arXiv subjects

Pascal Viot

Publications and source records attributed to Pascal Viot.

35 records · Page 2Linked to original sources

arXiv2017

Stationary ordered non-equilibrium states of long-range interacting systems

Long-range interacting Hamiltonian systems are believed to relax generically towards non-equilibrium states called "quasi-stationary" because they evolve towards thermodynamic equilibrium very slowly, on a time-scale diverging with particle number. We show here that, by applying a suitable perturbation operator for a finite time interval, we obtain, in a family of long-range systems, non-equilibrium states which appear to be strictly stationary. They exist even in the case of a harmonic potential, and are characterised by an ordered microscopic phase space structure. We give some simple heuristic arguments which predict reasonably well some properties of these states.

cond-mat.stat-mech↗

arXiv2016

Attractor non-equilibrium stationary states in perturbed long-range interacting systems

Isolated long-range interacting particle systems appear generically to relax to non-equilibrium states ("quasi-stationary states" or QSS) which are stationary in the thermodynamic limit. A fundamental open question concerns the "robustness" of these states when the system is not isolated. In this paper we explore, using both analytical and numerical approaches to a paradigmatic one dimensional model, the effect of a simple class of perturbations. We call them "internal local perturbations" in that the particle energies are perturbed at collisions in a way which depends only on the local properties. Our central finding is that the effect of the perturbations is to drive all the very different QSS we consider towards a unique QSS. The latter is thus independent of the initial conditions of the system, but determined instead by both the long-range forces and the details of the perturbations applied. Thus in the presence of such a perturbation the long-range system evolves to a unique non-equilibrium stationary state, completely different to its state in absence of the perturbation, and it remains in this state when the perturbation is removed. We argue that this result may be generic for long-range interacting systems subject to perturbations which are dependent on the local properties (e.g. spatial density or velocity distribution) of the system itself.

cond-mat.stat-mech↗

arXiv2015

Mode-coupling approach for the slow dynamics of a liquid on a spherical substrate

We study the dynamics of a one-component liquid constrained on a spherical substrate, a 2-sphere, and investigate how the mode-coupling theory (MCT) can describe the new features brought by the presence of curvature. To this end we have derived the MCT equations in a spherical geometry. We find that, as seen from the MCT, the slow dynamics of liquids in curved space at low temperature does not qualitatively differ from that of glass-forming liquids in Euclidean space. The MCT predicts the right trend for the evolution of the relaxation slowdown with curvature but is dramatically off at a quantitative level.

cond-mat.soft↗

arXiv2014

Dynamics of a monodisperse Lennard-Jones system on a sphere

We investigate by Molecular Dynamics simulation a system of $N$ particles moving on the surface of a two-dimensional sphere and interacting by a Lennard-Jones potential. We detail the way to account for the changes brought by a nonzero curvature, both at a methodological and at a physical level. When compared to a two-dimensional Lennard-Jones liquid on the Euclidean plane, where a phase transition to an ordered hexagonal phase takes place, we find that the presence of excess defects imposed by the topology of the sphere frustrates the hexagonal order. We observe at high density a rapid increase of the relaxation time when the temperature is decreased, whereas in the same range of temperature the pair correlation function of the system evolves only moderately.

cond-mat.stat-mech↗

arXiv2014

Scaling quasi-stationary states in long range systems with dissipation

Hamiltonian systems with long-range interactions give rise to long lived out of equilibrium macroscopic states, so-called quasi-stationary states. We show here that, in a suitably generalized form, this result remains valid for many such systems in the presence of dissipation. Using an appropriate mean-field kinetic description, we show that models with dissipation due to a viscous damping or due to inelastic collisions admit "scaling quasi-stationary states", i.e., states which are quasi-stationary in rescaled variables. A numerical study of one dimensional self-gravitating systems confirms both the relevance of these solutions, and gives indications of their regime of validity in line with theoretical predictions. We underline that the velocity distributions never show any tendency to evolve towards a Maxwell-Boltzmann form.

cond-mat.stat-mech↗

arXiv2013

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/nano-channels 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.

cond-mat.stat-mech↗

arXiv2011

Effect of dynamic and static friction on an asymmetric granular piston

We investigate the influence of dry friction on an asymmetric, granular piston of mass $M$ composed of two materials undergoing inelastic collisions with bath particles of mass $m$. Numerical simulations of the Boltzmann-Lorentz equation reveal the existence of two scaling regimes depending on the strength of friction. In the large friction limit, we introduce an exact model giving the asymptotic behavior of the Boltzmann-Lorentz equation. For small friction and for large mass ratio $M/m$, we derive a Fokker-Planck equation for which the exact solution is also obtained. Static friction attenuates the motor effect and results in a discontinuous velocity distribution.

cond-mat.stat-mech↗

arXiv2011

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.

cond-mat.stat-mech↗

arXiv2011

Kinetic analysis of a chiral granular motor

We study the properties of a heterogeneous, chiral granular rotor that is capable of performing useful work when immersed in a bath of thermalized particles. The dynamics can be obtained in general from a numerical solution of the Boltzmann-Lorentz equation. We show that a mechanical approach gives the exact mean angular velocity in the limit of an infinitely massive rotor. We examine the dependence of the mean angular velocity on the coefficients of restitution of the two materials composing the motor. We compute the power and efficiency and compare with numerical simulations. We also perform a realistic numerical simulation of a granular rotor which shows that the presence of non uniformity of the bath density within the region where the motor rotates, and that the ratchet effect is slightly weakened, but qualitatively sustained. Finally we discuss the results in connection with recent experiments.

