Gas Transport in Porous Media: Simulations and Experiments on Partially Densified Aerogels

The experimental density dependence of gas (argon and nitrogen) permeability of partially densified silica aerogels in the Knudsen regime is quantitatively accounted for by a computer model. The model simulates both the structure of the sintered material and the random ballistic motion of a point particle inside its voids. The same model is also able to account for the densit y dependence of the specific pore surface as measured from nitrogen adsorption experiments.Comment: RevTex, 11 pages + 5 postscript figures appended using "uufiles". Published in Europhys. Lett. 29, p. 567 (1995

Classical molecular dynamics simulations of amorphous silica surfaces

We have adapted classical molecular dynamics to study the structural and dynamical properties of amorphous silica surfaces. Concerning the structure, the density profile exhibits oscillations perpendicularly to the surface as observed in liquid metal surfaces and the pair correlation functions as well as the angle distributions show features (absent in the interior of the films) that can be attributed to the presence of 2-fold rings which are perpendicular to the surface. From the mean-squared displacement of the non bridging oxygen atoms we find that in the interior region they move perpendicular to the surface while they move parallel to it in the surface region.Comment: 7 pages,5 figures - To be published in J. Phys. C.

Phase diagram of the frustrated spin ladder

We re-visit the phase diagram of the frustrated spin-1/2 ladder with two competing inter-chain antiferromagnetic exchanges, rung coupling J_\perp and diagonal coupling J_\times. We suggest, based on the accurate renormalization group analysis of the low-energy Hamiltonian of the ladder, that marginal inter-chain current-current interaction plays central role in destabilizing previously predicted intermediate columnar dimer phase in the vicinity of classical degeneracy line J_\perp = 2J_\times. Following this insight we then suggest that changing these competing inter-chain exchanges from the previously considered antiferromagnetic to the ferromagnetic ones eliminates the issue of the marginal interactions altogether and dramatically expands the region of stability of the columnar dimer phase. This analytical prediction is convincingly confirmed by the numerical density matrix renormalization group and exact diagonalization calculations as well as by the perturbative calculation in the strong rung-coupling limit. The phase diagram for ferromagnetic J_\perp and J_\times is determined.Comment: 12 pages, 12 figures, 1 Table. v2: version to appear in Phys. Rev.

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

Small Angle Scattering by Fractal Aggregates: A Numerical Investigation of the Crossover Between the Fractal Regime and the Porod Regime

Fractal aggregates are built on a computer using off-lattice cluster-cluster aggregation models. The aggregates are made of spherical particles of different sizes distributed according to a Gaussian-like distribution characterised by a mean $a_0$ and a standard deviation $\sigma$. The wave vector dependent scattered intensity $I(q)$ is computed in order to study the influence of the particle polydispersity on the crossover between the fractal regime and the Porod regime. It is shown that, given $a_0$, the location $q_c$ of the crossover decreases as $\sigma$ increases. The dependence of $q_c$ on $\sigma$ can be understood from the evolution of the shape of the center-to-center interparticle-distance distribution function.Comment: RevTex, 4 pages + 6 postscript figures, compressed using "uufiles", published in Phys. Rev. B 50, 1305 (1994

Discontinuous percolation transitions in real physical systems

We study discontinuous percolation transitions (PT) in the diffusion-limited cluster aggregation model of the sol-gel transition as an example of real physical systems, in which the number of aggregation events is regarded as the number of bonds occupied in the system. When particles are Brownian, in which cluster velocity depends on cluster size as $v_s \sim s^{\eta}$ with $\eta=-0.5$, a larger cluster has less probability to collide with other clusters because of its smaller mobility. Thus, the cluster is effectively more suppressed in growth of its size. Then the giant cluster size increases drastically by merging those suppressed clusters near the percolation threshold, exhibiting a discontinuous PT. We also study the tricritical behavior by controlling the parameter $\eta$, and the tricritical point is determined by introducing an asymmetric Smoluchowski equation.Comment: 5 pages, 5 figure

Kinetic Antiferromagnetism in the Triangular Lattice

We show that the motion of a single hole in the infinite $U$ Hubbard model with frustrated hopping leads to weak metallic antiferromagnetism of kinetic origin. An intimate relationship is demonstrated between the simplest versions of this problem in 1 and 2 dimensions, and two of the most subtle many body problems, namely the Heisenberg Bethe ring in 1-d and the 2-dimensional triangular lattice Heisenberg antiferromagnet.Comment: 10 pages, 2 figures, 5 supplementary figures; Figures fixe

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

A new conjecture extends the GM law for percolation thresholds to dynamical situations

The universal law for percolation thresholds proposed by Galam and Mauger (GM) is found to apply also to dynamical situations. This law depends solely on two variables, the space dimension d and a coordinance numberq. For regular lattices, q reduces to the usual coordination number while for anisotropic lattices it is an effective coordination number. For dynamical percolation we conjecture that the law is still valid if we use the number q_2 of second nearest neighbors instead of q. This conjecture is checked for the dynamic epidemic model which considers the percolation phenomenon in a mobile disordered system. The agreement is good.Comment: 8 pages, latex, 3 figures include