Force distribution in a randomly perturbed lattice of identical particles with $1/r^2$ pair interaction

We study the response of a two-dimensional hexagonal packing of massless, rigid, frictionless spherical grains due to a vertically downward point force on a single grain at the top layer. We use a statistical approach, where each mechanically stable configuration of contact forces is equally likely. We show that this problem is equivalent to a correlated $q$-model. We find that the response is double-peaked, where the two peaks, sharp and single-grain diameter wide, lie on th...

We present exact results on the dynamics of a biased, by an external force ${\bf F}$, intruder (BI) in a two-dimensional lattice gas of unbiased, randomly moving hard-core particles. Going beyond the usual analysis of the force-velocity relation, we study the probability distribution $P({\bf R}_n)$ of the BI displacement ${\bf R}_n$ at time {\it n}. We show that despite the fact that the BI drives the gas to a non-equilibrium steady-state, $P({\bf R}_n)$ converges to a Gaussi...

We show that the self-gravitating gas at thermal equilibrium has an infinite volume limit in the three ensembles (GCE, CE, MCE) when (N, V) -> infty, keeping N/V^{1/3} fixed, that is, with eta = G m^2 N/[ V^{1/3} T] fixed. We develop MonteCarlo simulations, analytic mean field methods (MF) and low density expansions. We compute the equation of state and find it to be locally p(r) = T rho_V(r), that is a local ideal gas equation of state. The system is in a gaseous phase for e...

We study the statistical properties of the gravitational field generated by galaxy distribution observed bythe Sloan Digital Sky Survey (DR7). We characterize the probability density function of gravitational force fluctuations and relate its limiting behaviors to the correlation properties of the underlying density field. In addition, we study whether the PDF converges to an asymptotic shape within sample volumes. We consider several volume-limited samples of the Sloan Digit...

It has been recently shown that randomly charged surfaces can exhibit long range electrostatic interactions even when they are net neutral. These forces depend on the specific realization of charge disorder and thus exhibit sample to sample fluctuations about their mean value. We analyze the fluctuations of these forces in the parallel slab configuration and also in the sphere-plane geometry via the proximity force approximation. The fluctuations of the normal forces, that ha...

Purely self-gravitating systems of point particles have been extensively studied in astrophysics and cosmology, mainly through numerical simulations, but understanding of their dynamics still remains extremely limited. We describe here results of a detailed study of a simple class of cold quasi-uniform initial conditions, for both finite open systems and infinite systems. These examples illustrate well the qualitative features of the quite different dynamics observed in each ...

We present an extension of a simple automaton model to incorporate non-local interactions extending over a spatial range in lattice gases. {}From the viewpoint of Statistical Mechanics, the lattice gas with interaction range may serve as a prototype for non-ideal gas behavior. {}From the density fluctuations correlation function, we obtain a quantity which is identified as a potential of mean force. Equilibrium and transport properties are computed theoretically and by numeri...

A simple lattice gas model with random fields and gravity is introduced to describe a system of grains moving in a disordered environment. Off equilibrium relaxations of bulk density and its two time correlation functions are numerically found to show logarithmic time dependences and "aging" effects. Similitudes with dry granular media are stressed. The connections with off equilibrium dynamics in others kinds of "frustrated" lattice models in presence of a directional drivin...

We present an analysis of different sets of gravitational N-body simulations, all describing the dynamics of discrete particles with a small initial velocity dispersion. They encompass very different initial particle configurations, different numerical algorithms for the computation of the force, with or without the space expansion of cosmological models. Despite these differences we find in all cases that the non-linear clustering which results is essentially the same, with ...

In infinite dimension, many-body systems of pairwise interacting particles provide exact analytical benchmarks for features of amorphous materials, such as the stress-strain curve of glasses under quasistatic shear. Here, instead of a global shear, we consider an alternative driving protocol as recently introduced in Ref. [1], which consists of randomly assigning a constant local displacement on each particle, with a finite spatial correlation length. We show that, in the inf...