Topology of definable Hausdorff limits

Let $A\sub \R^{n+r}$ be a set definable in an o-minimal expansion $\S$ of the real field, $A' \sub \R^r$ be its projection, and assume that the non-empty fibers $A_a \sub \R^n$ are compact for all $a \in A'$ and uniformly bounded, {\em i.e.} all fibers are contained in a ball of fixed radius $B(0,R).$ If $L$ is the Hausdorff limit of a sequence of fibers $A_{a_i},$ we give an upper-bound for the Betti numbers $b_k(L)$ in terms of definable sets explicitly constructed from a fiber $A_a.$ In particular, this allows to establish effective complexity bounds in the semialgebraic case and in the Pfaffian case. In the Pfaffian setting, Gabrielov introduced the {\em relative closure} to construct the o-minimal structure \S_\pfaff generated by Pfaffian functions in a way that is adapted to complexity problems. Our results can be used to estimate the Betti numbers of a relative closure $(X,Y)_0$ in the special case where $Y$ is empty.Comment: Latex, 23 pages, no figures. v2: Many changes in the exposition and notations in an attempt to be clearer, references adde

Performance and test section flow characteristics of the National Full-Scale Aerodynamics Complex 80- by 120-Foot Wind Tunnel

Results from the performance and test section flow calibration of the 80- by 120-Foot Wind Tunnel are presented. Measurements indicating the 80- by 120-ft test section flow quality were obtained throughout the tunnel operational envelope and for atmospheric wind speeds up to approximately 20 knots. Tunnel performance characteristics and a dynamic pressure system calibration were also documented during the process of mapping the test section flow field. Experimental results indicate that the test section flow quality is relatively insensitive to dynamic pressure and the level of atmospheric winds experienced during the calibration. The dynamic pressure variation in the test section is within +/-75 percent of the average. The axial turbulence intensity is less than 0.5 percent up to the maximum test section speed of 100 knots, and the vertical and lateral flow angle variations are within +/-5 deg and +/-7 deg, respectively. Atmospheric winds were found to affect the pressure distribution in the test section only at high ratios of wind speed to test section speed