Generalized model of blockage in particulate flow limited by channel carrying capacity.

We investigate stochastic models of particles entering a channel with a random time distribution. When the number of particles present in the channel exceeds a critical value N, a blockage occurs and the particle flux is definitively interrupted. By introducing an integral representation of the n-particle survival probabilities, we obtain exact expressions for the survival probability, the distribution of the number of particles that pass before failure, the instantaneous flux of exiting particles, and their time correlation. We generalize previous results for N=2 to an arbitrary distribution of entry times and obtain exact solutions for N=3 for a Poisson distribution and partial results for N≥4.

Non-markovian models of blocking in concurrent and countercurrent flows.

We investigate models in which blocking can interrupt a particulate flow process at any time. Filtration, and flow in micro or nanochannels and traffic flow are examples of such processes. We first consider concurrent flow models where particles enter a channel randomly. If at any time two particles are simultaneously present in the channel, failure occurs. The key quantities are the survival probability and the distribution of the number of particles that pass before failure. We then consider a counterflow model with two opposing Poisson streams. There is no restriction on the number of particles passing in the same direction, but blockage occurs if, at any time, two opposing particles are simultaneously present in the passage.

Formulation and mechanical properties of emulsion-based model polymer foams.

We produce cellular material based on the formulation of model emulsions whose drop size and composition may be continuously tuned. The obtained solid foams are characterized by narrow cell and pore size distributions in direct relation with the emulsion structure. The mechanical properties are examined, by varying independently the cell size and the foam density, and compared to theoretical predictions. Surprisingly, at constant density, Young's modulus depends on the cell size. We believe that this observation results from the heterogeneous nature of the solid material constituting the cell walls and propose a mean-field approach that allows describing the experimental data. We discuss the possible origin of the heterogeneity and suggest that the presence of an excess of surfactant close to the interface results in a softer polymer layer near the surface and a harder layer in the bulk.

Kinetics of a frictional granular motor.

Within the framework of a Boltzmann-Lorentz equation, we analyze the dynamics of a granular rotor immersed in a bath of thermalized particles in the presence of a frictional torque on the axis. In numerical simulations of the equation, we observe two scaling regimes at low and high bath temperatures. In the large friction limit, we obtain the exact solution of a model corresponding to asymptotic behavior of the Boltzmann-Lorentz equation. In the limit of large rotor mass and small friction, we derive a Fokker-Planck equation for which the exact solution is also obtained.

Thermostatistics of a single particle on a granular dimer lattice: influence of defects.

We study the thermostatistical fluctuations of a single Delrin monomer on a granular lattice of dimer particles using both experiment and simulation. The goal is to examine the collision frequency, energy injection, and sidewall effects on a single second-layer particle in a bilayer granular gas experiment. Non-Gaussian velocity statistics are observed for the single particle of the top layer and result from the presence of defects in the first layer. These deviations are not directly due to the presence of the boundary wall, since the form of velocity distributions is quite spatially homogeneous, but are the consequence of the presence of a few mobile defects in the first layer.

Equilibrium adsorption on a random site surface.

We examine the reversible adsorption of spherical solutes on a random site surface in which the adsorption sites are uniformly and randomly distributed on a substrate. Each site can be occupied by one solute provided that the nearest occupied site is at least one diameter away. The model is characterized by the site density and the bulk phase activity of the adsorbate. We develop a general statistical mechanical description of the model, and we obtain exact expressions for the adsorption isotherms in limiting cases of large and small activity and site density, particularly for the one-dimensional version of the model. We also propose approximate isotherms that interpolate between the exact results. These theories are in good agreement with numerical simulations of the model in two dimensions.

Angular velocity distribution of a granular planar rotator in a thermalized bath.

The kinetics of a granular planar rotator with a fixed center undergoing inelastic collisions with bath particles is analyzed both numerically and analytically by means of the Boltzmann equation. The angular velocity distribution evolves from quasi-Gaussian in the Brownian limit to an algebraic decay in the limit of an infinitely light particle. In addition, we compare this model to that of a planar rotator with a free center and discuss the prospects for experimental confirmation of these results.

