Modified Sonine approximation for the Navier-Stokes transport coefficients of a granular gas

Motivated by the disagreement found at high dissipation between simulation data for the heat flux transport coefficients and the expressions derived from the Boltzmann equation by the standard first Sonine approximation [Brey et al., Phys. Rev. E 70, 051301 (2004); J. Phys.: Condens. Matter 17, S2489 (2005)], we implement in this paper a modified version of the first Sonine approximation in which the Maxwell-Boltzmann weight function is replaced by the homogeneous cooling state distribution. The structure of the transport coefficients is common in both approximations, the distinction appearing in the coefficient of the fourth cumulant $a_2$. Comparison with computer simulations shows that the modified approximation significantly improves the estimates for the heat flux transport coefficients at strong dissipation. In addition, the slight discrepancies between simulation and the standard first Sonine estimates for the shear viscosity and the self-diffusion coefficient are also partially corrected by the modified approximation. Finally, the extension of the modified first Sonine approximation to the transport coefficients of the Enskog kinetic theory is presented.Comment: 10 pages, 6 figures; v2: slightly shortene

Foreword

Preface to the Volume by O. Rak on the Neolithic Rhyta, cult vessels distributed in most of the Balkan peninsul

A frequency division multiplex technique for transmitting commands

Reliable random access multiplexer is controlled and operated over two twisted-pair telephone lines at distances of 5.6 to 8.0 km with control signals of less than 10 volts rms. Technique adapts to any process or environmental control system where data source is necessary

Frequency division multiplex technique

A system for monitoring a plurality of condition responsive devices is described. It consists of a master control station and a remote station. The master control station is capable of transmitting command signals which includes a parity signal to a remote station which transmits the signals back to the command station so that such can be compared with the original signals in order to determine if there are any transmission errors. The system utilizes frequency sources which are 1.21 multiples of each other so that no linear combination of any harmonics will interfere with another frequency