arXiv subjects

J. Javier Brey

Publications and source records attributed to J. Javier Brey.

At least 37 records · Page 2Linked to original sources

arXiv2013

The homogeneous steady state of a confined granular gas

The non-equilibrium statistical mechanics and kinetic theory for a model of a confined quasi-two-dimensional gas of inelastic hard spheres is presented. The dynamics of the particles includes an effective mechanism to transfer the energy injected in the vertical direction to the horizontal degrees of freedom. The Enskog approximation is formulated and used as the basis to investigate the temperature and the distribution function of the steady state eventually reached by the system. An exact scaling of the distribution function of the system having implications on the form of its moments is pointed out. The theoretical predictions are compared with numerical results obtained by a particle simulation method, and a good agreement is found.

cond-mat.stat-mech↗

arXiv2013

Uniform self-diffusion in a granular gas

A granular gas composed of inelastic hard spheres or disks in the homogeneous cooling state is considered. Some of the particles are labeled and their number density exhibits a time-independent linear profile along a given direction. As a consequence, there is a uniform flux of labeled particles in that direction. It is shown that the inelastic Boltzmann-Enskog kinetic equation has a solution describing this self-diffusion state. Approximate expressions for the transport equation and the distribution function of labeled particles are derived. The theoretical predictions are compared with simulation results obtained using the direct Monte Carlo method to generate solutions of the kinetic equation. A fairly good agreement is found.

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arXiv2013

Steady self-diffusion in classical gases

A steady self-diffusion process in a gas of hard spheres at equilibrium is analyzed. The system exhibits a constant gradient of labeled particles. Neither the concentration of these particles nor its gradient are assumed to be small. It is shown that the Boltzmann-Enskog kinetic equation has an exact solution describing the state. The hydrodynamic transport equation for the density of labeled particles is derived, with an explicit expression for the involved self-diffusion transport coefficient. Also an approximated expression for the one-particle distribution function is obtained. The system does not exhibit any kind of rheological effects. The theoretical predictions are compared with numerical simulations using the direct simulation Monte Carlo method and a quite good agreement is found.

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arXiv2013

The shearing instability of a dilute granular mixture

The shearing instability of a dilute granular mixture composed of smooth inelastic hard spheres or disks is investigated. By using the Navier-Stokes hydrodynamic equations, it is shown that the scaled transversal velocity mode exhibits a divergent behaviour, similarly to what happens in one-component systems. The theoretical prediction for the critical size is compared with direct Monte Carlo simulations of the Boltzmann equations describing the system, and a good agreement is found. The total energy fluctuations in the vicinity of the transition are shown to scale with the second moment of the distribution. The scaling distribution function is the same as found in other equilibrium and non-equilibrium phase transitions, suggesting the existence of some kind of universality.

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arXiv2012

Rheological effects in the linear response and spontaneous fluctuations of a sheared granular gas

The decay of a small homogeneous perturbation of the temperature of a dilute granular gas in the steady uniform shear flow state is investigated. Using kinetic theory based on the inelastic Boltzmann equation, a closed equation for the decay of the perturbation is derived. The equation involves the generalized shear viscosity of the gas in the time-dependent shear flow state, and therefore it predicts relevant rheological effects beyond the quasi-elastic limit. A good agreement is found when comparing the theory with molecular dynamics simulation results. Moreover, the Onsager postulate on the regression of fluctuations is fulfilled.

cond-mat.stat-mech↗

arXiv2012

Internal energy fluctuations of a granular gas under steady uniform shear flow

The stochastic properties of the total internal energy of a dilute granular gas in the steady uniform shear flow state are investigated. A recent theory formulated for fluctuations about the homogeneous cooling state is extended by analogy with molecular systems. The theoretical predictions are compared with molecular dynamics simulation results. Good agreement is found in the limit of weak inelasticity, while systematic and relevant discrepancies are observed when the inelasticity increases. The origin of this behavior is discussed.

