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J. J. Brey

Publications and source records attributed to J. J. Brey.

12 recordsLinked to original sources
arXiv2019

Homogeneous dynamics in a vibrated granular monolayer

A simple model of a vibrated granular monolayer is studied. It consists of inelastic hard spheres confined between two parallel hard plates separated a distance smaller than twice the diameter of the particles. Both walls are elastic and one of them is vibrating in a sawtooth way. For low densities, a kinetic equation is proposed from which closed evolution equations for the horizontal and vertical temperatures are derived assuming spatial homogeneity and that the system is very thin. An excellent agreement between the theoretical predictions and Molecular Dynamics simulation results is obtained both, for the stationary values and for the dynamics of the temperatures.

cond-mat.stat-mech↗
arXiv2010

Breakdown of hydrodynamics in the inelastic Maxwell model of granular gases

Both the right and left eigenfunctions and eigenvalues of the linearized homogeneous Boltzmann equation for inelastic Maxwell molecules corresponding to the hydrodynamic modes are calculated. Also, some non-hydrodynamic modes are identified. It is shown that below a critical value of the parameter characterizing the inelasticity, one of the kinetic modes decays slower than one of the hydrodynamic ones. As a consequence, a closed hydrodynamic description does not exist in that regime. Some implications of this behavior on the formally computed Navier-Stokes transport coefficients are discussed.

cond-mat.stat-mech↗
arXiv2010

The Kovacs effect: a master equation analysis

The Kovacs or crossover effect is one of the peculiar behaviours exhibited by glasses and other complex, slowly relaxing systems. Roughly it consists in the non-monotonic relaxation to its equilibrium value of a macroscopic property of a system evolving at constant temperature, when starting from a non-equilibrium state. Here, this effect is investigated for general systems whose dynamics is described by a master equation. To carry out a detailed analysis, the limit of small perturbations in which linear response theory applies is considered. It is shown that, under very general conditions, the observed experimental features of the Kovacs effect are recovered. The results are particularized for a very simple model, a two-level system with dynamical disorder. An explicit analytical expression for its non-monotonic relaxation function is obtained, showing a resonant-like behaviour when the dependence on the temperature is investigated.

cond-mat.stat-mech↗
arXiv2008

Breakdown of fluctuation-dissipation relations in granular gases

A numerical molecular dynamics experiment measuring the two-time correlation function of the transversal velocity field in the homogeneous cooling state of a granular gas is reported. By measuring the decay rate and the amplitude of the correlations, the accuracy of the Landau-Langevin equation of fluctuating hydrodynamics is checked. The results indicate that although a Langevin approach can be valid, the fluctuation-dissipation relation must be modified, since the viscosity parameter appearing in it differs from the usual hydrodynamic shear viscosity.

cond-mat.stat-mech↗
arXiv2007

Scaling and aging in the homogeneous cooling state of a granular fluid of hard particles

The presence of the aging phenomenon in the homogeneous cooling state (HCS) of a granular fluid composed of inelastic hard spheres or disks is investigated. As a consequence of the scaling property of the $N$-particle distribution function, it is obtained that the decay of the normalized two-time correlation functions slows down as the time elapsed since the beginning of the measurement increases. This result is confirmed by molecular dynamics simulations for the particular case of the total energy of the system. The agreement is also quantitative in the low density limit, for which an explicit analytical form of the time correlation function has been derived. The reported results also provide support for the existence of the HCS as a solution of the N-particle Liouville equation.

cond-mat.stat-mech↗
arXiv2007

Volume fluctuations and linear response in a simple model of compaction

By means of a simple model system, the total volume fluctuations of a tapped granular material in the steady state are studied. In the limit of a system with a large number of particles, they are found to be Gaussian distributed, and explicit expressions for the average and the variance are provided. Experimental and molecular dynamics results are analyzed and qualitatively compared with the model predictions. The relevance of considering open or closed systems is discussed, as well as the meaning and properties of the Edwards compactivity and the effective (configurational) temperature introduced by some authors. Finally, the linear response to a change in the vibration intensity is also investigated. A KWW decay of the volume response function is clearly identified. This seems to confirm some kind of similarity between externally excited granular systems and structural glasses.

cond-mat.stat-mech↗
arXiv2005

Adsorption of a binary mixture of monomers with nearest-neighbour cooperative effects

A model for the adsorption of a binary mixture on a one-dimensional infinite lattice with nearest neighbour cooperative effects is considered. The particles of the two species are both monomers but differ in the repulsive interaction experienced by them when trying to adsorb. An exact expression for the coverage of the lattice is derived. In the jamming limit, it is a monotonic function of the ratio between the attempt frequencies of the two species, varying between the values corresponding to each of the two single species. This is in contrast with the results obtained in other models for the adsorption of particles of different sizes. The structure of the jamming state is also investigated.

cond-mat.stat-mech↗
arXiv2004

Brownian Motion in a Granular Fluid

The Fokker-Planck equation for a heavy particle in a granular fluid is derived from the Liouville equation. The host fluid is assumed to be in its homogeneous cooling state and all interactions are idealized as smooth, inelastic hard spheres. The similarities and differences between the Fokker-Planck equation for elastic and inelastic collisions are discussed in detail. Although the fluctuation-dissipation relation is violated and the reference fluid is time dependent, it is shown that diffusion occurs at long times for a wide class of initial conditions. The results presented here generalize previous results based on the Boltzmann-Lorentz equation to higher densities.

cond-mat.stat-mech↗
arXiv2003

Closed model for granular compaction under weak tapping

A one dimensional lattice model is formulated to study tapping dynamics and the long time steady distribution in granular media. The dynamics conserves the number of particles in the system, and density changes are associated to the creation and destruction of empty sites. The model is shown to be consistent with Edwards thermodynamics theory of powders. The relationship with lattice models in which the number of particles is not conserved is discussed.

cond-mat.stat-mech↗
arXiv2003

Dynamics and steady state of a vibrated granular binary mixture model

A model for the dynamical evolution of a granular binary mixture is analyzed. This system is submitted to a tapping procedure, similarly to what is done in real experiments. In the weak vibration limit, an effective dynamics for the tapping process is derived, and the steady state probability distribution is analytically found. The steady probability does not depend on the details of the configuration, but only on the number of particles of each of the two species. Depending on the values of their fugacities, the system can be either almost full of small or big particles, i.e., segregation effects are present.

cond-mat.stat-mech↗
arXiv2001

Glass-like dynamical behavior in hierarchical models submitted to continuous cooling and heating processes

The dynamical behavior of a kind of models with hierarchically constrained dynamics is investigated. The models exhibit many properties resembling real structural glasses. In particular, we focus on the study of time-dependent temperature processes. In cooling processes, a phenomenon analogous to the laboratory glass transition appears. The residual properties are analytically evaluated, and the concept of fictive temperature is discussed on a physical base. The evolution of the system in heating processes is governed by the existence of a normal solution of the evolution equations, which is approached by all the other solutions. This trend of the system is directly related to the glassy hysteresis effects shown by these systems. The existence of the normal solution is not restricted to the linear regime around equilibrium, but it is defined for any arbitrary, far from equilibrium, situation.

cond-mat.stat-mech↗