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We present the simulation results of merging harmonically confined rotating Bose-Einstein condensates in two dimensions. Merging of the condensate is triggered by positioning the rotation axis at the trap minima and moving both condensates towards each other while slowly ramping their rotation frequency. We analyze the dynamics of the merged condensate by letting them evolve under a single harmonic trap. We systematically investigate the formation of solitonic and vortex structures in the final, unified condensate, considering both non-rotating and rotating initial states. In both cases, merging leads to the formation of solitons that decay into vortex pairs through snake instability, and subsequently, these pairs annihilate. Soliton formation and decay-induced phase excitations generate sound waves, more pronounced when the merging time is short. We witness no sound wave generation at sufficiently longer merging times that finally leads to the condensate reaching its ground state. With rotation, we notice off-axis merging (where the rotation axes are not aligned), leading to the distortion and weakening of soliton formation. The incompressible kinetic energy spectrum exhibits a Kolmogorov-like cascade [$E(k) \sim k^{-5/3}$] in the initial stage for merging condensates rotating above a critical frequency and a Vinen-like cascade [$E(k) \sim k^{-1}$] at a later time for all cases. Our findings hold potential significance for atomic interferometry, continuous atomic lasers, and quantum sensing applications., Comment: 14 pages, 20 figures

We investigate the scaling of the energy cascade in a harmonically trapped, turbulent, rotating Bose-Einstein condensate (BEC) in two dimensions. We achieve turbulence by injecting a localized perturbation into the condensate and gradually increasing its rotation frequency from an initial value to a maximum. The main characteristics of the resulting turbulent state depend on the initial conditions, rotation frequency, and ramp-up time. We analyze the energy and the fluxes of kinetic energy by considering initial profiles without vortices and with vortex lattices. In the case without initial vortices, we find the presence of Kolmogorov-like scaling ($k^{-5/3}$) of the incompressible kinetic energy in the inertial range. However, with initial vortex lattices, the energy spectrum follows Vinen scaling ($k^{-1}$) at transient iterations. For cases with high rotating frequencies, Kolmogorov-like scaling emerges at longer durations. We observe positive kinetic energy fluxes with both initial states across all final frequencies, indicating a forward cascade of incompressible and compressible kinetic energy., Comment: 14 pages, 22 figures, 2 Tables

Relativistic jets are intrinsic phenomena of active galactic nuclei (AGN) and quasars. They have been observed to also emanate from systems containing compact objects, such as white dwarfs, neutron stars and black hole candidates. The corresponding Lorentz factors, $\Gamma$, were found to correlate with the compactness of the central objects. In the case of quasars and AGNs, plasmas with $\Gamma$-factors larger than $8$ were detected. However, numerically consistent modelling of propagating shock-fronts with $\Gamma \geq 4$ is a difficult issue, as the non-linearities underlying the transport operators increase dramatically with $\Gamma$, thereby giving rise to a numerical stagnation of the time-advancement procedure or alternatively they may diverge completely. In this paper, we present a unified numerical solver for modelling the propagation of one-dimensional shock fronts with high Lorentz factors. The numerical scheme is based on the finite-volume formulation with adaptive mesh refinement (AMR) and domain decomposition for parallel computation. It unifies both time-explicit and time-implicit numerical schemes within the framework of the pre-conditioned defect-correction iteration solution procedure. We find that time-implicit solution procedures are remarkably superior over their time-explicit counterparts in the very high $\Gamma$-regime and therefore most suitable for consistent modelling of relativistic outflows in AGNs and micro-quasars.

A general relativistic model for the formation and acceleration of low mass-loaded jets from systems containing accreting black holes is presented. The model is based on previous numerical results and theoretical studies in the Newtonian regime, but modified to include the effects of space-time curvature in the vicinity of the event horizon of a spinning black hole. It is argued that the boundary layer between the Keplerian accretion disk and the event horizon is best suited for the formation and acceleration of the accretion-powered jets in active galactic nuclei and micro-quasars. The model is based on matching the solutions of three different regions: i- a weakly magnetized Keplerian accretion disk in the outer part, where the transport of angular momentum is mediated through the magentorotational instability, ii- a strongly magnetized, advection-dominated and turbulent-free boundary layer (BL) between the outer cold accretion disk and the event horizon, where the plasma rotates sub-Keplerian and iii- a transition zone (TZ) between the BL and the overlying corona, where the electrons and protons are thermally uncoupled, highly dissipative and rotate super-Keplerian. Our model predicts the known correlation between the Lorentz-factor and the spin parameter of the BH. It also shows that the effective surface of the BL, through which the baryons flow into the TZ, shrinks with increasing the spin parameter, implying therefore that low mass-loaded jets most likely originate from around Kerr black holes. When applying our model to the jet in the elliptical galaxy M87, we find a spin parameter in the range 0.99 - 0.998, a transition radius of about 30 gravitational radii and a fraction of 0.05 - 0.1 of the mass accretion rate goes into the TZ, where the plasma speeds up its outward-oriented motion to reach a Lorentz factor of 2.5 - 5.0 at the transition radius., Comment: 17 pages, 8 figures

An implicit algorithm for solving the equations of general relativistic hydrodynamics in conservative form in three-dimensional axi-symmetry is presented. This algorithm is a direct extension of the pseudo-Newtonian implicit radiative magnetohydrodynamical solver -IRMHD- into the general relativistic regime. We adopt the Boyer-Lindquist coordinates and formulate the hydrodynamical equations in the fixed background of a Kerr black hole. The set of equations are solved implicitly using the hierarchical solution scenario (HSS). The HSS is efficient, robust and enables the use of a variety of solution procedures that range from a purely explicit up to fully implicit schemes. The discretization of the HD-equations is based on the finite volume formulation and the defect-correction iteration strategy for recovering higher order spatial and temporal accuracies. Depending on the astrophysical problem, a variety of relaxation methods can be applied. In particular the vectorized black-white Line-Gauss-Seidel relaxation method is most suitable for modeling accretion flows with shocks, whereas the Approximate Factorization Method is for weakly compressible flows. The results of several test calculations that verify the accuracy and robustness of the algorithm are shown. Extending the algorithm to enable solving the non-ideal MHD equations in the general relativistic regime is the subject of our ongoing research., Comment: 30 pages, 8 figures, to be published in New Astronomy