## Abstract

In this paper we use a matrix approach to investigate the distribution of particles in nucleation coalescence models with discrete lattices, both in the irreversible coagulation case and in the reversible one. In the irreversible case

(A + A → A), the evolution of the particle distribution is described by means of a

simple recursive procedure. In two particular cases the model is analytically solvable: with high density and particles that always fuse into one, and in the case of constant density. In the reversible case (A + A A) offspring production is allowed, and the system can reach a stationary distribution, which is jointly calculated with the equilibrium density. The particular case, in which meeting particles react with probability one, admits an exact solution.

(A + A → A), the evolution of the particle distribution is described by means of a

simple recursive procedure. In two particular cases the model is analytically solvable: with high density and particles that always fuse into one, and in the case of constant density. In the reversible case (A + A A) offspring production is allowed, and the system can reach a stationary distribution, which is jointly calculated with the equilibrium density. The particular case, in which meeting particles react with probability one, admits an exact solution.

Original language | English |
---|---|

Pages (from-to) | 302-312 |

Journal | Nonlinear Dynamics and Systems Theory |

Volume | 19 |

Issue number | 2 |

Publication status | Published - 2019 |