The Limit of the Boltzmann Equation to the Euler Equations for Riemann Problems

The convergence of the Boltzmann equaiton to the compressible Euler equations when the Knudsen number tends to zero has been a long standing open problem in the kinetic theory. In the setting of Riemann solution that contains the generic superposition of shock, rarefaction wave and contact discontinuity to the Euler equations, we succeed in justifying this limit by introducing hyperbolic waves with different solution backgrounds to capture the extra masses carried by the hyperbolic approximation of the rarefaction wave and the diffusion approximation of contact discontinuity.Comment: 59 page

Gauge and Lorentz Covariant Quark Propagator in an Arbitrary Gluon Field

The quark propagator in presence of an arbitrary gluon field is calculated gauge and Lorentz covariantly order by order in terms of powers of gluon field and its derivatives. The result is independent of path connecting ends of propagator and leading order result coincides with the exact propagator in the trivial case of vanishing gluon field.Comment: 9 page

Measurement of Flow Characteristics in a Bubbling Fluidized Bed Using Electrostatic Sensor Arrays

Fluidized beds are widely applied in a range of industrial processes. In order to maintain the efficient operation of a fluidized bed, the flow parameters in the bed should be monitored continuously. In this paper, electrostatic sensor arrays are used to measure the flow characteristics in a bubbling fluidized bed. In order to investigate the electrostatic charge distribution and the flow dynamics of solid particles in the dense region, time and frequency domain analysis of the electrostatic signals is conducted. In addition, the correlation velocities and weighted average velocity of Geldart A particles in the dense and transit regions are calculated, and the flow dynamics of Geldart A and D particles in the dense and transit regions are compared. Finally, the influence of liquid antistatic agents on the performance of the electrostatic sensor array is investigated. According to the experimental results, it is proved that the flow characteristics in the dense and transit regions of a bubbling fluidized bed can be measured using electrostatic sensor arrays