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arXiv2012

Heat Flux in a Granular Gas

A peculiarity of the hydrodynamic Navier-Stokes equations for a granular gas is the modification of the Fourier law, with the presence of an additional contribution to the heat flux that is proportional to the density gradient. Consequently, the constitutive relation involves, in the case of a one-component granular gas, two transport coefficients: the usual (thermal) heat conductivity and a diffusive heat conductivity. A very simple physical interpretation of this effect, in terms of the mean free path and the mean free time is provided. It leads to the modified Fourier law with an expression for the diffusive Fourier coefficient that differs in a factor of the order of unity from the expression obtained by means of the inelastic Boltzmann equation. Also, some aspects of the Chapman-Enskog computation of the new transport coefficients as well as of the comparison between simulation results and theory are discussed.

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arXiv2011

Thermal segregation of intruders in the Fourier state of a granular gas

A low density binary mixture of granular gases is considered within the Boltzmann kinetic theory. One component, the intruders, is taken to be dilute with respect to the other, and thermal segregation of the two species is described for a special exact solution to the Boltzmann equation. This solution has a macroscopic hydrodynamic representation with a constant temperature gradient and is referred to as the Fourier state. The thermal diffusion factor characterizing conditions for segregation is calculated without the usual restriction to Navier-Stokes hydrodynamics. Molecular dynamics simulations are reported for comparison with the results for this idealized Fourier state.

cond-mat.stat-mech↗

arXiv2011

Choosing Hydrodynamic fields

Continuum mechanics (e.g., hydrodynamics, elasticity theory) is based on the assumption that a small set of fields provides a closed description on large space and time scales. Conditions governing the choice for these fields are discussed in the context of granular fluids and multi-component fluids. In the first case, the relevance of temperature or energy as a hydrodynamic field is justified. For mixtures, the use of a total temperature and single flow velocity is compared with the use of multiple species temperatures and velocities.

cond-mat.stat-mech↗

arXiv2011

Equilibration and symmetry breaking in vibrated granular systems

The steady states of two vibrated granular gases separated by an adiabatic piston are investigated. The system exhibits a non-equilibrium phase transition with an spontaneous symmetry breaking. Even if the gases at both sides of the piston have the same number of particles and are mechanically identical, their steady volumes and temperatures can be rather different. The transition can be explained by a simple kinetic theory model expressing mechanical equilibrium and the energy balance occurring in the system. The model predictions are in good agreement with molecular dynamics simulation results. The macroscopic description of the steady states is discussed, as well as some physical implications of the symmetry breaking.

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arXiv2011

Thermal Segregation Beyond Navier-Stokes

A dilute suspension of impurities in a low density gas is described by the Boltzmann and Boltzman-Lorentz kinetic theory. Scaling forms for the species distribution functions allow an exact determination of the hydrodynamic fields, without restriction to small thermal gradients or Navier-Stokes hydrodynamics. The thermal diffusion factor characterizing sedimentation is identified in terms of collision integrals as functions of the mechanical properties of the particles and the temperature gradient. An evaluation of the collision integrals using Sonine polynomial approximations is discussed. Conditions for segregation both along and opposite the temperature gradient are found, in contrast to the Navier-Stokes description for which no segregation occurs.

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arXiv2011

Fluctuating Navier-Stokes equations for inelastic hard spheres or disks

Starting from the fluctuating Boltzmann equation for smooth inelastic hard spheres or disks, closed equations for the fluctuating hydrodynamic fields to Navier-Stokes order are derived. This requires to derive constitutive relations for both the fluctuating fluxes and the correlations of the random forces. The former are identified as having the same form as the macroscopic average fluxes and involving the same transport coefficients. On the other hand, the random force terms exhibit two peculiarities as compared with their elastic limit for molecular systems. Firstly, they are not white, but have some finite relaxation time. Secondly, their amplitude is not determined by the macroscopic transport coefficients, but involves new coefficients.

cond-mat.stat-mech↗

arXiv2010

Critical behavior of two freely evolving granular gases separated by an adiabatic piston

Two granular gases separated by an adiabatic piston and initially in the same macroscopic state are considered. It is found that a phase transition with an spontaneous symmetry breaking occurs. When the mass of the piston is increased beyond a critical value, the piston moves to a stationary position different from the middle of the system. The transition is accurately described by a simple kinetic model that takes into account the velocity fluctuations of the piston. Interestingly, the final state is not characterized by the equality of the temperatures of the subsystems but by the cooling rates being the same. Some relevant consequences of this feature are discussed.

