Related papers: Free volume distributions inside a bidimensional g…
The probability distribution for the free energy of directed polymers in random media (DPRM) with uncorrelated noise in $d=1+1$ dimensions satisfies the Tracy-Widom distribution. We inquire if and how this universal distribution is modified…
Using an ensemble of high resolution 2D numerical simulations, we explore the scaling properties of cosmological density fluctuations in the non-linear regime. We study the scaling behaviour of the usual $N$--point volume-averaged…
A random network is grown by introducing at unit rate randomly selected nodes on the Euclidean space. A node is randomly connected to its $i$-th predecessor of degree $k_i$ with a directed link of length $\ell$ using a probability…
The average node-to-node distance of scale-free graphs depends logarithmically on N, the number of nodes, while the probability distribution function (pdf) of the distances may take various forms. Here we analyze these by considering…
We determine the non-equilibrium grain size distribution during the crystallization of a solid in $d$ dimensions at fixed thermodynamic conditions, for the random nucleation and growth model, and in absence of grain coalescence. Two…
A gravity-driven flow of grains through a narrow pipe in vacuum is studied by means of a one-dimensional model with two coefficients of restitution. Numerical simulations show clearly how density waves form when a strikingly simple…
The evolution of occupied volume under progressive fragmentation of granular matter is studied using a purely geometric model. Rather than modelling disorder directly, properties are investigated by analysing highly ordered reference…
We study a percolation model on the square lattice, where clusters "freeze" (stop growing) as soon as their volume (i.e. the number of sites they contain) gets larger than N, the parameter of the model. A model where clusters freeze when…
We characterize semicircular distribution by the freeness of linear and quadratic forms in noncommutative random variables from a tracial $W^*$-probability space with relaxed moment conditions.
Formulating a statistical mechanics for granular matter remains a significant challenge, in part, due to the difficulty associated with a complete characterization of the systems under study. We present a fully characterized model of a…
A scale-free network is grown in the Euclidean space with a global directional bias. On a vertical plane, nodes are introduced at unit rate at randomly selected points and a node is allowed to be connected only to the subset of nodes which…
We show random polymer is diffusive in dimensions 1 and 2 in probability in an intermediate scaling regime. The scale is $\beta= o(N^{-1/4})$ in d=1 and $\beta=o((\log N)^{-1/2})$ in $d=2$ as $N\rightarrow \infty$.
Let $G$ be a free-by-cyclic group or a 2-dimensional right-angled Artin group. We provide an algebraic and a geometric characterization for when each aspherical simplicial complex with fundamental group isomorphic to $G$ has minimal volume…
We measure the two-point density correlations and Voronoi cell distributions of cyclically sheared granular spheres obtained with a fluorescence technique and compare them with random packing of frictionless spheres. We find that the radial…
We study minima statistics of the 2d Gaussian Free Field on circles in the unit disk with Dirichlet boundary condition. Free energy distributions of the associated Random Energy models are exactly calculated in the high temperature phase,…
We study the evolution of random graphs where edges are added one by one between pairs of weighted vertices so that resulting graphs are scale-free with the degree exponent $\gamma$. We use the branching process approach to obtain scaling…
We show that entanglement entropy of free fermions scales faster then area law, as opposed to the scaling $L^{d-1}$ for the harmonic lattice, for example. We also suggest and provide evidence in support of an explicit formula for the…
Granular flow problems characterized by large deformations are widespread in various applications, including coastal and geotechnical engineering. The paper deals with the application of a rigid-perfectly plastic two-phase model extended by…
A possible approach to the statistical description of granular assemblies starts from Edwards' assumption that all blocked states occupying the same volume are equally probable (S.F. Edwards, R. Oakeshott, Physica A 157, 1080 (1989)). We…
By means of a simple model system, the total volume fluctuations of a tapped granular material in the steady state are studied. In the limit of a system with a large number of particles, they are found to be Gaussian distributed, and…