Biomedical subjects

J Javier Brey

Publications and source records attributed to J Javier Brey.

17 recordsLinked to original sources

PubMed2006

Mesoscopic theory of critical fluctuations in isolated granular gases.

Fluctuating hydrodynamics is used to describe the total energy fluctuations of a freely evolving gas of inelastic hard spheres near the threshold of the clustering instability. They are shown to be governed only by vorticity fluctuations that also lead to a renormalization of the average total energy. The theory predicts a power-law divergent behavior of the scaled second moment of the fluctuations, and a scaling property of their probability distribution, both in agreement with simulations results. A more quantitative comparison between theory and simulation for the critical amplitudes and the form of the scaling function is also carried out.

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PubMed2006

Hydrodynamic profiles for an impurity in an open vibrated granular gas.

The hydrodynamic state of an impurity immersed in a low density granular gas is analyzed. Explicit expressions for the temperature and density fields of the impurity in terms of the hydrodynamic fields of the gas are derived. It is shown that the ratio between the temperatures of the two components, measuring the departure from the energy equipartition, only depends on the mechanical properties of the particles, being therefore constant in the bulk of the system. This ratio plays an important role in determining the density profile of the intruder and its position with respect to the gas, since it determines the sign of the pressure diffusion coefficient. The theoretical predictions are compared with molecular dynamics simulation results for the particular case of the steady state of an open vibrated granular system in the absence of macroscopic fluxes, and a satisfactory agreement is found.

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PubMed2005

Energy partition and segregation for an intruder in a vibrated granular system under gravity.

The difference of temperatures between an impurity and the surrounding gas in an open vibrated granular system is studied. It is shown that, in spite of the high inhomogeneity of the state, the temperature ratio remains constant in the bulk of the system. The lack of energy equipartition is associated to the change of sign of the pressure diffusion coefficient for the impurity at certain values of the parameters of the system, leading to a segregation criterium. The theoretical predictions are consistent with previous experimental results, and also in agreement with molecular dynamics simulation results reported in this Letter.

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PubMed2005

Hydrodynamic modes for a granular gas from kinetic theory.

Small perturbations of the homogeneous cooling state for a low density granular gas are described by means of the linearized Boltzmann equation. The spectrum of the generator for this dynamics is shown to contain points corresponding to hydrodynamic excitations. The corresponding eigenvectors and eigenvalues are calculated to Navier-Stokes order and shown to agree with those obtained by the Chapman-Enskog method. The conditions for the hydrodynamic excitations to dominate all other excitations are discussed.

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PubMed2005

Scaling and universality of critical fluctuations in granular gases.

The total energy fluctuations of a low-density granular gas in the homogeneous cooling state near the threshold of the clustering instability are studied by means of molecular dynamics simulations. The relative dispersion of the fluctuations is shown to exhibit a power-law divergent behavior. Moreover, the probability distribution of the fluctuations presents data collapse as the system approaches the instability, for different values of the inelasticity. The function describing the collapse turns out to be the symmetric of the one found in several molecular equilibrium and nonequilibrium systems.

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PubMed2004

Simulation study of the Green-Kubo relations for dilute granular gases.

The Green-Kubo relations for dilute granular gases are employed to compute their transport coefficients by means of the direct simulation Monte Carlo method. This requires not only to follow the dynamics of the system, but also to identify some modified fluxes appearing in the time-correlation functions. The results are compared with those obtained from the Boltzmann equation by means of the Chapman-Enskog procedure in the first Sonine approximation. A good agreement is found for the shear viscosity over a wide range of inelasticities. Nevertheless, for the two transport coefficients associated with the heat flux, significant discrepancies appear for strong inelasticity. Their origin is discussed, showing that they are partially due to the presence of velocity correlations in the homogeneous cooling state of a dilute granular fluid.

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PubMed2004

Energy fluctuations in the homogeneous cooling state of granular gases.

Starting from the hierarchy of equations for microscopic densities in phase space, a general theory for fluctuations and correlations in a dilute granular gas of hard particles is developed. Then, the particular case of the homogeneous cooling state is addressed. Explicit expressions for some distributions describing the presence of velocity correlations and their dynamics are obtained. These correlations are inherent to the dissipative dynamics of the collisions. The implications for the behavior of the total energy of the system are analyzed and the results are expressed in terms of a fluctuation-dissipation theorem. The theoretical predictions are shown to be in agreement with results obtained by molecular dynamics simulations, which also indicate that energy fluctuations are well described by a Gaussian distribution.

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PubMed2004

Steady-state representation of the homogeneous cooling state of a granular gas.

The properties of a dilute granular gas in the homogeneous cooling state are mapped to those of a stationary state by means of a change in the time scale that does not involve any internal property of the system. The new representation is closely related with a general property of the granular temperature in the long time limit. The physical and practical implications of the mapping are discussed. In particular, simulation results obtained by the direct simulation Monte Carlo method applied to the scaled dynamics are reported. This includes ensemble averages and also the velocity autocorrelation function, as well as the self-diffusion coefficient obtained from the latter by means of the Green-Kubo representation. In all cases, the obtained results are compared with theoretical predictions.

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PubMed2004

Validity of the Boltzmann equation to describe low-density granular systems.

