Filtrations on the knot contact homology of transverse knots

We construct a new invariant of transverse links in the standard contact structure on R^3. This invariant is a doubly filtered version of the knot contact homology differential graded algebra (DGA) of the link. Here the knot contact homology of a link in R^3 is the Legendrian contact homology DGA of its conormal lift into the unit cotangent bundle S^*R^3 of R^3, and the filtrations are constructed by counting intersections of the holomorphic disks of the DGA differential with two conormal lifts of the contact structure. We also present a combinatorial formula for the filtered DGA in terms of braid representatives of transverse links and apply it to show that the new invariant is independent of previously known invariants of transverse links.Comment: 23 pages, v2: minor corrections suggested by refere

Laser velocimetry measurement in a transonic tunnel

Some preliminary velocity measurements were carried out inside the transonic tunnel using the laser velocimeter (LV) system in association with the smoke generator. Pressure measurements were also performed using a pressure tap located on the side wall of the test section slightly upstream of the windows. Though the pressure measurements and the LV measurements were not taken at exactly the same location, extrapolation of the pressure data into the location of the LV measurements indicated a very close agreement between the velocity values obtained using the two different methods. Thus it is believed that the smoke particle is following the air flow with little or no velocity slip. Velocity measurements with airfoil at various angles of attack are now being carried out in conjuction with schlieren flow visualization. In the near future pressure distribution around and on the airfoil will be obtained by putting pressure taps on the side windows and using a pressure tap model (currently under construction) of the airfoil