Although there is a vast engineering literature for granular materials, as a subject for physicists it has seen great growth in recent years. This is because, when stripped down to the fundamental problem, it is quite novel, and demands a rethink of the kind of laws familiar elsewhere in...

We consider the problem of stress transmission in granular materials. We formulate the simplest statically determinate problem of stress transmission through a static granular material. This is the case when grains are rigid and have an average coordination number of z̄=d+1. Under this...

For packed i.e., “jammed”, hard and rough objects kinetic energy is a minor and ignorable quantity, as is elastic strain. Hence in the static case, the stress equations need supplementing by “missing equations” depending solely on configurations. A different pathway of analysis is the...

A quantum spherical version of the site-random XY model in the presence of random field is presented in the boson space. In the phase diagram drawn as a function of the strength of random field, we find that the ferromagnetic and spin-glass phases are reduced by quantum fluctuations and...

We review the main tools which allow for the statistical characterization of weighted networks. We then present two case studies, the airline connection network and the scientific collaboration network which are representatives of critical infrastructure and social system, respectively. The main...

We present a simple mechanism for generating undirected scale-free networks using random walkers, where the network growth is determined by choosing parent vertices by sequential random walks. We show that this mechanism produces scale-free networks with degree exponent γ=3 and clustering...

Several studies on real complex networks from different fields as biology, economy, or sociology have shown that the degree of nodes (number of edges connected to each node) follows a scale-free power-law distribution like P(k)≈k-γ, where P(k) denotes the frequency of the nodes that are...

We introduce a “Hamiltonian”-like function, called the volume function, indispensable to describe the ensemble of jammed matter such as granular materials and emulsions from a geometrical point of view. The volume function represents the available volume of each particle in the jammed...

In an earlier paper, Ngan (Phys. Rev. E 68 (2003) 011301) proposed a statistical mechanics-based theory to predict the mathematical form of the probability force distribution of contact forces in stressed granular packings. However, the wrong choice of the mean-force constraint in that work...

The simplest solvable problem of stress transmission through a static granular material is when the grains are perfectly rigid and have an average coordination number of z̄=d+1. Under these conditions there exists an analysis of stress which is independent of the analysis of strain and the d...