاحب کے والد شیخ علی حسین نے عہد مغلیہ میں اسلام قبول کیا۔ان کے سپرد محکمہ مال کی اہم خدمات رہیں۔مغلیہ دور میں انہیں جو مراعات حاصل تھیں وہ انگریز وں کے دور میں بھی برقرار رہیں۔
تعلیم و تربیت:
مولوی عبدالحق نے ابتدائی تعلیم گھر پرحاصل کی۔ثانوی تعلیم میرٹھ سے حاصل کی۔ 1894ء میں علی گڑھ سے بی اے کیا۔علی گڑھ میں سر سید احمد خان کی شخصیت سے بہت متاثر ہوئے۔1895ء میں حیدر آباد کے ایک سکول میں ملازمت اختیار کی۔اورنگ آباد میں صدر محتتم تعلیمات کے عہدے پر فائز رہے۔عثمانیہ کالج اورنگ آباد میں 1920ء تک بحیثیت پرنسپل فرائض سر انجام دیتے رہے۔
انجمن ترقی اردو:
جنوری 1902ء میں آل انڈیا محمڈن ایجوکیشن کانفرنس علی گڑھ کے تحت ایک علمی شعبہ قائم کیا گیا جس کانام انجمن ترقی اردو تھا۔ مولانا شبلی نعمانی اس کے سیکرٹری رہے تھے۔ عزیز مرزا کے بعد 1912ء میں مولوی عبدالحق سیکرٹری منتخب ہوئے جنھوں نے بہت جلد انجمن ترقی اردو کو ایک فعال ترین علمی ادارہ بنا دیا۔ مولوی عبدالحق اورنگ آباد (دکن ) میں ملازم تھے ،وہ انجمن کو اپنے ساتھ لے گئے اور اس طرح حیدر آباد دکن اس کا مرکز بن گیا۔
فروغ اردو کے لیے انجمن کی خدمات:
انجمن کے زیر اہتمام ایک لاکھ سے زائد جدیدعلمی ، فنی اور سائنسی اصطلاحات کا اردو...

استنباط احکام میں حضرت عائشہ کا منہج قرآن کریم کی روشنی میں

In this article an effort has been made to describe Hazrat ‘฀ishah (R. A) ’s methodology of derivation of Ahk฀m from Holy Quran. Holy Quran and Sunnah of Holy Prophet (S. A. W) is basic source of Islamic Shar฀‘ah. Hazrat ‘฀ishah Sidd฀qah (R. A) was the wife of the Holy Prophet (S. A. W), and the daughter of Hazrat Ab฀ Bakr (R. A). She spent her time in learning and acquiring knowledge of the two most important sources of Islam, the Qur'an and the Sunnah of His Prophet (S. A. W). Hazrat ‘฀ishah (R. A) narrated 2210 Ah฀d฀th out of which 174 Ah฀d฀th are commonly agreed upon by Bukh฀ri and Muslim. She was an ardent and zealous student of Islamic jurisprudence. She has not only described Ah฀d฀th and reported her observations of events, but interpreted them for derivation of Ahk฀m. Umm Al-Mu’min฀n Hazrat ‘฀ishah (R. A) is a great scholar and interpreter of Islam, providing guidance to even the greatest of the Companions (R. A) of the Holy Prophet Muhammad (S. A. W). She has not only described Ah฀d฀th and reported her observations of events, but interpreted them for derivation of Ahk฀m. Whenever necessary, she corrected the views of the greatest of the Companions of the Holy Prophet (S. A. W). It is thus recognized, from the earliest times in Islam, that about one-fourth of Islamic Shar฀‘ah is based on reports and interpretations that have come from Hazrat ‘฀ishah (R. A). As a teacher she had a clear and persuasive manner of speech. Hazrat ‘฀ishah (R. A) is a role model for women. She taught Islam many people. She was an authority on many matters of Islamic Law, especially those concerning women.

