Studies on collective excitations of quasi-two-dimensional Bose-Einstein condensate

Theory Division Department of Physics

Novel Strategies for Heterocyclic Constructions via 1, 4-Dipolar Intermediates

In the thesis entitled " Novel Strategies for Heterocyclic Constructions via 1 ,4-Dipolar Intermediates"Synthesis of a complex organic molecules essentially involves the formation of carbon-carbon and carbon-heteroatom bonds. Various synthetic methods are available for these processes involving ionic, pericyclic and radical reactions. Among the pericyclic reactions, dipolar cycloaddition reactions, introduced by Huisgen, have emerged as a very powerful tool for heterocyclic construction. Heterocyclic compounds remain an important class of organic molecules due to their natural abundance and remarkable biological activity, thus constituting an intergral part of pharmaceutical industry. In this respect, developing newer synthetic methodology for heterocyclic construction has been an area of immense interest. In recent years, 1,3-dipolar cycloaddition reactions proved to be efficient routes to a wide variety of five membered heterocycles, as attested by their application in the total synthesis of various complex organic molecules. However, the potential application of similar 1,4- dipolar cycloaddition reactions for the construction of six memebered heterocycles remained underexploited. In this context, a systematic investigation of the reactivity of 1,4-dipoles generated from nitrogen heterocycles (pyridine and its analogues) and dimethyl acetylenedicarboxy!ate (DMAD) towards various dipolarophiles has been carried out and the results are embodied.

Novel1, 3-Dipolar Cycloaddition Reactions of Acyclic Carbonyl Ylides and Related Chemistry

The thesis entitled novel 1,3-dipolar cycloaddition reactions of acyclic carbonyl ylides and related chemistry embodies the results of the investigations carried out to explore the reactivity of acyclic carbonyl ylides,generated by the reaction of dicarbomethoxy carbine and aldehydes towards dipolarophiles such as activated styrenes,1,2-and 1,4-quinones. In conclusion ,we have explored the reactivity pattern of acyclic carbonyl ylides derived from dicarbomethoxycarbene and aldehyde towards activated styrenes with a view to develop a stereoselective synthesis of highly substituted tetrahydrofuran derivatives. It was also found that the ylide could be trapped by various 1,2-and 1,4-diones to form dioxolane derivatives. It is noteworthy that the cycloaddition is highly region- and stereoselective. With isatins the ylide preferentially adds to the more electrone deficient carbonyl group making it regiospecific. Hetrocyclic compounds are of pivotal importance in organic chemistry, and enormous efforts have been devoted to develop new methodologies for their synthesis. It is noteworthy in this context that, 1,3-dipolar cycloaddition reaction,otherwise called Huisgen reaction, constitutes one of the most efficient methods for the synthesis of five membered heterocycles. Among the various dipoles, carbonyl ylides have received substiancial attention in recent years largely due to their utility in the synthesis of a wide range of oxygen hetrocycles, which are often found as structural subunits of many bioactive natural products.

Studies on scattering and thermodynamics of black holes in f(R) theory and Einstein's theory

One of the interesting consequences of Einstein's General Theory of Relativity is the black hole solutions. Until the observation made by Hawking in 1970s, it was believed that black holes are perfectly black. The General Theory of Relativity says that black holes are objects which absorb both matter and radiation crossing the event horizon. The event horizon is a surface through which even light is not able to escape. It acts as a one sided membrane that allows the passage of particles only in one direction i.e. towards the center of black holes. All the particles that are absorbed by black hole increases the mass of the black hole and thus the size of event horizon also increases. Hawking showed in 1970s that when applying quantum mechanical laws to black holes they are not perfectly black but they can emit radiation. Thus the black hole can have temperature known as Hawking temperature. In the thesis we have studied some aspects of black holes in f(R) theory of gravity and Einstein's General Theory of Relativity. The scattering of scalar field in this background space time studied in the first chapter shows that the extended black hole will scatter scalar waves and have a scattering cross section and applying tunneling mechanism we have obtained the Hawking temperature of this black hole. In the following chapter we have investigated the quasinormal properties of the extended black hole. We have studied the electromagnetic and scalar perturbations in this space-time and find that the black hole frequencies are complex and show exponential damping indicating the black hole is stable against the perturbations. In the present study we show that not only the black holes exist in modified gravities but also they have similar properties of black hole space times in General Theory of Relativity. 2 + 1 black holes or three dimensional black holes are simplified examples of more complicated four dimensional black holes. Thus these models of black holes are known as toy models of black holes in four dimensional black holes in General theory of Relativity. We have studied some properties of these types of black holes in Einstein model (General Theory of Relativity). A three dimensional black hole known as MSW is taken for our study. The thermodynamics and spectroscopy of MSW black hole are studied and obtained the area spectrum which is equispaced and different thermo dynamical properties are studied. The Dirac perturbation of this three dimensional black hole is studied and the resulting quasinormal spectrum of this three dimensional black hole is obtained. The different quasinormal frequencies are tabulated in tables and these values show an exponential damping of oscillations indicating the black hole is stable against the mass less Dirac perturbation. In General Theory of Relativity almost all solutions contain singularities. The cosmological solution and different black hole solutions of Einstein's field equation contain singularities. The regular black hole solutions are those which are solutions of Einstein's equation and have no singularity at the origin. These solutions possess event horizon but have no central singularity. Such a solution was first put forward by Bardeen. Hayward proposed a similar regular black hole solution. We have studied the thermodynamics and spectroscopy of Hay-ward regular black holes. We have also obtained the different thermodynamic properties and the area spectrum. The area spectrum is a function of the horizon radius. The entropy-heat capacity curve has a discontinuity at some value of entropy showing a phase transition.