Passive venting technique for shallow cavities

A device is introduced for reducing drag and store separation difficulties caused by shallow cavities on aircraft in supersonic flight consisting of a group of hollow pipes the same length as the cavity. The pipes are attached to the cavity floor so as to allow air to flow through the pipes. This device allows air to flow through the pipes opposite to the direction of flow outside the pipes. This results in reduced drag and improved store separation characteristics

One-sided Heegaard splittings of RP^3

Using basic properties of one-sided Heegaard splittings, a direct proof that geometrically compressible one-sided splittings of RP^3 are stabilised is given. The argument is modelled on that used by Waldhausen to show that two-sided splittings of S^3 are standard.Comment: This is the version published by Algebraic & Geometric Topology on 20 September 200

Experimental cavity pressure distributions at supersonic speeds

An investigation was conducted to define pressure distributions for rectangular cavities over a range of free-stream Mach numbers and cavity dimensions. These pressure distributions together with schlieren photographs are used to define the critical values of cavity length-to-depth ratio that separate open type cavity flows from closed type cavity flows. For closed type cavity flow, the shear layer expands over the cavity leading edge and impinges on the cavity floor, whereas for open type cavity flow, the shear layer bridges the cavity. The tests were conducted by using a flat-plate model permitting the cavity length to be remotely varied from 0.5 to 12 in. Cavity depths and widths were varied from 0.5 to 2.5 in. The flat-plate boundary layer approaching the cavity was turbulent and had a thickness of approximately 0.2 in. at the cavity front face for the range of test Mach numbers from 1.5 to 2.86. Presented are a discussion of the results and a complete tabulation of the experimental data

Invariants for Lagrangian tori

We define an simple invariant of an embedded nullhomologous Lagrangian torus and use this invariant to show that many symplectic 4-manifolds have infinitely many pairwise symplectically inequivalent nullhomologous Lagrangian tori. We further show that for a large class of examples that lambda(T) is actually a C-infinity invariant. In addition, this invariant is used to show that many symplectic 4-manifolds have nontrivial homology classes which are represented by infinitely many pairwise inequivalent Lagrangian tori, a result first proved by S Vidussi for the homotopy K3-surface obtained from knot surgery using the trefoil knot in [Lagrangian surfaces in a fixed homology class: existence of knotted Lagrangian tori, J. Diff. Geom. (to appear)].Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper25.abs.htm

Primitive Words, Free Factors and Measure Preservation

Let F_k be the free group on k generators. A word w \in F_k is called primitive if it belongs to some basis of F_k. We investigate two criteria for primitivity, and consider more generally, subgroups of F_k which are free factors. The first criterion is graph-theoretic and uses Stallings core graphs: given subgroups of finite rank H \le J \le F_k we present a simple procedure to determine whether H is a free factor of J. This yields, in particular, a procedure to determine whether a given element in F_k is primitive. Again let w \in F_k and consider the word map w:G x G x ... x G \to G (from the direct product of k copies of G to G), where G is an arbitrary finite group. We call w measure preserving if given uniform measure on G x G x ... x G, w induces uniform measure on G (for every finite G). This is the second criterion we investigate: it is not hard to see that primitivity implies measure preservation and it was conjectured that the two properties are equivalent. Our combinatorial approach to primitivity allows us to make progress on this problem and in particular prove the conjecture for k=2. It was asked whether the primitive elements of F_k form a closed set in the profinite topology of free groups. Our results provide a positive answer for F_2.Comment: This is a unified version of two manuscripts: "On Primitive words I: A New Algorithm", and "On Primitive Words II: Measure Preservation". 42 pages, 14 figures. Some parts of the paper reorganized towards publication in the Israel J. of Mat

Embedding right-angled Artin groups into graph braid groups

We construct an embedding of any right-angled Artin group $G(\Delta)$ defined by a graph $\Delta$ into a graph braid group. The number of strands required for the braid group is equal to the chromatic number of $\Delta$. This construction yields an example of a hyperbolic surface subgroup embedded in a two strand planar graph braid group.Comment: 8 pages. Final version, appears in Geometriae Dedicata

Cosmic censorship of smooth structures

It is observed that on many 4-manifolds there is a unique smooth structure underlying a globally hyperbolic Lorentz metric. For instance, every contractible smooth 4-manifold admitting a globally hyperbolic Lorentz metric is diffeomorphic to the standard $\R^4$. Similarly, a smooth 4-manifold homeomorphic to the product of a closed oriented 3-manifold $N$ and $\R$ and admitting a globally hyperbolic Lorentz metric is in fact diffeomorphic to $N\times \R$. Thus one may speak of a censorship imposed by the global hyperbolicty assumption on the possible smooth structures on $(3+1)$-dimensional spacetimes.Comment: 5 pages; V.2 - title changed, minor edits, references adde