The departure of a granular gas in the instable region of parameters from the initial homogeneous cooling state is studied. Results from molecular dynamics and from direct Monte Carlo simulation of the Boltzmann equation are compared. The results indicate that the Boltzmann equation accurately predicts the low-density limit of the system. The relevant role played by the parallelization of the velocities as time proceeds and the dependence of this effect on the density is analyzed in detail.

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PubMed2003

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 with 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.

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PubMed2003

Hydrodynamic modes for granular gases.

The eigenfunctions and eigenvalues of the linearized Boltzmann equation for inelastic hard spheres (d=3) or disks (d=2) corresponding to d+2 hydrodynamic modes are calculated in the long wavelength limit for a granular gas. The transport coefficients are identified and found to agree with those from the Chapman-Enskog solution. The dominance of hydrodynamic modes at long times and long wavelengths is studied via an exactly solvable kinetic model. A collisional continuum is bounded away from the hydrodynamic spectrum, assuring a hydrodynamic description at long times. The bound is closely related to the power law decay of the velocity distribution in the reference homogeneous cooling state.

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PubMed2003

Velocity distribution of fluidized granular gases in the presence of gravity.

The velocity distribution of a fluidized dilute granular gas in the direction perpendicular to the gravitational field is investigated by means of molecular dynamics simulations. The results indicate that the velocity distribution can be exactly described neither by a Gaussian nor by a stretched exponential law. Moreover, it does not exhibit any kind of scaling. In fact, the actual shape of the distribution depends on the number of monolayers at rest, on the restitution coefficient and on the height at what it is measured. The role played by the number of particle-particle collisions as compared with the number of particle-wall collisions is discussed.

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PubMed2002

Effective dynamics and steady state of an Ising model submitted to tapping processes.

A one-dimensional Ising model with nearest neighbor interactions is applied to study compaction processes in granular media. An equivalent particle-hole picture is introduced, with the holes being associated to the domain walls of the Ising model. Trying to mimic the experiments, a series of taps separated by large enough waiting times, for which the system freely relaxes, is considered. The free relaxation of the system corresponds to a T=0 dynamics which can be analytically solved. There is an extensive number of metastable states, characterized by all the holes being isolated. In the limit of weak tapping, an effective dynamics connecting the metastable states is obtained. The steady state of this dynamics is analyzed, and the probability distribution function is shown to have the canonical form. Then, the stationary state is described by Edwards thermodynamic granular theory. Spatial correlation functions in the steady state are also studied.

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PubMed2002

Transversal inhomogeneities in dilute vibrofluidized granular fluids.

The spontaneous symmetry breaking taking place in the direction perpendicular to the energy flux in a dilute vibrofluidized granular system is investigated, using both a hydrodynamic description and simulation methods. The latter include molecular dynamics and direct Monte Carlo simulation of the Boltzmann equation. A marginal stability analysis of the hydrodynamic equations, carried out in the WKB approximation, is shown to be in good agreement with the simulation results. The shape of the hydrodynamic profiles beyond the bifurcation is discussed.

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PubMed2002

Diffusion in a granular fluid. I. Theory.

Many important properties of granular fluids can be represented by a system of hard spheres with inelastic collisions. Traditional methods of nonequilibrium statistical mechanics are effective for analysis and description of the inelastic case as well. This is illustrated here for diffusion of an impurity particle in a fluid undergoing homogeneous cooling. An appropriate scaling of the Liouville equation is described such that the homogeneous cooling ensemble and associated time correlation functions map to those of a stationary state. In this form the familiar methods of linear response can be applied, leading to Green-Kubo and Einstein representations of diffusion in terms of the velocity and mean-square displacement correlation functions. These correlation functions are evaluated approximately using a cumulant expansion and from kinetic theory, providing the diffusion coefficient as a function of the density and the restitution coefficients. Comparisons with results from molecular-dynamics simulation are given in the following companion paper.

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PubMed2002

Diffusion in a granular fluid. II. Simulation.

The linear-response description for impurity diffusion in a granular fluid undergoing homogeneous cooling is developed in the preceding paper. The formally exact Einstein and Green-Kubo expressions for the self-diffusion coefficient are evaluated there from an approximation to the velocity autocorrelation function. These results are compared here to those from molecular-dynamics simulations over a wide range of density and inelasticity, for the particular case of self-diffusion. It is found that the approximate theory is in good agreement with simulation data up to moderate densities and degrees of inelasticity. At higher density, the effects of inelasticity are stronger, leading to a significant enhancement of the diffusion coefficient over its value for elastic collisions. Possible explanations associated with an unstable long wavelength shear mode are explored, including the effects of strong fluctuations and mode coupling.

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PubMed2001

Hydrodynamic Maxwell demon in granular systems.

Spontaneous symmetry breaking in a vibrated system confined into two connected compartments in the absence of external fields is reported. For a small number of particles, the grains are equipartitioned, but if it is increased beyond a critical value, the number of particles in each of the compartments becomes different in the steady state, and the number of particles in one of the compartments decreases monotonically tending to a given value. This phase transition is accurately described by the hydrodynamic equations for a granular gas. The relationship with previous phenomena of phase separation in vibrofluidized granular materials is discussed.

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