We investigate the probability of observing a given pattern of n rises and falls in a random stationary data series. The data are modeled as a sequence of n+1 independent and identically distributed random numbers. This probabilistic approach has a combinatorial equivalent, where the data are...

In our model, $n$ traders interact with each other and with a central bank; they are taxed on the money they make, some of which is dissipated away by corruption. A generic feature of our model is that the richest trader always wins by 'consuming' all the others: another is the existence of a...

We investigate the full phase diagram of a column of grains near jamming, as a function of varying levels of frustration. Frustration is modelled by the effect of two opposing fields on a grain, due respectively to grains above and below it. The resulting four dynamical regimes (ballistic,...

Granular media jam into a panoply of metastable states. The way in which these states are achieved depends on the nature of local and global constraints on grains; here we investigate this issue by means of a non-equilibrium stochastic model of a hindered granular column near its jamming limit....

We investigate a model of interacting clusters which compete for growth. For a finite assembly of coupled clusters, the largest one always wins, so that all but this one die out in a finite time. This scenario of ‘survival of the biggest’ still holds in the mean-field limit, where the model...

The competing roles of grains and clusters in the dynamics of a driven sandpile are investigated via two models. First, we present a coupled-map lattice model of a slowly rotating sandpile: we find that our inclusion of parameters to represent grain reorganisation and inertia leads to a rich...

The loss angle δ is used to characterize the dielectric properties of inhomogeneous materials, in the framework of percolation theory. We have shown that δ takes the universal value δ = πs/2(s + t) at the percolation threshold (p = pc), and low frequency (ε → 0), where s and t are the...