Mathematical Modeling of Lopsided Structures in Self Gravitating Systems

In recent years, an exceptional progress has exposed a great deal of information about the formation and evolution of large-scale structures in this stunning star-spangled Universe.But, with more information 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 nonlinear stage of their evolution; therefore modern extragalactic astronomy is compelled to study early non-linear stages of evolution of selfgravitational 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 nonlinear 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 stationary models of self-gravitating systems. Although the stationary models 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.Therefore it seemed necessary to develop a new non-linear model which is non-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 selfgravitating isks 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.The calculationsshow the relationship between initial virial ratio(2T|U|)◦ and degree of rotation Ω.A comparative analysis of increment (growth rate) of lopsided 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 stability of lopsided mode for this model.This new composite model investigates intermediate stages between isotropic and anisotropic models.In the end, the application of lopsidedness in our solar system is discussed.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 earthmoon system and calculated that at the initial moment of collapse, the kinetic energy will be lesser than 22.3% of the potential energy where instability occurred and the earth became lopsided and then split into two parts and hence the moon came into existence