Incompressible Limit of Solutions of Multidimensional Steady Compressible Euler Equations

A compactness framework is formulated for the incompressible limit of approximate solutions with weak uniform bounds with respect to the adiabatic exponent for the steady Euler equations for compressible fluids in any dimension. One of our main observations is that the compactness can be achieved by using only natural weak estimates for the mass conservation and the vorticity. Another observation is that the incompressibility of the limit for the homentropic Euler flow is directly from the continuity equation, while the incompresibility of the limit for the full Euler flow is from a combination of all the Euler equations. As direct applications of the compactness framework, we establish two incompressible limit theorems for multidimensional steady Euler flows through infinitely long nozzles, which lead to two new existence theorems for the corresponding problems for multidimensional steady incompressible Euler equations.Comment: 17 pages; 2 figures. arXiv admin note: text overlap with arXiv:1311.398

Measurement of Absorption Cross Section of a Lossy Object in Reverberation Chamber Without the Need for Calibration

A reliable and simple procedure is proposed to measure the averaged absorption cross section (ACS) of a lossy object in a reverberation chamber (RC). This procedure is based on the time-domain measurement of the ACS in an RC. In the time-domain, to obtain the ACS, the chamber decay time needs to be known. Conventionally, the ACS is normally measured in the frequency domain, and a full two-port calibration must be carried out before collecting the S-parameters, which is tedious and time-consuming. In reality, the chamber decay time depends on the diffused loss of the RC, not the insertion loss of the cables. In this paper, by making use of this fact, the ACS can be measured accurately without calibration, which will simplify the measurement process and shorten the measurement time at the same time