On the 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. It is shown 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

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

Instability of the symmetric Couette-flow in a granular gas: hydrodynamic field profiles and transport

We investigate the inelastic hard disk gas sheared by two parallel bumpy walls (Couette-flow). In our molecular dynamic simulations we found a sensitivity to the asymmetries of the initial condition of the particle places and velocities and an asymmetric stationary state, where the deviation from (anti)symmetric hydrodynamic fields is stronger as the normal restitution coefficient decreases. For the better understanding of this sensitivity we carried out a linear stability analysis of the former kinetic theoretical solution [Jenkins and Richman: J. Fluid. Mech. {\bf 171} (1986)] and found it to be unstable. The effect of this asymmetry on the self-diffusion coefficient is also discussed.Comment: 9 pages RevTeX, 14 postscript figures, sent to Phys. Rev.

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

Transport coefficients for dense hard-disk systems

A study of the transport coefficients of a system of elastic hard disks, based on the use of Helfand-Einstein expressions is reported. The self-diffusion, the viscosity, and the heat conductivity are examined with averaging techniques especially appropriate for the use in event-driven molecular dynamics algorithms with periodic boundary conditions. The density and size dependence of the results is analyzed, and comparison with the predictions from Enskog's theory is carried out. In particular, the behavior of the transport coefficients in the vicinity of the fluid-solid transition is investigated and a striking power law divergence of the viscosity in this region is obtained, while all other examined transport coefficients show a drop in that density range.Comment: submitted to PR

Piezoelectric mechanism of orientation of stripe structures in two-dimensional electron systems

A piezoelectric mechanism of orientation of stripes in two-dimensional quantum Hall systems in GaAs heterostructures is considered. The anisotropy of the elastic moduli and the boundary of the sample are taken into account. It is found that in the average the stripes line up with the [110] axis. In double layer systems the wave vector of the stripe structure rotates from the [110] to [100] axis if the period of density modulation becomes large than the interlayer distance. From the experimental point of view it means that in double layer systems anisotropic part of resistivity changes its sign under variation of the external magnetic field.Comment: 8 page

Navier-Stokes transport coefficients of dd-dimensional granular binary mixtures at low density

The Navier-Stokes transport coefficients for binary mixtures of smooth inelastic hard disks or spheres under gravity are determined from the Boltzmann kinetic theory by application of the Chapman-Enskog method for states near the local homogeneous cooling state. It is shown that the Navier-Stokes transport coefficients are not affected by the presence of gravity. As in the elastic case, the transport coefficients of the mixture verify a set of coupled linear integral equations that are approximately solved by using the leading terms in a Sonine polynomial expansion. The results reported here extend previous calculations [V. Garz\'o and J. W. Dufty, Phys. Fluids {\bf 14}, 1476 (2002)] to an arbitrary number of dimensions. To check the accuracy of the Chapman-Enskog results, the inelastic Boltzmann equation is also numerically solved by means of the direct simulation Monte Carlo method to evaluate the diffusion and shear viscosity coefficients for hard disks. The comparison shows a good agreement over a wide range of values of the coefficients of restitution and the parameters of the mixture (masses and sizes).Comment: 6 figures, to be published in J. Stat. Phy

Disorder-Induced First Order Transition and Curie Temperature Lowering in Ferromagnatic Manganites

We study the effect that size disorder in the cations surrounding manganese ions has on the magnetic properties of manganites. This disorder is mimic with a proper distribution of spatially disordered Manganese energies. Both, the Curie temperature and the order of the transition are strongly affected by disorder. For moderate disorder the Curie temperature decreases linearly with the the variance of the distribution of the manganese site energies, and for a disorder comparable to that present in real materials the transition becomes first order. Our results provide a theoretical framework to understand disorder effects on the magnetic behavior of manganites.Comment: 4 pages, three figures include

Canted phase in double quantum dots

We perform a Hartree-Fock calculation in order to describe the ground state of a vertical double quantum dot in the absence of magnetic fields parallel to the growth direction. Intra- and interdot exchange interactions determine the singlet or triplet character of the system as the tunneling is tuned. At finite Zeeman splittings due to in-plane magnetic fields, we observe the continuous quantum phase transition from ferromagnetic to symmetric phase through a canted antiferromagnetic state. The latter is obtained even at zero Zeeman energy for an odd electron number.Comment: 5 pages, 3 figure

Heat to Electricity Conversion by a Graphene Stripe with Heavy Chiral Fermions

A conversion of thermal energy into electricity is considered in the electrically polarized graphene stripes with zigzag edges where the heavy chiral fermion (HCF) states are formed. The stripes are characterized by a high electric conductance Ge and by a significant Seebeck coefficient S. The electric current in the stripes is induced due to a non-equilibrium thermal injection of "hot" electrons. This thermoelectric generation process might be utilized for building of thermoelectric generators with an exceptionally high figure of merit Z{\delta}T \simeq 100 >> 1 and with an appreciable electric power densities \sim 1 MW/cm2.Comment: 8 pages, 3 figure