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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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