|
During the past decades our theoretical understanding of the physical properties of liquids has been transformed by the synergy of theory and numerical simulation. By comparison, our understanding of the properties of granular packings is still at a much less advanced stage, not least because of a lack of hard numerical data for a key quantity: the packing entropy. The aim of the proposed research is to fill this gap. The theoretical work of Edwards and collaborators [1,2] suggests that, in exactly the same way that knowledge of the partition function of thermal many-body systems makes it possible to predict equilibrium properties and equations of state, so knowledge of the packing entropy would enable the prediction of the bulk behaviour of granular matter. However, we cannot currently test this suggestion because we have no hard numerical data on the packing entropy. Without numerical tests of the existing theories, fundamental progress is blocked. The key to progress is therefore a quantitative knowledge of the packing entropy of granular materials. To evaluate this entropy, we need techniques to compute the number of distinct configurations that assemblies of particles can pack into. This is a daunting task because the number of distinct jammed states grows exponentially with system size. Yet, progress is now within reach. One of the applicants (DF) has recently developed and tested a numerical scheme that makes it possible to count the number of jammed states, even if this number is so large that direct enumeration is utterly impossible. In this project, we will combine the Monte Carlo sampling approach of DF with the methods developed by RB to distinguish topologically distinct jammed structures using basic volume elements, called 'quadrons'. The simulations will be used to test existing theoretical predictions on properties of granular media and, where necessary, to modify the existing theoretical understanding. To establish contact with experiments, we will then investigate the relation between the history of preparation of granular packings and the number of accessible jammed states. As a specific, and very interesting example, we will study the factors that determine whether a granular material will form a crystalline or a disordered structure. The understanding of the nature of random packings is not only an intriguing fundamental theoretical problem, but is also key to advancing on a wide range of scientific and technological problems, as granular matter is ubiquitous in nature and of great importance in technology.[1]. S.F. Edwards, IMA Bulletin 25, A03 3/4 (1989); S.F. Edwards and R.B. Oakeshott, Physica D 38, 88 (1989); S.F. Edwards and R.B. Oakeshott, Physica A 157, 1080 (1989); A. Mehta, S.F. Edwards, Physica A 157, 1091 (1989); S.F. Edwards, Rheologica Acta 29, 493 (1990)[2]. R. Blumenfeld and S. F. Edwards, Phys. Rev. Lett. 90, 114303 (2003); R. Blumenfeld and S. F. Edwards, Eur. Phys. J. E 19, 23-30 (2006)
|