cond-mat.stat-mech↗

arXiv2010

Statistical Mechanics of liquids and fluids in curved space

In this article, we review the progress made on the statistical mechanics of liquids and fluids embedded in curved space. Our main focus will be on two-dimensional manifolds of constant nonzero curvature and on the influence of the latter on the phase behavior, thermodynamics and structure of simple liquids. Reference will also be made to existing work on three-dimensional curved space and two-dimensional manifolds with varying curvature.

cond-mat.stat-mech↗

arXiv2009

Thermodynamics and structure of simple liquids in the hyperbolic plane

We provide a consistent statistical-mechanical treatment for describing the thermodynamics and the structure of fluids embedded in the hyperbolic plane. In particular, we derive a generalization of the virial equation relating the bulk thermodynamic pressure to the pair correlation function and we develop the appropriate setting for extending the integral-equation approach of liquid-state theory in order to describe the fluid structure. We apply the formalism and study the influence of negative space curvature on two types of systems that have been recently considered: Coulombic systems, such as the one- and two-component plasma models, and fluids interacting through short-range pair potentials, such as the hard-disk and the Lennard-Jones models.

cond-mat.stat-mech↗

arXiv2008

Quasi-gaussian velocity distribution of a vibrated granular bilayer system

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.

cond-mat.soft↗

arXiv2008

Tuning the fragility of a glassforming liquid by curving space

We investigate the influence of space curvature, and of the associated "frustration", on the dynamics of a model glassformer: a monatomic liquid on the hyperbolic plane. We find that the system's fragility, i.e. the sensitivity of the relaxation time to temperature changes, increases as one decreases the frustration. As a result, curving space provides a way to tune fragility and make it as large as wanted. We also show that the nature of the emerging "dynamic heterogeneities", another distinctive feature of slowly relaxing systems, is directly connected to the presence of frustration-induced topological defects.

cond-mat.stat-mech↗

arXiv2008

Velocity-correlation distributions in granular systems

We investigate the velocity-correlation distributions after $n$ collisions of a tagged particle undergoing binary collisions. Analytical expressions are obtained in any dimension for the velocity-correlation distribution after the first-collision as well as for the velocity-correlation function after an infinite number of collisions, in the limit of Gaussian velocity distributions. It appears that the decay of the first-collision velocity-correlation distribution for negative argument is exponential in any dimension with a coefficient that depends on the mass and on the coefficient of restitution. We also obtained the velocity-correlation distribution when the velocity distributions are not Gaussian: by inserting Sonine corrections of the velocity distributions, we derive the corrections to the velocity-correlation distribution which agree perfectly with a DSMC (Direct Simulation Monte Carlo) simulation. We emphasize that these new quantities can be easily obtained in simulations and likely in experiments: they could be an efficient probe of the local environment and of the degree of inelasticity of the collisions.

cond-mat.stat-mech↗

arXiv2008

Thermal destruction of chiral order in a two-dimensional model of coupled trihedra

We introduce a minimal model describing the physics of classical two-dimensional (2D) frustrated Heisenberg systems, where spins order in a non-planar way at T=0. This model, consisting of coupled trihedra (or Ising-$\mathbb{R}P^3$ model), encompasses Ising (chiral) degrees of freedom, spin-wave excitations and $\Z_2$ vortices. Extensive Monte Carlo simulations show that the T=0 chiral order disappears at finite temperature in a continuous phase transition in the 2D Ising universality class, despite misleading intermediate-size effects observed at the transition. The analysis of configurations reveals that short-range spin fluctuations and $\Z_2$ vortices proliferate near the chiral domain walls explaining the strong renormalization of the transition temperature. Chiral domain walls can themselves carry an unlocalized $\Z_2$ topological charge, and vortices are then preferentially paired with charged walls. Further, we conjecture that the anomalous size-effects suggest the proximity of the present model to a tricritical point. A body of results is presented, that all support this claim: (i) First-order transitions obtained by Monte Carlo simulations on several related models (ii) Approximate mapping between the Ising-$\mathbb{R}P^3$ model and a dilute Ising model (exhibiting a tricritical point) and, finally, (iii) Mean-field results obtained for Ising-multispin Hamiltonians, derived from the high-temperature expansion for the vector spins of the Ising-$\mathbb{R}P^3$ model.

cond-mat.stat-mech↗

arXiv2000

The viscous slowing down of supercooled liquids as a temperature-controlled superArrhenius activated process: a description in terms of frustration-limited domains

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 $α$ relaxation, can be described by an approach based on frustration-limited domains.

cond-mat.stat-mech↗

arXiv1999

Enhanced Saturation Coverages in Adsorption-Desorption Processes

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, $ρ_1$, and the density of the depleted configuration, $ρ_2$. 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 $ρ_2={2/3}ρ_1$. The theoretical results are in qualitative and in semi-quantitative agreement with the results of numerical simulations.

cond-mat.stat-mech↗