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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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Screening and Molecular Identification of Chloroquine Resistant Genes in Plasmodium Falciparum from Muzaffargarh, Pakistan

The current research work reports on the incidences of Plasmodium infections and its chloroquine resistant genes from Muzaffargarh, Pakistan. Samples collection continued from November, 2008 to November, 2010 (25 months). The analysis focused on the inter relationship of Plasmodium vivax and P.falciparum infection with particular months, seasons, genders, age groups, socio-economic status, symptoms and the Plasmodium stages. Another core objective of the analysis was the scrutiny of mutant and wild types of pfcrt (codon 72-76) and pfmdr1 N86Y, and their association with different months, seasons, genders, age groups, socio-economic status, symptoms and the Plasmodium stages. The overall positivity rates that consisted of slide positivity rate (SPR), P.vivax positivity rate (VPR) and P.falciparum positivity rate (FPR) were 21.40%, 19.37% and 2.03% respectively. The difference between P.vivax infection (90.49%) and P.falciparum infection (9.51%) was highly significant (χ2=1456; p<0.001). Month- wise variations in incidences of Plasmodium infection were highly significant (χ2=8306.63; p<0.001) and association between P.vivax and P.falciparum infection with monthly variations was highly significant (χ2= 69.8; p<0.001). Season-wise analysis revealed that variations in incidence of Plasmodium infection were highly significant (χ2=1886.08; p<0.001). The association between the incidences of P.vivax and P.falciparum infection with seasonal variations was also found to be highly significant (χ2=44.99; p<0.001). Gender based analyses evidenced that Plasmodium infection was significantly higher (χ2=344.08; p<0.001) in males (69.68%) than females (30.32%). The association between the incidence of P.vivax and P.falciparum infection with gender was found to be non-significant (χ2=0.103; p>0.0.05). Plasmodium infection showed highly significant difference (χ2 =1216.4; p<0.001), when it was analyzed age-wise, whereas, a non-significant (χ2=1.895; p>0.05) association, between the incidence of P.vivax and P.falciparum infection with age groups was noted. People aging between 16 and 30 years were affected far more, both in the case of P.vivax infection (48.78%) and in that of P.falciparum (45.02%). Age group 0 to 5 years was the least hit: 1.00% by P.vivax infection and 0.95% by the P.falciparum. The disease frequency was significantly higher (χ 2=12.41; p<0.001) in lower income class (53.74%) and was comparatively lower (46.26%) in the mediocre. Analysis further discovered that people in the lower socio-economic class were more endangered, both in case of P.vivax infection (53.86%) and in that of P.falciparum infection (52.61%). The association between the incidence of P.vivax and P.falciparum infection with socio-economic status was found to be non-significant (χ2=0.120; p>0.05). In the course of this research work, symptom specific analyses were conducted for both types of the infection. The difference in symptoms was found to be highly significant (χ2=1149.49; p<0.001). Symptoms such as periodic fever, chill and headache were observed more frequently both in P.vivax (82.63%) and P.falciparum infection (82.46%). Symptoms of continuous fever, vomiting and weakness were observed at a lesser degree, both in cases of P.vivax infection (7.72%) and in the P.falciparum (5.21%). The association between the incidence of P.vivax and P.falciparum infections with symptoms was found to be non-significant (χ2=2.97; p>0.05). In case of malarial infection, maximum number (77.75%) of stages observed consisted of trophozoites with gametocytes, whereas the minimum number (0.86%) of stages observed were gametocytes. The difference analyzed in stages was highly significant (χ2=6081.24; p<0.001). Highly significant (χ2=20.60; p<0.001) association was found between the incidences of P.vivax and P.falciparum infection with stages of Plasmodium. Molecular analysis of the P.falciparum positive cases showed that presence of gene pfcrt (codon 72-76) contained in sequence of SagtVMNT was 100%. Sequencing results of pfmdr1 gene fragment showed that wild type pfmdr1 N86 (TAT) existed 33% and pfmdr1 Y86 (AAT) existed 84.30%. The difference in numbers of mutant and wild type was found to be highly significant (χ2=99.64; p<0.001). No significant (p>0.05) association was found between mutant (pfmdr1 Y86) and wild type (pfmdr1N86) with different months, seasons, genders, ages, socioeconomic status, disease symptoms and Plasmodium stages. However, more studies are required to find Patterns of antimalarial drug resistant mutations, especially in endemic areas.