Modelling Complex Multi-particle Transport: From Smooth Flow to Cluster Formation
One of the major problems with multi-particle flows is their tendency to spontaneously form clusters. This is a hot topic in contemporary science not only because of its fundamental interest but also because of its ubiquity in industrial applications and everyday life. Here we present a clear-cut method to model the clustering, dividing the available space in a grid of discrete cells and describing the dynamics from cell to cell by means of a flux function. The method is illustrated by two representative examples: the onset of clustering in granular flow on a conveyor belt and the formation of traffic jams on the highway. Further insight is gained by studying the continuum limit of the model.
KeywordsPattern formation Granular transport Clustering
This work is part of the research programme of the European Complexity-NET project “Complex Matter”, which is financially supported by the Greek General Secretariat for Research and Technology (GSRT).
- 14.Van der Weele K, Mikkelson R, Van der Meer D, Lohse D (2004) Cluster formation in compartmentalized granular gases. In: Hinrichsen H, Wolf DE (eds) The physics of granular media. Wiley, New York, pp 117–139 Google Scholar
- 17.Wolf DE, Schreckenberg ME, Bechem A (eds) (1996) Traffic and granular flow. World Scientific, Singapore. See also in: Schreckenberg ME, Wolf DE (eds) (1998) Traffic and granular flow ’97. Springer, Berlin; Helbing D et al (eds) (2000) Traffic and granular flow ’99. Springer, Berlin; Fukui M et al (eds) (2003) Traffic and granular flow ’01. Springer, Berlin; Hoogendoorn SP, Luding S, Bovy PHL, Schreckenberg M, Wolf DE (eds) (2005) Traffic and granular flow ’03. Springer, Berlin Google Scholar