Exactly solvable model of reversible adsorption on a disordered substrate.

We consider the reversible adsorption of particles (monomers with exclusion nearest-neighbor sites) on a one-dimensional lattice, where adsorption occurs on a finite fraction of sites selected randomly. By comparing this one-dimensional system to the pure system where all sites are available for adsorption, we show that when the activity goes to infinity, there exists a mapping between this model and the pure system at the same density. By examining the susceptibilities, we demonstrate that there is no mapping at finite activity. However, when the site density is small or moderate, the mapping exists up to second order in site density. We also propose and evaluate approximate approaches that may be applied to systems where no analytic result is known.

Boltzmann equation for a granular capped rectangle in a thermalized bath of hard disks.

By using the Boltzmann approach, we study the steady-state dynamics of a granular capped rectangle placed in a two-dimensional bath of thermalized hard disks. Hard core collisions are assumed elastic between disks and inelastic between the capped rectangle and the disks, with a normal coefficient of restitution alpha < 1. Assuming a Gaussian ansatz for the probability distribution functions, we obtain analytical expressions for the granular temperatures. We show the absence of equipartition and investigate both the role of the anisotropy of the capped rectangle and of the relative ratio of the bath particles to the linear sizes of the capped rectangle. In addition, we investigate a model of a capped rectangle with two normal coefficients of restitution for collisions along the straight and curved surfaces of the capped rectangle. In this case one observes equipartition for a nontrivial ratio of the normal coefficient of restitutions.

Thermalization of an anisotropic granular particle.

We investigate the dynamics of a needle in a two-dimensional bath composed of thermalized point particles. Collisions between the needle and points are inelastic and characterized by a normal restitution coefficient alpha<1. By using the Enskog-Boltzmann equation, we obtain analytical expressions for the translational and rotational granular temperatures of the needle and show that these are, in general, different from the bath temperature. The translational temperature always exceeds the rotational one, though the difference decreases with increasing moment of inertia. The predictions of the theory are in very good agreement with numerical simulations of the model.

Statistical mechanical description of the parking-lot model for vibrated granular materials.

We apply the statistical mechanical approach proposed by Edwards and co-workers to the parking-lot model, a model that reproduces the main features of the phenomenology of vibrated granular materials. We first build the compactivity-based measure for the case of vanishingly small tapping strength and then generalize the approach to finite tapping strengths by introducing a "thermodynamic" parameter, the available volume for particle insertion, in addition to the particle density. This description is able to take into account the various memory effects observed in vibrated granular media. Although not exact, the approach gives a good description of the behavior of the parking-lot model in the regime of slow compaction.

Langevin dynamics of the Coulomb frustrated ferromagnet: A mode-coupling analysis.

We study the Langevin dynamics of the soft-spin, continuum version of the Coulomb-frustrated Ising ferromagnet. By using the dynamical mode-coupling approximation, supplemented by reasonable approximations for describing the equilibrium static correlation function, and the somewhat improved dynamical self-consistent screening approximation, we find that the system displays a transition from an ergodic to a nonergodic behavior. This transition is similar to that obtained in the idealized mode-coupling theory of glass-forming liquids and in the mean-field generalized spin glasses with one-step replica symmetry breaking. The significance of this result and the relation to the appearance of a complex free-energy landscape are also discussed.

Evidence for "fragile" glass-forming behavior in the relaxation of Coulomb frustrated three-dimensional systems.

We show by means of a Monte Carlo simulation study that three-dimensional models with long-range frustration display the generic phenomena seen in fragile glass-forming liquids. Due to their properties (absence of quenched disorder, physical motivation in terms of structural frustration, and tunable fragility), these systems appear as promising minimal theoretical models for describing the glass transition of supercooled liquids.

