An example of numerical simulation in causal set dynamics

6th International Workshop DICE2012 Spacetime – Matter – Quantum Mechanics: From the Planck Scale to Emergent Phenomena

物理学;力学

Krugly, Alexey L.^1 ; Tserkovnikov, Ivan A.^2

Scientific Research Institute for System Analysis, Russian Academy of Science, Nahimovskiy pr. 36 k. 1, 117218, 36, Moscow, Russia^1

Russian Presidential Academy of National Economy and Public Administration, Faculty of Economics, Vernadskogo pr. 82, 119571, Moscow, Russia^2

关键词: Directed acyclic graph (DAG);    Discrete fourier transformation;    Microscopic scale;    Outdegree;    Random Walk;    Repetitive structure;    Sequential growth;    Simple stochastic;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/442/1/012042/pdf
DOI  :  10.1088/1742-6596/442/1/012042

学科分类：力学，机械学

来源: IOP

【 摘 要 】

The model of a discrete pregeometry on a microscopic scale is an x-graph. This is a directed acyclic graph. An outdegree and an indegree of each vertex are not more than 2. The sets of vertices and edges of x-graph are particular cases of causal sets. The sequential growth of a graph is an addition of new vertices one by one. A simple stochastic algorithm of sequential growth of x-graph are considered. It is based on a random walk at the x-graph. The particles in this model must be self-organized repetitive structures. We introduce the method of search of such repetitive structures. It is based on a discrete Fourier transformation. An example of numerical simulation is introduced.