Influence of surfactants on the structure of titanium oxide gels : experiments and simulations

We report here on experimental and numerical studies of the influence of surfactants on mineral gel synthesis. The modification of the gel structure when the ratios water-precursor and water-surfactant vary is brought to the fore by fractal dimension measures. A property of {\em polydispersity of the initial hydrolysis} is proposed to explain these results, and is successfuly tested through numerical experiments of three dimensional chemically limited aggregation.Comment: 12 pages, 4 Postscript figures, uses RevTe

New universality class for the three-dimensional XY model with correlated impurities: Application to 4^4He in aerogels

Encouraged by experiments on $^4$He 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 {\it hidden} long-range correlations within disorder distributions.Comment: 4 pages, 4 figures, submitted to Phys. Rev. Let

Fluctuating Bond Aggregation: a Model for Chemical Gel Formation

The Diffusion-Limited Cluster-Cluster Aggregation (DLCA) model is modified by including cluster deformations using the {\it bond fluctuation} algorithm. From 3$d$ computer simulations, it is shown that, below a given threshold value $c_g$ of the volumic fraction $c$, the realization of all intra-aggregate bonding possibilities prevents the formation of a gelling network. For $c>c_g$, the sol-gel transition occurs at a time $t_g$ which, in contrast to DLCA, doesnot diverge with the box size. Several results are reported including small angle scattering curves and possible applications are discussed.Comment: RevTex, 9 pages + 3 postscript figures appended using "uufiles". To appear in Phys. Rev. Let

Stochastic Model for the Motion of a Particle on an Inclined Rough Plane and the Onset of Viscous Friction

Experiments on the motion of a particle on an inclined rough plane have yielded some surprising results. For example, it was found that the frictional force acting on the ball is viscous, {\it i.e.} proportional to the velocity rather than the expected square of the velocity. It was also found that, for a given inclination of the plane, the velocity of the ball scales as a power of its radius. We present here a one dimensional stochastic model based on the microscopic equations of motion of the ball, which exhibits the same behaviour as the experiments. This model yields a mechanism for the origins of the viscous friction force and the scaling of the velocity with the radius. It also reproduces other aspects of the phase diagram of the motion which we will discuss.Comment: 19 pages, latex, 11 postscript figures in separate uuencoded fil

Spin Gap in a Doped Kondo Chain

We show that the Kondo chain away from half-filling has a spin gap upon the introduction of an additional direct Heisenberg coupling between localized spins. This is understood in the weak-Kondo-coupling limit of the Heisenberg-Kondo lattice model by bosonization and in the strong-coupling limit by a mapping to a modified t-J model. Only for certain ranges of filling and Heisenberg coupling does the spin gap phase extend from weak to strong coupling.Comment: 4 pages RevTeX including 4 eps figures; minor corrections and clarification

Size segregation and convection

The size segregation of granular materials in a vibrating container is investigated using Molecular Dynamics. We find that the rising of larger particles is accompanied by the existence of convection cells even in the case of the lowest possible frequencies. The convection can, however, also be triggered by the larger particle itself. The possibility of rising through this mechanism strongly depends on the depth of the larger particle.Comment: 7 pages, 4 figure

Kondo Insulators Modeled by the One Dimensional Anderson Lattice: A Numerical Renormalization Group Study

In order to better understand Kondo insulators, we have studied both the symmetric and asymmetric Anderson lattices at half-filling in one dimension using the density matrix formulation of the numerical renormalization group. We have calculated the charge gap, spin gap and quasiparticle gap as a function of the repulsive interaction U using open boundary conditions for lattices as large as 24 sites. We find that the charge gap is larger than the spin gap for all U for both the symmetric and asymmetric cases. RKKY interactions are evident in the f-spin-f-spin correlation functions at large U in the symmetric case, but are suppressed in the asymmetric case as the f-level approaches the Fermi energy. This suppression can also be seen in the staggered susceptibility and it is consistent with neutron scattering measurements in CeNiSn.Comment: 32 pages, Latex file with Postcript figures

Fractal formation and ordering in random sequential adsorption

We reveal the fractal nature of patterns arising in random sequential adsorption of particles with continuum power-law size distribution, $P(R)\sim R^{\alpha-1}$, $R \le R_{\rm max}$. We find that the patterns become more and more ordered as $\alpha$ increases, and that the Apollonian packing is obtained at $\alpha \to \infty$ limit. We introduce the entropy production rate as a quantitative criteria of regularity and observe a transition from an irregular regime of the pattern formation to a regular one. We develop a scaling theory that relates kinetic and structural properties of the system.Comment: 4 pages, RevTex, 4 postscript figures. To appear in Phys.Rev.Let

Two-phase densification of cohesive granular aggregates

When poured into a container, cohesive granular materials form low-density, open granular aggregates. If pressed upon with a ram, these aggregates densify by particle rearrangement. Here we introduce experimental evidence to the effect that particle rearrangement is a spatially heterogeneous phenomenon, which occurs in the form of a phase transformation between two configurational phases of the granular aggregate. We then show that the energy landscape associated with particle rearrangement is consistent with our interpretation of the experimental results. Besides affording insight into the physics of the granular state, our conclusions are relevant to many engineering processes and natural phenomena.Comment: 7 pages, 3 figure