Modeling correctly the transport of neutrinos is crucial in some astrophysical scenarios such as core-collapse supernovae and binary neutron star mergers. In this paper, we focus on the truncatedmoment formalism, considering only the first two moments (M1 scheme) within the grey approximation, which reduces Boltzmann seven-dimensional equation to a system of 3+1 equations closely resembling the hydrodynamic ones. Solving the M1 scheme is still mathematically challenging, since it is necessary to model the radiation-matter interaction in regimes where the evolution equations become stiff and behave as an advection-diffusion problem. Here, we present different global, high-order time integration schemes based on Implicit-Explicit Runge-Kutta (IMEX) methods designed to overcome the time-step restriction caused by such behavior while allowing us to use the explicit RK commonly employed for the MHD and Einstein equations. Finally, we analyze their performance in several numerical tests.

Modeling correctly the transport of neutrinos is crucial in some astrophysical scenarios such as core-collapse supernovae and binary neutron star mergers. In this paper, we focus on the truncatedmoment formalism, considering only the first two moments (M1 scheme) within the grey approximation, which reduces Boltzmann seven-dimensional equation to a system of 3 + 1 equations closely resembling the hydrodynamic ones. Solving the M1 scheme is still mathematically challenging, since it is necessary to model the radiation-matter interaction in regimes where the evolution equations become stiff and behave as an advection-diffusion problem. Here, we present different global, highorder time integration schemes based on Implicit-Explicit Runge-Kutta (IMEX) methods designed to overcome the time-step restriction caused by such behavior while allowing us to use the explicit RK commonly employed for the MHD and Einstein equations. Finally, we analyze their performance in several numerical tests.

We have numerically computed planar central configurations of n = 1000 bodies of equal masses. A classification of central configurations is proposed based on the numerical value of the complexity, C. The main result of our work is the discovery of filaments and voids in planar central configurations with random complexity values. Suggestions are given for future work in the context of central configurations with random complexity values.