Solvable structures of a simple model of earthquakes

23rd International Conference on Integrable Systems and Quantum Symmetries

Bialecki, Mariusz^1

Institute of Geophysics, Polish Academy of Sciences, Warszawa, Poland^1

关键词: Between clusters;    Distance interaction;    Motzkin numbers;    Simple modeling;    Solvable case;    Stationary state;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/670/1/012010/pdf
DOI  :  10.1088/1742-6596/670/1/012010

来源: IOP

【 摘 要 】

This paper propose an extension of Random Domino Automaton by introducing extra parameter related to a very short-distance interactions between clusters which allows to isolate influence two mechanisms of clusters grow, namely enlarging and coalescence. In this setting statistically stationary state under assumption of independence of clusters is investigated and respective set of equations is derived. Moreover, a special solvable case is studied in detail and it is shown how to derive Motzkin numbers out of the automaton for a family of parameters without considering a limit.