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The phase diagram of the classical \jj model on the \kag lattice is investigated using extensive \mc simulations. In a realistic range of parameters, this model has a low-temperature chiral-ordered phase without long-range spin order. We show that the critical transition marking the destruction of chiral order is preempted by the first order proliferation of \Zdeux point defects. The core energy of these vortices appears to vanish when approaching the T=0 phase boundary, where both \Zdeux defects and gapless magnons contribute to disordering the system at very low temperature. This situation might be typical of a large class of frustrated magnets. Possible relevance for real materials is also discussed., Comment: 4 pages, 4 figures

We show by using a Discrete Element Method that a bilayer of vibrated granular bidisperse spheres exhibits the striking feature that the horizontal velocity distribution of the top layer particles has a quasi-Gaussian shape, whereas that of the bottom layer is far from Gaussian. We examine in detail the relevance of all physical parameters (acceleration of the bottom plate, mass ratio, layer coverage). Moreover, a microscopic analysis of the trajectories and the collision statistics reveal how the mechanism of randomization., Comment: 5 pages, 6 figures

We consider the reversible adsorption of dimers on a regular lattice, where adsorption occurs on a finite fraction of sites selected randomly. By comparing this 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, this 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.

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 with a planar rotator with a free center. We propose experimental tests that might confirm the predicted behaviors., Comment: 10 Pages, 9 Figures

We show how the Gillespie algorithm, originally developed to describe coupled chemical reactions, can be used to perform numerical simulations of a granular intruder particle colliding with thermalized bath particles. The algorithm generates a sequence of collision ``events'' separated by variable time intervals. As input, it requires the position-dependent flux of bath particles at each point on the surface of the intruder particle. We validate the method by applying it to a one-dimensional system for which the exact solution of the homogeneous Boltzmann equation is known and investigate the case where the bath particle velocity distribution has algebraic tails. We also present an application to a granular needle in bath of point particles where we demonstrate the presence of correlations between the translational and rotational degrees of freedom of the intruder particle. The relationship between the Gillespie algorithm and the commonly used Direct Simulation Monte Carlo (DSMC) method is also discussed., Comment: 13 pages, 8 figures, to be published in J. Phys. A Math. Gen

We consider a one-dimensional system consisting of a granular tracer particle of mass $M$ in a bath of thermalized particles each of mass $m$. When the mass ratio, $M/m$, is equal to the coefficient of restitution, $\alpha$, the system maps to a a one-dimensional elastic gas. In this case, Boltzmann equation can be solved exactly. We also obtain expressions for the velocity autocorrelation function and the diffusion coefficient. Numerical simulations of the Boltzmann equation are performed for $M/m\neq \alpha$ where no analytical solution is available. It appears that the dynamical features remain qualitatively similar to those found in the exactly solvable case., Comment: 17 pages, 3 figures, Accepted in Physica A

The behavior of an ultrasonic shot peening process is observed and analyzed by using a model of inelastic hard spheres in a gravitational field that are fluidized by a vibrating bottom wall (sonotrode) in a cylindrical chamber. A marked heterogeneous distribution of impacts appears when the collision between the shot and the side wall becomes inelastic with constant dissipation. This effect is one order of magnitude larger than the simple heterogeneity arising from boundary collision on the cylinder. Variable restitution coefficients bring the simulation closer to the general observation and allows the investigation of peening regimes with changing shot density. We compute within this model other physical quantities (impact velocities, impact angle, temperature and density profile) that are influenced by the number $N$ of spheres., Comment: 8 pages, 10 figures

We show how inelastic collisions induce a power law with exponent -3 in the decay of the angular velocity distribution of anisotropic particles with sufficiently small moment of inertia. We investigate this question within the Boltzmann kinetic theory for an elongated granular particle immersed in a bath. The power law persists so long as the collisions are inelastic for a large range of angular velocities provided the mass ratio of the anisotropic particle and the bath particles remains small. Suggestions for observing this peculiar feature are made., Comment: 8 pages, 4 figures

One of the most spectacular phenomena in physics in terms of dynamical range is the glass transition and the associated slowing down of flow and relaxation with decreasing temperature. That it occurs in many different liquids seems to call for a "universal" theory. In this article, we review one such theoretical approach which is based on the concept of "frustration". Frustration in this context describes an incompatibility between extension of the locally preferred order in a liquid and tiling of the whole space. We provide a critical assessment of what has been achieved within this approach and we discuss the relation with other theories of the glass transition., Comment: 48 pages, 13 figures, submitted to J. Phys : Cond. Matter

