AR_final file_2018-19

law of the average scale factor, which is a product of power and exponential type of functions that results in time dependent deceleration parameter ( q ). The equation of state parameter of dark en- ergy ( ω de ) has been discussed and we have observed that for the three models it crosses the phantom divide line ( ω de = -1) and shows quintom like be- haviour. The density of dark energy ( ρ de ) is an increasing function of redshift and remains posi- tive throughout the evolution of the universe for the three models. Moreover, in KantowskiSachs and LRS Bianchi type-I geometries, the dark en- ergy density dominates the string tension density ( λ ) and proper density ( ρ ) throughout the evolu- tion of the universe. The physical and geometrical aspects of the statefinder parameter ( r, s ), squared speed of sound ( v 2 s ) and ω de − ω ′ de plane are also discussed. This study has been done in collabora- tion with V. U. M. Rao, Bekele Getaneh, and Molla Mengesha. Bianchi type-III generalized ghost pilgrim dark en- ergy model in a scalar tensor theory of gravitation This study is devoted to the Bianchi type-III anisotropic generalized ghost pilgrim dark energy (GGPDE) cosmological model in the frame work of Saez-Ballester scalar-tensor theory of gravitation. With the help of hybrid expansion law of scale fac- tor (i.e., a ( t ) = ( t l e t ) 1 k ), a cosmological model is obtained, which yields a time dependent deceler- ation parameter, and exhibits a transition of the Universe from early decelerated phase to the re- cent accelerating phase. We also discuss the equa- tion of state (EoS) parameter and statefinders r − s , and ω de − ω ′ de planes for the obtained model. The EoS parameter and r − s plane analysis provide quintessence-like behaviour of the model. More- over, the ω de − ω ′ de cosmological plane corresponds to thawing region. This study has been done in col- laboration with V. U. M. Rao, and Molla Menge- sha. Paniveni Udayashankar A study of supergranulation through its parameters Supergranulation is examined through its various parameters such as area, perimeter, circularity and fractal dimension. A connection amongst these pa- rameters throws light on the turbulent aspect of this convective feature. The spread shows an asym- metric dispersion with a minimum dimension at around ± 25 ◦ because there is a theoretical calcu- lation which indicates that the enhanced fields will reduce the supergranular cell sizes (Chandrasekhar, 1961) around these latitudes. A different technique of analysis on a larger sample could consolidate these findings. Sudhaker Upadhyay Logarithmic corrected Van der Waals black holes in higher dimensional AdS space We consider the anti-de Sitter black hole in d - dimensional spacetime, and calculate the loga- rithmiccorrected thermodynamics quantities. We study the effects of thermal fluctuations on the thermodynamics of higherdimensional AdS black holes. We exploit such logarithmic corrected fluc- tuations on the equation of state. We find that the Van der Waals black hole is completely stable in the presence of the logarithmic correction. This study has been done in collaboration with Behnam Pourthassan. Thermodynamics and phase transitions of galactic clustering in higher-order modified gravity We study the thermodynamics of galactic cluster- ing under the higher-order corrected Newtonian dy- namics. The clustering of galaxies is considered as a gravitational phase transition. In order to study the effects of higher-order correction to the ther- modynamics of gravitational system, we compute more exact equations of state. Moreover, we inves- tigate the corrected probability distribution func- tion for such a gravitating system. A relation be- tween order parameter and the critical temperature is also established. This study has been done in collaboration with Behnam Pourhassan, and Sal- vatore Capozziello. Deepak Vaid Regular bardeen AdS black hole as a heat engine Interpreting cosmological constant as thermody- namic pressure, we study the thermodynamics us- ing T-S and P-v plots. Specific heat studies also carried out in detail. A first order phase transition is evident from these studies. These are followed by the construction of a heat engine, considering the black hole as working substance. The efficiency is obtained via a thermodynamic cycle in the P-v ( 218 )