Hydrodynamic Model for Conductivity in Graphene

Based on the recently developed picture of an electronic ideal relativistic fluid at the Dirac point, we present an analytical model for the conductivity in graphene that is able to describe the linear dependence on the carrier density and the existence of a minimum conductivity. The model treats impurities as submerged rigid obstacles, forming a disordered medium through which graphene electrons flow, in close analogy with classical fluid dynamics. To describe the minimum conductivity, we take into account the additional carrier density induced by the impurities in the sample. The model, which predicts the conductivity as a function of the impurity fraction of the sample, is supported by extensive simulations for different values of ${\cal E}$, the dimensionless strength of the electric field, and provides excellent agreement with experimental data.Comment: 19 pages, 4 figure

An evaluation of the method for determining the Whitham F-function using distributions of downwash and sidewash angles

The method of computing the Whitham F function using distributions of downwash and sidewash angles was evaluated with two different models. F functions which were calculated for a half angle cone cylinder at M infinites = 2.01, using theoretically and experimentally derived flow angles, show that the method is sensitive to small inaccuracies in the measured flow angles. An oblique wing transport model was tested at 0 deg angle of attack at M infinitely = 2.01. In this test, two different probes were used at two different distances from the model. The pressure signature derived from the F function was extrapolated and compared to the pressure signature measured at the distance of 0.87 body lengths with the static pressure probe. The agreement between the two pressure signatures was poor due to the many inaccuracies involved in using a probe designed to measure flow angularity