By using the Enskog-Boltzmann approach, we study the steady-state dynamics of a granular discorectangle placed in a two-dimensional bath of thermalized hard disks. Hard core collisions are assumed elastic between disks and inelastic between the discorectangle and the disks, with a normal restitution coefficient $\alpha<1$. 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 discorectangle and of the relative ratio of the bath particles to the linear sizes of the discorectangle. In addition, we investigate a model of a discorectangle with two normal restitution coefficients for collisions along the straight and curved surfaces of the discorectangle. In this case one observes equipartition for a non trivial ratio of normal restitution coefficients., Comment: 10 pages, 8 figures

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., Comment: 7 pages, 6 Figures, submitted to PRE. Revised version (Fig1, Fig5 and Fig6 corrected + minor typos)

The parking-lot model provides a qualitative description of the main features of the phenomenology of granular compaction. We derive here approximate kinetic equations for this model, equations that are based on a $2-$parameter generalization of the statistical-mechanical formalism first proposed by Edwards and coworkers. We show that history-dependent effects, such as memory and Kovacs effects, are captured by this approach., Comment: 11 pages 6 figures Proceeding Capri 2003 conference "Unifying concepts in granular media and glasses"

We apply the statistical mechanical approach based on the ``flat'' measure proposed by Edwards and coworkers to the parking lot model, a model that reproduces the main features of the phenomenology of vibrated granular materials. We first build the flat measure for the case of vanishingly small tapping strength and then generalize the approach to finite tapping strengths by introducing a new ``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., Comment: 10 pages, 10 figures, submitted to Phys. Rev.E

A well known argument in cosmology gives that the power spectrum (or structure function) $P(k)$ of mass density fluctuations produced from a uniform initial state by physics which is causal (i.e. moves matter and momentum only up to a finite scale) has the behaviour $P(k) \propto k^4$ at small $k$. Noting the assumption of analyticity at $k=0$ of $P(k)$ in the standard derivation of this result, we introduce a class of solvable one dimensional models which allows us to study the relation between the behaviour of $P(k)$ at small $k$ and the properties of the probability distribution $f(l)$ for the spatial extent $l$ of mass and momentum conserving fluctuations. We find that the $k^4$ behaviour is obtained in the case that the first {\it six} moments of $f(l)$ are finite. Interestingly the condition that the fluctuations be localised - taken to correspond to the convergence of the first two moments of $f(l)$ - imposes only the weaker constraint $P(k) \propto k^n$ with $n$ anywhere in the range $0< n \leq 4$. We interpret this result to suggest that the causality bound will be loosened in this way if quantum fluctuations are permitted., Comment: 7 pages, 2 figures; revised version with considerable changes to presentation (including modified title), results and conclusions unchanged; version to appear in Europhys. Lett

We obtain exact results for the acceptance ratio and mean squared displacement in Monte Carlo simulations of the simple harmonic oscillator in $D$ dimensions. When the trial displacement is made uniformly in the radius, we demonstrate that the results are independent of the dimensionality of the space. We also study the dynamics of the process via a spectral analysis and we obtain an accurate description for the relaxation time., Comment: 17 pages, 8 figures. submitted to J. Phys. A

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 non-ergodic behavior. This transition is similar to that obtained in the idealized mode-coupling theory of glassforming 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., Comment: 13 pages, 11 figures, submitted to Phys. Rev. E

We propose that the concept of liquids characterized by a given locally preferred structure (LPS) could help in understanding the observed phenomenon of polyamorphism. ``True polyamorphism'' would involve the competition between two (or more) distinct LPS, one favored at low pressure because of its low energy and one favored at high pressure because of its small specific volume, as in tetrahedrally coordinated systems. ``Apparent polyamorphism'' could be associated with the existence of a poorly crystallized defect-ordered phase with a large unit cell and small crystallites, which may be illustrated by the metastable glacial phase of the fragile glassformer triphenylphosphite; the apparent polyamorphism might result from structural frustration, i. e., a competition between the tendency to extend the LPS and a global constraint that prevents tiling of the whole space by the LPS., Comment: 11, 6 figures, Proceedings of the Conference "Horizons in Complex Systems", Messina; in honor of the 60th birthday of H.E. Stanley

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 glassforming 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., Comment: 4 pages, 4 figures

An event-driven molecular dynamics simulation of inelastic hard spheres contained in a cylinder and subject to strong vibration reproduces accurately experimental results[1] 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., Comment: 4 pages, 6 figures

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 paramgnetic phase is driven first-order by the fluctuations. Transitions between ordered phases with different modulation patterns is observed in some regions of the diagram, in agreement with a recent mean-field analysis., Comment: 14 pages, 10 figures, submitted to Phys. Rev. E

comment on J. Schmalian and P. Wolynes, Phys. Rev. Lett. {\bf 85}, 836 (2000)., Comment: 1 page, 1 Figure, accepted in Phys. Rev. Letters

