2,579 research outputs found
The Cayley transform and uniformly bounded representations
No full textLet G be a simple Lie group of real rank one, with Iwasawa decomposition KA \bar N and Bruhat
big cell NMA\bar N: Then the space G/MA \bar N may be (almost) identified with N and with K /M,
and these identifications induce the (generalised) Cayley transform C : N \to K /M. We show
that C is a conformal map of Carnot–Caratheodory manifolds, and that composition with the
Cayley transform, combined with multiplication by appropriate powers of the Jacobian,
induces isomorphisms of Sobolev spaces on N
and on K/M. We use this to construct
uniformly bounded and slowly growing representations of G
A weak type (1,1) estime for a maximal operator on a group ofisometries of homogeneous trees
No full textWe give a simple proof of a result of R. Rochberg and M. H. Taibleson that various maximal operators on a homogeneous tree, including the Hardy-Littlewood and spherical maximal operators, are of weak type (1, 1). This result extends to corresponding maximal operators on a transitive group of isometrics of the tree, and in particular for (nonabelian finitely generated) free groups
Aerodynamic analysis of cowling misalignment on a two-man bobsleigh
No full textBobsleighing is one of the fastest winter sports and races are decided within seconds over total times up to four minutes. Therefore marginal gains in performance of the bobsleigh and its crew can determine the race outcome. In order to improve the performance of a bobsleigh the aerodynamic drag can be investigated. A bobsleigh consists of two parts which are connected pivotally: the nose and the rear part of the sleigh. In a track curve the bobsleigh nose will be misaligned with the rear cowling. This phenomena is believed to influence the aerodynamic drag of a bobsleigh. Therefore the objective of this research is to investigate the effect of cowling misalignment between front and rear cowling on the aerodynamic drag of a two-man bobsleigh. To analyse this effect on the aerodynamic drag two types of drag measuring campaigns are performed: wind tunnel experiments and numerical simulations. Flowvisualisation (bothwoollen tuft measurements and particle image velocimetry) is performed and force measurements are executed on a simplified bobsleigh model in the wind tunnel. As bobsleigh features such as bumpers, skies and frame are influencing the flow behaviour these are not integrated in the model such that the measurements solely focus on the effect of nose rotation. Next to these wind tunnel measurements numerical simulations are performed on the samemodel to predict and visualise the internal and external bobsleigh flow behaviour. A bobsleigh is a bluff body which means that the drag is mostly influenced by the geometry and flow separation causing a pressure difference between the flow in front of and the flow trailing the body. This pressure difference causes a suction force on the bobsleigh which accounts for the major drag component. As the air flows over the bobsleigh it separates behind the head of the pilot and at the cowling edges. A low pressure region is therefore seen behind the pilot and brakeman which causes the the external streamlines to be sucked into the cavity. This causes a low pressure wake with rotational flows. It is shown that the aerodynamic drag increases with nose rotation. This increase is partly due to the fact that the frontal area increases with nose rotation. The flow stagnates on one side of the body whereas an overlap is found on the opposite site of the bobsleigh. Behind this overlap a separated region develops where air enters the nose due to backflow in the separation bubble behind the nose on the rear body. This separated flow reattaches to the rear body such that an effective frontal area increase increases the aerodynamic drag. However, it is found that this effective frontal area increase is not the only contributor to the total drag. The air entering the nose influences the internal flow behaviour causing a loss inmomentumdue to the internal blockage imposed by both the crew and the equipment. As the distance between the nose and rear cowling increases the aerodynamic drag increases as well. In order to minimise the influence of nose rotation on the aerodynamic drag a shape optimisation of the nose is recommended. This can lead to better aerodynamic performance of the bobsleigh both on a straight track segment as in a curve.Aerospace EngineeringAerodynamics, Wind Energy & Propulsio
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