AR_final file_2018-19

plane, which receives and ejects heat. The heat en- gine efficiency is improved by adding a quintessence field. The analytical expression for heat engine ef- ficiency is derived in terms of quintessence dark energy parameter. This result may deepen our un- derstanding about thermodynamics of asymptoti- cally AdS black holes. This study has been done in collaboration with V. K. Ranjani, C. L. Ahmed Rizwan, A. Naveena Kumara, and K. M. Ajith. Effect of dark energy in geometrothermodynamics and phase transitions of regular bardeen AdS black hole We investigate thermodynamics and geometrother- modynamics of regular Bardeen AdS black hole with quintessence. The thermodynamics of the black hole is studied using temperature-entropy (T- S) and Pressure-Volume (P-v) plots, which indicate critical behaviour. This is also confirmed from the divergence of specific heat against entropy, which shows a second order phase transition. Using the concept of thermodynamic Ruppeiner and Wein- hold geometry, we calculate the thermodynamic curvature scalar in the quintessence dark energy regime. While these curvature scalars enable us to identify the critical behaviour, they do not show divergence at the phase transition points observed in specific heat study. To resolve this puzzle, we have adopted the method of geometrothermody- namics proposed by Hernando Quevedo. Choosing a Legendre invariant Quevedo metric, the curvature scalar shows singularity at the same point as seen in specific heat study. This investigation has been done in collaboration with C. L. Ahmed Rizwan, A. Naveena Kumara, K. V. Ranjani, and K. M. Ajith. Bhargav Pradeep Vaidya A particle module for the PLUTO Code: I. An Im- plementation of the MHD-PIC equations We describe an implementation of a particle physics module available for the PLUTO code appropriate for the dynamical evolution of a plasma consist- ing of a thermal fluid and a non-thermal compo- nent represented by relativistic charged particles or cosmic rays (CRs). While the fluid is approached using standard numerical schemes for magneto- hydrodynamics, CR particles are treated kinet- ically using conventional Particle-In-Cell (PIC) techniques. The module can be used either to de- scribe test-particle motion in the fluid electromag- netic field or to solve the fully coupled magneto- hydrodynamics (MHD)-PIC system of equations with particle back-reaction on the fluid as orig- inally introduced by Bai, et al. Particle back- reaction on the fluid is included in the form of momentum-energy feedback and by introducing the CR-induced Hall term in Ohms law. The hybrid MHD-PIC module can be employed to study CR kinetic effects on scales larger than the (ion) skin depth provided that the Larmor gyration scale is properly resolved. When applicable, this formu- lation avoids resolving microscopic scales, offering substantial computational savings with respect to PIC simulations. We present a fully conservative formulation that is second-order accurate in time and space, and extends to either the Runge-Kutta (RK) or the corner transport upwind time-stepping schemes (for the fluid), while a standard Boris in- tegrator is employed for the particles. For highly energetic relativistic CRs and in order to overcome the time-step restriction, a novel sub-cycling strat- egy that retains second-order accuracy in time is presented. Numerical benchmarks and applications including Bell instability, diffusive shock acceler- ation, and test-particle acceleration in reconnect- ing layers are discussed. This work has been done in collaboration with Andrea Mignone, Gianluigi Bodo, and G. Maltia. A particle module for the PLUTO Code: II. Hy- brid framework for modelling non-thermal emission from relativistic magnetized flows We describe a new hybrid framework to model non- thermal spectral signatures from highly energetic particles embedded in a large-scale classical or rel- ativistic magneto-hydrodynamic (MHD) flow. This method makes use of Lagrangian particles mov- ing through an Eulerian grid, where the (relativis- tic) MHD equations are solved concurrently. La- grangian particles follow fluid streamlines and rep- resent ensembles of (real) relativistic particles with a finite energy distribution. The spectral distribu- tion of each particle is updated in time by solving the relativistic cosmic ray transport equation based on local fluid conditions. This enables us to account for a number of physical processes, such as adia- batic expansion, synchrotron, and inverse Compton emission. An accurate semi-analytically numerical scheme that combines the method of characteristics with a Lagrangian discretization in the energy co- ordinate is described. In the presence of (relativis- ( 219 )