An adsorption-desorption (or parking-lot) model can reproduce qualitatively the densification kinetics and other features of a weakly vibrated granular material. Here we study the the two-time correlation and response functions of the model and demonstrate that their behavior is consistent with recently observed memory effects in granular materials. Although the densification kinetics and hysteresis are robust properties, we show that the aging behavior of the adsorption-desorption model is different from other models of granular compaction. We propose an experimental test to distinguish the possible aging behaviors., Comment: 9 pages, 7 figures, to appear in Eur. Phys. Jour. E

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., Comment: 32 pages, 7 figures

We propose that the salient feature to be explained about the glass transition of supercooled liquids is the temperature-controlled superArrhenius activated nature of the viscous slowing down, more strikingly seen in weakly-bonded, fragile systems. In the light of this observation, the relevance of simple models of spherically interacting particles and that of models based on free-volume congested dynamics are questioned. Finally, we discuss how the main aspects of the phenomenology of supercooled liquids, including the crossover from Arrhenius to superArrhenius activated behavior and the heterogeneous character of the $\alpha$ relaxation, can be described by an approach based on frustration-limited domains., Comment: 13 pages, 4 figures, accepted in J. Phys.: Condensed Matter, proceedings of the Trieste workshop on "Unifying Concepts in Glass Physics"

We investigate both analytically and by numerical simulation the kinetics of a microscopic model of hard rods adsorbing on a linear substrate, a model which is relevant for compaction of granular materials. The computer simulations use an event-driven algorithm which 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 a 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., Comment: 28 pages, 7 figures

Many experimental studies of protein deposition on solid surfaces involve alternating adsorption/desorption steps. In this paper, we investigate the effect of a desorption step (separating two adsorption steps) on the kinetics, the adsorbed-layer structure, and the saturation density. Our theoretical approach involves a density expansion of the pair distribution function and an application of an interpolation formula to estimate the saturation density as a function of the density at which the desorption process commences, $\rho_1$, and the density of the depleted configuration, $\rho_2$. The theory predicts an enhancement of the saturation density compared with that of a simple, uninterrupted RSA process and a maximum in the saturation density when $\rho_2={2/3}\rho_1$. The theoretical results are in qualitative and in semi-quantitative agreement with the results of numerical simulations., Comment: 11 pages, 5 figures, Submitted to J. Chem. Phys

The adsorption or adhesion of large particles (proteins, colloids, cells, >...) at the liquid-solid interface plays an important role in many diverse applications. Despite the apparent complexity of the process, two features are particularly important: 1) the adsorption is often irreversible on experimental time scales and 2) the adsorption rate is limited by geometric blockage from previously adsorbed particles. A coarse-grained description that encompasses these two properties is provided by sequential adsorption models whose simplest example is the random sequential adsorption (RSA) process. In this article, we review the theoretical formalism and tools that allow the systematic study of kinetic and structural aspects of these sequential adsorption models. We also show how the reference RSA model may be generalized to account for a variety of experimental features including particle anisotropy, polydispersity, bulk diffusive transport, gravitational effects, surface-induced conformational and orientational change, desorption, and multilayer formation. In all cases, the significant theoretical results are presented and their accuracy (compared to computer simulation) and applicability (compared to experiment) are discussed., Comment: 51 pages, 18 Figures, to appear in a special volume entitled "Adhesion of Submicron Particles on Solid Surfaces" of Colloids and Surfaces A, guest-edited by V. Privman.to appear in a special volume entitled

We investigate, both analytically and by computer simulation, the kinetics of a microscopic model of hard rods adsorbing on a linear substrate. For a small, but finite desorption rate, the system reaches the 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. A mean-field approach fails to predict the relaxation rate associated with the latter. We show that the correct answer can only be provided by using a systematic description based on a gap-distribution approach., Comment: 7 pages, 5 figures, submitted to J. Phys. A

We study a 3-dimensional Ising model in which the tendency to order due to short-range ferromagnetic interactions is frustrated by competing long-range (Coulombic) interactions. Complete ferromagnetic ordering is impossible for any nonzero value of the frustration parameter, but the system displays a variety of phases characterized by periodically modulated structures. We have performed extensive Monte-Carlo simulations which provide strong evidence that the microphase separation transition between paramagnetic and modulated phases is a fluctuation-induced first-order transition. Additional transitions to various commensurate phases may also occur when further lowering the temperature., Comment: 6 pages, 4 figures, accepted in Europhys. Letters