Wall-enhanced convection in vibrofluidized granular systems.

An event-driven molecular dynamics simulation of inelastic hard spheres contained in a cylinder and subject to strong vibration reproduces accurately experimental results [R. D. Wildman et al., Phys. Rev. Lett. 86, 3304 (2001)] for a system of vibrofluidized glass beads. In particular, we are able to obtain the velocity field and the density and temperature profiles observed experimentally. In addition, we show that the appearance of convection rolls is strongly influenced by the value of the sidewall-particle restitution coefficient. Suggestions for observing more complex convection patterns are proposed.

Monte Carlo study of the three-dimensional Coulomb frustrated Ising ferromagnet.

We have investigated, by Monte Carlo simulation, the phase diagram of a three-dimensional Ising model with nearest-neighbor ferromagnetic interactions and small, but long-range (Coulombic) antiferromagnetic interactions. We have developed an efficient cluster algorithm and used different lattice sizes and geometries, which allows us to obtain the main characteristics of the temperature-frustration phase diagram. Our finite-size scaling analysis confirms that the melting of the lamellar phases into the paramagnetic phase is driven first order by the fluctuations. Transitions between ordered phases with different modulation patterns are observed in some regions of the diagram, in agreement with a recent mean-field analysis.

Adsorption-desorption model and its application to vibrated granular materials.

We investigate both analytically and by numerical simulation the kinetics of a microscopic model of hard rods adsorbing on a linear substrate, a model that is relevant for compaction of granular materials. The computer simulations use an event-driven algorithm that is particularly efficient at very long times. For a small, but finite desorption rate, the system reaches an equilibrium state very slowly, and the long-time kinetics display three successive regimes: an algebraic one where the density varies as 1/t, a logarithmic one where the density varies as 1/ln(t), followed by a terminal exponential approach. The characteristic relaxation time of the final regime, though incorrectly predicted by mean field arguments, can be obtained with a systematic gap-distribution approach. The density fluctuations at equilibrium are also investigated, and the associated time-dependent correlation function exhibits a power law regime followed by a final exponential decay. Finally, we show that denser particle packings can be obtained by varying the desorption rate during the process.

Phase diagram of an ising model with long-range frustrating interactions: A theoretical analysis

We present a theoretical study of the phase diagram of a frustrated Ising model with nearest-neighbor ferromagnetic interactions and long-range (Coulombic) antiferromagnetic interactions. For nonzero frustration, long-range ferromagnetic order is forbidden, and the ground state of the system consists of phases characterized by periodically modulated structures. At finite temperatures, the phase diagram is calculated within the mean-field approximation. Below the transition line that separates the disordered and the ordered phases, the frustration-temperature phase diagram displays an infinite number of "flowers," each flower being made by an infinite number of modulated phases generated by structure combination branching processes. The specificities introduced by the long-range nature of the frustrating interaction and the limitation of the mean-field approach are finally discussed.

A Particle-Level Model of Irreversible Protein Adsorption with a Postadsorption Transition.

Modeling the kinetics of protein adsorption at solid surfaces is needed to predict protein separations, design biosensors, and determine the body's initial response to foreign objects. We develop, at the particle level, a kinetic model that accounts geometrically for the surface blockage due to adsorption and postadsorption conformational (or orientational) transitions. Proteins are modeled as disk-shaped particles of diameter final sigmaalpha that adsorb irreversibly at random positions onto a surface at a rate kac (c is the concentration of protein in the bulk solution). Adsorption occurs only where the surface is empty. Following adsorption, a particle attempts to spread (symmetrically) to a larger diameter final sigmabeta at a rate ks. Spreading only occurs if no overlap with any previously placed particle would result. A set of equations is developed for determining the time evolution of the adsorbed protein density. These predictions are compared to new experimental data for fibronectin onto silica-titania obtained using optical waveguide lightmode spectroscopy (OWLS). We also discuss the general application of this model to experimental data. Copyright 1998 Academic Press.