cond-mat.stat-mech↗

arXiv2010

Volume fluctuations and compressibility of a vibrated granular gas

The volume fluctuations in the steady state reached by a vibrated granular gas of hard particles confined by a movable piston on the top are investigated by means of event driven simulations. Also, a compressibility factor, measuring the response in volume of the system to a change in the mass of the piston, is introduced and measured. From the second moment of the volume fluctuations and the compressibility factor, an effective temperature is defined, by using the same relation as obeyed by equilibrium molecular systems. The interpretation of this effective temperature and its relationship with the granular temperature of the gas, and also with the velocity fluctuations of the movable piston, is discussed. It is found that the ratio of the temperature based on the volume fluctuations to the temperature based on the piston kinetic energy, obeys simple dependencies on the inelasticity and on the piston-particle mass ratio.

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arXiv2009

Hydrodynamic Character of the Non-equipartition of Kinetic Energy in Binary Granular Gases

The influence of the heating mechanism on the kinetic energy densities of the components of a vibrated granular mixture is investigated. Collisions of the particles with the vibrating wall are inelastic and characterized by two coefficients of normal restitution, one for each of the two species. By means of molecular dynamics simulations, it is shown that the non-equipartition of kinetic energy is not affected by the differential mechanism of energy injection, aside the usual boundary layer around the wall. The macroscopic state of the mixture in the bulk is defined by intensive variables that do not include the partial granular temperatures of the components.

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arXiv2009

The Fourier state of a dilute granular gas described by the inelastic Boltzmann equation

The existence of two stationary solutions of the nonlinear Boltzmann equation for inelastic hard spheres or disks is investigated. They are restricted neither to weak dissipation nor to small gradients. The one-particle distribution functions are assumed to have an scaling property, namely that all the position dependence occurs through the density and the temperature. At the macroscopic level, the state corresponding to both is characterized by uniform pressure, no mass flow, and a linear temperature profile. Moreover, the state exhibits two peculiar features. First, there is a relationship between the inelasticity of collisions, the pressure, and the temperature gradient. Second, the heat flux can be expressed as being linear in the temperature gradient, i.e. a Fourier-like law is obeyed. One of the solutions is singular in the elastic limit. The theoretical predictions following from the other one are compared with molecular dynamics simulation results and a good agreement is obtained in the parameter region in which the Fourier state can be actually observed in the simulations, namely not too strong inelasticity.

cond-mat.soft↗

arXiv2009

Fluctuating hydrodynamics for dilute granular gases

Starting from the kinetic equations for the fluctuations and correlations of a dilute gas of inelastic hard spheres or disks, a Boltzmann-Langevin equation for the one-particle distribution function of the homogeneous cooling state is constructed. This equation is the linear Boltzmann equation with a fluctuating white noise term. Balance equations for the fluctuating hydrodynamic fields are derived. New fluctuating forces appear as compared with the elastic limit. The particular case of the transverse velocity field is investigated in detail. Its fluctuations can be described by means of a Langevin equation, but exhibiting two main differences with the Landau-Lifshitz theory: the noise is not white, and its second moment is not determined by the shear viscosity. This shows that the fluctuation-dissipation relations for molecular fluids do not straightforwardly carry over to inelastic gases. The theoretical predictions are shown to be in good agreement with molecular dynamics simulation results.

cond-mat.stat-mech↗

arXiv2009

Vibrated granular gas confined by a piston

The steady state of a vibrated granular gas confined by a movable piston on the top is discussed. Particular attention is given to the hydrodynamic boundary conditions to be used when solving the inelastic Navier-Stokes equations. The relevance of an exact general condition relating the grain fluxes approaching and moving away from each of the walls is emphasized. It is shown how it can be used to get a consistent hydrodynamic description of the boundaries. The obtained expressions for the fields do not contain any undetermined parameter. Comparison of the theoretical predictions with molecular dynamics simulation results is carried out, and a good agreement is observed for low density and not too large inelasticity. A practical way of introducing small finite density corrections to the dilute limit theory is proposed, to improve the accuracy of the theory.

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