Scaling exponents and phase separation in a nonlinear network model inspired by the gravitational accretion

• An effective algorithm for modeling of gravitational accretion was developed.
• Very efficient implementation of this algorithm enabled large-scale simulations.
• The dynamics of the model is found to lead to phase separation of condensates.
• Light condensates obey power laws, with several universal scaling exponents.
• The analyzed properties of heavy condensates have been found to be scale-free.

We study dynamics and scaling exponents in a nonlinear network model inspired by the formation of planetary systems. Dynamics of this model leads to phase separation to two types of condensate, light and heavy, distinguished by how they scale with mass. Light condensate distributions obey power laws given in terms of several identified scaling exponents that do not depend on initial conditions. The analyzed properties of heavy condensates have been found to be scale-free. Calculated mass distributions agree well with more complex models and fit observations of both our own Solar System and the best observed extra-solar planetary systems.