N-body decomposition of bipartite networks

In this paper, we present a method to project co-authorship networks, that accounts in detail for the geometrical structure of scientists collaborations. By restricting the scope to 3-body interactions, we focus on the number of triangles in the system, and show the importance of multi-scientists (more than 2) collaborations in the social network. This motivates the introduction of generalized networks, where basic connections are not binary, but involve arbitrary number of components. We focus on the 3-body case, and study numerically the percolation transition.Comment: 5 pages, submitted to PR

Strong Shock Waves and Nonequilibrium Response in a One-dimensional Gas: a Boltzmann Equation Approach

We investigate the nonequilibrium behavior of a one-dimensional binary fluid on the basis of Boltzmann equation, using an infinitely strong shock wave as probe. Density, velocity and temperature profiles are obtained as a function of the mixture mass ratio \mu. We show that temperature overshoots near the shock layer, and that heavy particles are denser, slower and cooler than light particles in the strong nonequilibrium region around the shock. The shock width w(\mu), which characterizes the size of this region, decreases as w(\mu) ~ \mu^{1/3} for \mu-->0. In this limit, two very different length scales control the fluid structure, with heavy particles equilibrating much faster than light ones. Hydrodynamic fields relax exponentially toward equilibrium, \phi(x) ~ exp[-x/\lambda]. The scale separation is also apparent here, with two typical scales, \lambda_1 and \lambda_2, such that \lambda_1 ~ \mu^{1/2} as \mu-->0$, while \lambda_2, which is the slow scale controlling the fluid's asymptotic relaxation, increases to a constant value in this limit. These results are discussed at the light of recent numerical studies on the nonequilibrium behavior of similar 1d binary fluids.Comment: 9 pages, 8 figs, published versio

Singular forces and point-like colloids in lattice Boltzmann hydrodynamics

We present a second-order accurate method to include arbitrary distributions of force densities in the lattice Boltzmann formulation of hydrodynamics. Our method may be used to represent singular force densities arising either from momentum-conserving internal forces or from external forces which do not conserve momentum. We validate our method with several examples involving point forces and find excellent agreement with analytical results. A minimal model for dilute sedimenting particles is presented using the method which promises a substantial gain in computational efficiency.Comment: 22 pages, 9 figures. Submitted to Phys. Rev.

Coupling of thermal and mass diffusion in regular binary thermal lattice-gases

We have constructed a regular binary thermal lattice-gas in which the thermal diffusion and mass diffusion are coupled and form two nonpropagating diffusive modes. The power spectrum is shown to be similar in structure as for the one in real fluids, in which the central peak becomes a combination of coupled entropy and concentration contributions. Our theoretical findings for the power spectra are confirmed by computer simulations performed on this model.Comment: 5 pages including 3 figures in RevTex

Field induced stationary state for an accelerated tracer in a bath

Our interest goes to the behavior of a tracer particle, accelerated by a constant and uniform external field, when the energy injected by the field is redistributed through collision to a bath of unaccelerated particles. A non equilibrium steady state is thereby reached. Solutions of a generalized Boltzmann-Lorentz equation are analyzed analytically, in a versatile framework that embeds the majority of tracer-bath interactions discussed in the literature. These results --mostly derived for a one dimensional system-- are successfully confronted to those of three independent numerical simulation methods: a direct iterative solution, Gillespie algorithm, and the Direct Simulation Monte Carlo technique. We work out the diffusion properties as well as the velocity tails: large v, and either large -v, or v in the vicinity of its lower cutoff whenever the velocity distribution is bounded from below. Particular emphasis is put on the cold bath limit, with scatterers at rest, which plays a special role in our model.Comment: 20 pages, 6 figures v3:minor corrections in sec.III and added reference

Generalized dynamical density functional theory for classical fluids and the significance of inertia and hydrodynamic interactions

We study the dynamics of a colloidal fluid including inertia and hydrodynamic interactions, two effects which strongly influence the non-equilibrium properties of the system. We derive a general dynamical density functional theory (DDFT) which shows very good agreement with full Langevin dynamics. In suitable limits, we recover existing DDFTs and a Navier-Stokes-like equation with additional non-local terms.Comment: 5 pages, 4 figures, 4 supplementary movie files, I supplementary pd

On the velocity distributions of the one-dimensional inelastic gas

We consider the single-particle velocity distribution of a one-dimensional fluid of inelastic particles. Both the freely evolving (cooling) system and the non-equilibrium stationary state obtained in the presence of random forcing are investigated, and special emphasis is paid to the small inelasticity limit. The results are obtained from analytical arguments applied to the Boltzmann equation along with three complementary numerical techniques (Molecular Dynamics, Direct Monte Carlo Simulation Methods and iterative solutions of integro-differential kinetic equations). For the freely cooling fluid, we investigate in detail the scaling properties of the bimodal velocity distribution emerging close to elasticity and calculate the scaling function associated with the distribution function. In the heated steady state, we find that, depending on the inelasticity, the distribution function may display two different stretched exponential tails at large velocities. The inelasticity dependence of the crossover velocity is determined and it is found that the extremely high velocity tail may not be observable at ``experimentally relevant'' inelasticities.Comment: Latex, 14 pages, 12 eps figure

Kinetics and scaling in ballistic annihilation

We study the simplest irreversible ballistically-controlled reaction, whereby particles having an initial continuous velocity distribution annihilate upon colliding. In the framework of the Boltzmann equation, expressions for the exponents characterizing the density and typical velocity decay are explicitly worked out in arbitrary dimension. These predictions are in excellent agreement with the complementary results of extensive Monte Carlo and Molecular Dynamics simulations. We finally discuss the definition of universality classes indexed by a continuous parameter for this far from equilibrium dynamics with no conservation laws

Kinetic Theory of Response Functions for the Hard Sphere Granular Fluid

The response functions for small spatial perturbations of a homogeneous granular fluid have been described recently. In appropriate dimensionless variables, they have the form of stationary state time correlation functions. Here, these functions are expressed in terms of reduced single particle functions that are expected to obey a linear kinetic equation. The functional assumption required for such a kinetic equation, and a Markov approximation for its implementation are discussed. If, in addition, static velocity correlations are neglected, a granular fluid version of the linearized Enskog kinetic theory is obtained. The derivation makes no a priori limitation on the density, space and time scale, nor degree of inelasticity. As an illustration, recently derived Helfand and Green-Kubo expressions for the Navier-Stokes order transport coefficients are evaluated with this kinetic theory. The results are in agreement with those obtained from the Chapman-Enskog solution to the nonlinear Enskog kinetic equation.Comment: Submitted to J. Stat. Mec