ANNUAL REPORT 2005 - Universiteit Utrecht

2 Scientific highlightsThis chapter presents two highlights of theoretical research carried out by members ofthe Research School. One concerns work on granular matter by the groups of Amsterdamand Leiden. This work belongs to statistical physics, one of the topics in theme2 of the school. The contribution has been written by Bernard Nienhuis. The secondhighlight concerns a topic in quantum gravity and belongs to theme 1. It deals withthe emergence of space and time. This work was carried out by the group in Utrechtin collaboration with researchers in Copenhagen and Krakow. The contribution hasbeen written by Renate Loll.Scale invariance and universality of force networks in staticgranular matter (Bernard Nienhuis, UvA)Pebbles in a heap and grains of rice in a bag are kept in place by a network of contactforces which forms a fractal structure. The associated fractal dimensions and distributionfunction are universal, i.e. independent of the details of the grains considered.This is the surprising outcome of a study of force networks in so-called static granularmatter, carried out by Srdjan Ostojic, Ellák Somfai and Bernard Nienhuis belongingto the groups of Amsterdam and Leiden. The discovery of these properties providesa new test for theoretical models, and promises a more elaborate mathematical descriptionof force networks in granular matter, but also other systems such as foamand emulsions. These results were published in Nature [1].Granular matter has been an extremely active field of research in the recent years.It concerns a form of matter, ubiquitous in both nature and industry: sand dunes,piles of apples at the grocer’s, or pills in a conveyor belt are just a few examples. Thebehaviour of such assemblies of macroscopic particles is far from being understoodsatisfactorily and any insight gained on their properties is of direct consequence forcivil engineering and industrial processing technology.Static granular matter, formed by grains at rest, behaves in many aspects as a solid.If an external stress is applied, the assembly will resist it and remain at rest, as longas the stress is not too large. This rigidity is in first place due to inter-grain contactforces, which form a tenuous network (see Figure 2.1). These force networks determinefundamental physical properties of granular materials such as stability, elasticityand sound transmission.A striking feature of the networks is the existence of irregular spatial patterns. As alarge contact force on one side of a particle is typically balanced by another one on theother side, large forces tend to align in filamentary structures called “force chains”.