R. Jullien’s research while affiliated with Université de Montpellier and other places

A model for the random deposition of spherical particles under the influence of a strong external field has been investigated numerically. In this model particles fall, one at a time, along vertical trajectories until they reach the surface of the deposit. They then follow a path of steepest descent on the surface of the deposit until a local minimum is reached. For a binary mixture of particles with different radii the density is larger than that found for the monodisperse case. A segregation transition is found which occurs when the smaller spheres can penetrate into the random deposit of larger spheres. The exponent characterizing the divergence of the penetration length is estimated to have a value of 0.55.

A two-dimensional model for particle size segregation by shaking has been developed and applied to a binary mixture of discs with radius ratio Φ. The simulation results can be understood in terms of a simple theoretical model that becomes exact in the limit Φ → ∞. When a single large disc is imbedded in a regular packing of small discs, it is shown that segregation occurs only for values of Φ above a critical value Φc which depends on the angle of repose α and varies between 2.993... and 12 when α varies from 30° to 60°.

A recently introduced version of the Eden model is numerically investigated in strips of width l and height h in 2d, reaching clusters containing up to 108 ÷ 2 109 particles. The surface thickness is shown to obey the scaling σ ~ lαf(h/lα/β) with f(x) → const, for x → ∞ and f(x) ~ xβ for x → 0. Our result for α is very close to 0.5 (within less than 1%) and we estimate β = 0.307 ± 0.007. Two directions of the growth on a square lattice have been chosen (along an axis and diagonal to the axis). While the exponents seem to be insensitive to the direction of growth, there is a very small anisotropy in the amplitudes of σ and in the number of surface sites.

The effects of spatial correlations on ballistic deposition have been investigated using two-dimensional lattice models in which particles are deposited at the end of the steps in a horizontal Levy flight with a step length distribution exponent of f. The exponents α and β which describe how the surface thickness (ξ) depends on the strip width (L) and the mean deposit thickness (or time) have been measured. The exponents α and β satisfy the theoretical scaling relationship α + α/β = 2 for f < 1. For 1 < f < 2 the deposit has a finite asymptotic density, but the scaling relationship is not obeyed. Finally, for f > 2 the deposit structure becomes fractal. With restructuring the exponents α and β increase linearly from 1/2 and 1/4, respectively, for f = 0 to 1 and 1/2 for f = 1. For f > 1, α = 1 and β = 1/2.

The random packing of identical hard disks generated by a ballistic model with complete restructuring has been investigated. The density of defects (i.e. particles having a number of contacts different from 4) was found to decrease as a power law with the distance from the bottom of the packing in the limit of very large distances. In the asymptotic very large height regime, a random structure without defect was found which is characterized by a broad angular distribution for the orientations of the bonds between contacting disks.

The sintering of aerogels is modelled by combining two known methods: the method of the array of cylinders used by Scherer and the dressing of particles of fractal aggregates. In this paper, bonds between particles of an on-lattice computed gel are replaced by cylinders. During sintering, the radius of the cylinders increases. We compute this radius vs. the renormalized concentration of the gel, in a first step by an analytical method and then by a numerical method. By deriving the volume as a function of the concentration, we also obtain the specific surface during sintering.

Several three-dimensional off-lattice models for ballistic deposition including simple rearrangement processes have been explored. These models are intended to represent the sort of restructuring processes which might occur in the sedimentation of small particles under the influence of an external (gravitational) field. Accurate values are obtained for the densities of the deposits generated by these models and some of their surface properties are investigated.

Recent work to understand aggregation of particles using the concept of fractal is reviewed. We introduce all the tools issued from the theory of fractals, and which are useful for our study. Then we define and detail the two main models: the particle-cluster process where individual particles come to stick on large clusters, and the cluster-cluster process where clusters diffuse and stick when they collide. The important parameters of these models are varied and their influence on the resulting geometrical disordered structure is discussed. All along the paper, the connections with existing experiments are given.

To find the origin of the diffusion channels observed in sodium silicate glasses, we have performed classical molecular dynamics simulations of Na2O-4SiO2 during which the mass of the Si and O atoms has been multiplied by a tuning coefficient. We observe that the channels disappear and that the diffusive motion of the sodium atoms vanishes if this coefficient is larger than a threshold value. Above this threshold the vibrational states of the matrix are not compatible with those of the sodium ions. We thus interpret the decrease of the diffusion by the absence of resonance conditions.

Encouraged by experiments on 4He in aerogels, we confine planar spins in the pores of simulated aerogels (diffusion limited cluster-cluster aggregation) in order to study the effect of quenched disorder on the critical behavior of the three-dimensional XY model. Monte Carlo simulations and finite-size scaling are used to determine critical couplings K(c) and exponents. In agreement with experiments, clear evidence of change in the thermal critical exponents nu and alpha is found at nonzero volume fractions of impurities. These changes are explained in terms of hidden long-range correlations within disorder distributions.