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

Theory Division Department of Physics

Influence of Major Operational Parameters on Aerobic Granulation for the Treatment of Wastewater

Effective solids-liquid separation is the basic concept of any wastewater treatment system. Biological treatment methods involve microorganisms for the treatment of wastewater. Conventional activated sludge process (ASP) poses the problem of poor settleability and hence require a large footprint. Biogranulation is an effective biotechnological process which can overcome the drawbacks of conventional ASP to a great extent. Aerobic granulation represents an innovative cell immobilization strategy in biological wastewater treatment. Aerobic granules are selfimmobilized microbial aggregates that are cultivated in sequencing batch reactors (SBRs). Aerobic granules have several advantages over conventional activated sludge flocs such as a dense and compact microbial structure, good settleability and high biomass retention. For cells in a culture to aggregate, a number of conditions have to be satisfied. Hence aerobic granulation is affected by many operating parameters. The organic loading rate (OLR) helps to enrich different bacterial species and to influence the size and settling ability of granules. Hence, OLR was argued as an influencing parameter by helping to enrich different bacterial species and to influence the size and settling ability of granules. Hydrodynamic shear force, caused by aeration and measured as superficial upflow air velocity (SUAV), has a strong influence and hence it is used to control the granulation process. Settling time (ST) and volume exchange ratio (VER) are also two key influencing factors, which can be considered as selection pressures responsible for aerobic granulation based on the concept of minimal settling velocity. Hence, these four parameters - OLR, SUAV, ST and VER- were selected as major influencing parametersfor the present study. Influence of these four parameters on aerobic granulation was investigated in this work

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.