Examples of Non-Rigid CAT(0) Groups from the Category of Knot Groups

C Croke and B Kleiner have constructed an example of a CAT(0) group with more than one visual boundary. J Wilson has proven that this same group has uncountably many distinct boundaries. In this article we prove that the knot group of any connected sum of two non-trivial torus knots also has uncountably many distinct CAT(0) boundaries.Comment: 16 pages, 2 figure

Locally covariant quantum field theory with external sources

We provide a detailed analysis of the classical and quantized theory of a multiplet of inhomogeneous Klein-Gordon fields, which couple to the spacetime metric and also to an external source term; thus the solutions form an affine space. Following the formulation of affine field theories in terms of presymplectic vector spaces as proposed in [Annales Henri Poincare 15, 171 (2014)], we determine the relative Cauchy evolution induced by metric as well as source term perturbations and compute the automorphism group of natural isomorphisms of the presymplectic vector space functor. Two pathological features of this formulation are revealed: the automorphism group contains elements that cannot be interpreted as global gauge transformations of the theory; moreover, the presymplectic formulation does not respect a natural requirement on composition of subsystems. We therefore propose a systematic strategy to improve the original description of affine field theories at the classical and quantized level, first passing to a Poisson algebra description in the classical case. The idea is to consider state spaces on the classical and quantum algebras suggested by the physics of the theory (in the classical case, we use the affine solution space). The state spaces are not separating for the algebras, indicating a redundancy in the description. Removing this redundancy by a quotient, a functorial theory is obtained that is free of the above mentioned pathologies. These techniques are applicable to general affine field theories and Abelian gauge theories. The resulting quantized theory is shown to be dynamically local.Comment: v2: 42 pages; Appendix C on deformation quantization and references added. v3: 47 pages; compatible with version to appear in Annales Henri Poincar

An experimental study of interceptors for drag reduction on high-performance sailing yachts

Interceptors have been widely used in recent years in fast ferries and small high-speed leisure and commercial craft for ride and trim control, and steering. In the context of high-performance sailing yachts, they first appeared in 2008 on the yacht Ecover 3 which was dismasted while leading the Vendee Globe Challenge race. However, in spite of their popularity in power craft, few studies have been published investigating the impact of interceptors on vessel performance, and apparently none in the case of sailing yachts. In the current study, interceptors are compared with an aerodynamic device known as a Gurney flap. It is shown that interceptors are generally substantially smaller than Gurney flaps. A comprehensive experiment programme is presented exploring the impact of interceptors on the performance of an Open 60 yacht hull. Results show a marked reduction in calm-water resistance over a wide speed range, with benefits of 10–18% in the speed range between 8 and 20 knots, accompanied by reduced sinkage and trim. The gains observed are much larger than those observed in powercraft, and also substantially greater than those achievable through trim changes by moving ballast longitudinally. The benefits appear to be largely sustained in small waves