Time- and Event-oriented Spreadsheet Modelling of ARGESIM Benchmark C12 'Collision Processes in Rows of Spheres'

Abstract

This Benchmark Study with educational key aspects presents a spreadsheet-based approach to ARGESIM Benchmark C12 ‘Collision Processes in Rows of Spheres’. The process, the collision of spheres in a row, is seen as discrete process with a discrete time base, using two modelling approaches. A classical time-oriented approach describes the movement of the spheres by a discrete-time model, the collisions are approximated within the discretization points. The event-oriented approach makes use of the explicit movement formula and determines a sequence of exact collision times and collision events. Both approaches are implemented in the spreadsheet program Excel, which is quite suitable for simulation of discrete processes by means of recursive formulas. The implementation uses standard features of Excel, so that the provided sources can be used in arbitrary spreadsheet programs. Interestingly, with given medium accuracy and sufficient time resolution, time-oriented and event-oriented results coincide. The study also concentrates on educational aspects in giving a sketch on the physical background of elastic and inelastic collisions, in giving hints for proper implementation, and in providing background information on the selection of required experiments with the model (benchmark tasks). Introduction Collision Processes in Rows of Spheres 1 Model Equations mi d a Bicher et al. Spreadsheet Modelling of ARGESIM Benchmark C12 ‘Collision of Spheres’ 206 SNE 28(4) – 12/2018 B N E Figure 1: Spheres in a row – pendulum with infinite length.