Granular matter and networks: three related examples

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Granular matter is broadly defined as the class of materials composed of large numbers of discrete solid particles or grains, where the grains are large enough so that they do not suffer thermal fluctuations, and with a cut-off size being approximately one micron. On first viewing granular matter constitutes a simpler class of matter than soft matter, since quantum effects and temperature play no role. This view, however, is misleading. Granular matter displays a rich set of behaviors and serves as a test-bed for an array of complex systems tools with a potentially wide range of applicability that goes well outside the realm of granular materials and can be extended to concentrated emulsions and pastes. It may be argued that some of the mathematical representations of complex systems, such as networks or agent-based representations, are but charicatures of the actual systems. However, it is undeniably true that some representations have the power to transcend disciplines. Consider for example the highly idealized model of segregation in cities by Thomas Schelling, the co-winner of the 2005 Nobel Memorial Prize for Economic Science. In his book Micromotives and Macrobehavior (WW Norton, New York, 2006) Schelling considers many forms of collective behavior. In one of them, dealing with segregation in cities, a city is represented by a square grid and individuals by colors, say red and green. Green individuals have a degree of tolerance towards red, and red towards green. The surprise is that even if individuals are tolerant the result is a macroscopically segregated system with structures representing spinodal decomposition. And that is precisely the point: someone looking at this problem in social sciences with the perspective of material scientist and spinodal decomposition may have anticipated the qualitative aspects of the result. This short article considers three topics in granular physics, connected though a networks approach, starting with small scales and moving progressively towards larger scales. Although these topics can, in principle, be studied from a more traditional perspective, one finds that the networks viewpoint can inspire new analysis techniques, provide new clues as to the underlying phenomena and generate new, broad interpretations of results that might not always be gained from the more traditional viewpoints.