Virulence Analysis of Xanthomonas Campestris Pv. Sesami and Pseudomonas Syringae Pv. Sesami the Causal Organisms of Sesame Sesamum Indicum L. Bacterial Blight

Sesame (Sesamum indicum L.) locally called as til is an important conventional oilseed crop of Pakistan. Pakistan ranks 14th among major sesame producing countries in the world. Pakistan is facing a chronic shortage in edible oil and the situation is getting serious with alarmingly explosion of population. Its indegenious production is below the utilization level and there exists wide gap between production and utilization. Sesame crop is subjected to various abiotic and biotic stresses in all stages of growth. Two prominent bacterial pathogens associated with sesame are bacterial blight caused by Xanthomonas campestris pv. sesami (Xcs) and bacterial leaf spot caused by Pseudomonas syringae pv. sesami (Psse). These pathogens are responsible for sesame production constraints during monsoon season. Despite the shortage of edible oil, no profound efforts have been made on this important oilseed crop with reference to diseases. To handle the shortage of edible oil, there was an urgent need to explore the basic information on host pathogen interaction. The present work consisted of five experiments. The first study was the standardization of mass culturing of stored Xcs and Psse isolates to enhance their virulence and confirmation of their ability to induce hypersensitive reaction. All isolates were revived on non host plant and confirmation was made on the basis of pigmentation they produced in their respective media and hypersensitive test was performed in tomato and potato plants. The second study was conducted to analyse the virulence of virulent isolates in vitro by comparing symptoms induction and bacterial multiplication in different genotypes. Plants were inoculated by pin prick method and were monitored daily for symptoms development and measurements of lesions were taken until fully symptoms induction. Bacterial populations were determined by counting bacterial colonies. Psse isolates showed necrotic lesions (chl+) surrounded by halos as well as only black necrotic lesions (chl-). Size of the lesions and bacterial population between chl+ and chl- was the same and at maximum at 7 DAI in susceptible genotypes, while tolerant showed delayed in reaction. Similar mode of lesions expansion and rate of bacterial growth between chl+ and chl- isolates of Psse indicated that the virulence factor involved in symptomatology function as pathogenicity factor and only contributed to induction of chlorotic producing symptoms for Psse. Water soaking to blight symptoms along with maximum bacterial growth in all the susceptible and moderately susceptible genotypes by Xcs was recorded at 12 DAI. The third study was conducted to confirm process of infection of these bacterial pathogens in susceptible and tolerant genotypes by light microscopy. Inoculation was done by Injection method (IM) and Bacterial suspension dip method (BSDM). Xcs colonized tracheary elements of xylem vessels through intercellular spaces of the spongy parenchyma at 7 DAI and bacterial masses were identified as dark blue infected structures using toluidine blue O stain. Blight symptoms by Xcs were reported to be due to the blockage of nutrients and water flow. Psse showed thining and disruption of mesophyll tissues on the appearance of chlorotic symptoms 3-4 DAI. There were only empty spaces of tissues were observed 7 DAI. Overall the infection was same but delayed in tolerant genotypes. Disruption of mesophyll tissues might be due to the action of chlorosis producing toxin (coronatine) that degraded chloroplast membrane of host tissues. The forth study was conducted to detect the virulence factors of Xcs and Psse using suitables bioassays such as antibacterial test, induction of potato hypertrophic outgrowth and seedlings assay. Xcs and Psse (chl-) isolates showed zone of inhibition. The zone of inhibition produced by chl- isolates showed that chl- was not the defective mutant of chl+ isolates as reported in third study, but this test confirmed that these isolates produced another class of toxin that showed antibacterial activity. Induction of hypertrophic outgrowth in potato tuber and seedlings inhibition from culture filtrate of chl+ isolates of Psse confirmed that the toxin produced by these isolates was similar to phytotoxin coronatine (a polyketide molecule) and it might mimics the action of one of the phytohormones. The fifth study was conducted to extract the virulence factors as well as their purification and identification was also performed. Identification was made on the basis of reference data. Crude extracts of acetone preparation of Xcs and Psse (chl-) isolates were concentrated on silica TLC plates. Further purification was carried out by HPLC and TLC. The toxic aciticity eluted from the HPLC column after 10 min corresponding with single active peak showed antibacterial activity. Reverse phase HPLC of chl- isolates extracted partially purified produced an elution pattern like reported in mangotoxin from Pss strain UMAF0158. Acetone praperation of cell free culture filtrates of virulent Xcs also showed active peaks having phytotoxic activity obtained from the HPLC column after 10 min.