K-Theory for group C^*-algebras

These notes are based on a lecture course given by the first author in the Sedano Winter School on K-theory held in Sedano, Spain, on January 22-27th of 2007. They aim at introducing K-theory of C^*-algebras, equivariant K-homology and KK-theory in the context of the Baum-Connes conjecture.Comment: 22 pages, 2 figures, to be published in Springer Lecture Note

Composition-induced structural transitions in mixed rare-gas clusters

The low-energy structures of mixed Ar--Xe and Kr--Xe Lennard-Jones clusters are investigated using a newly developed parallel Monte Carlo minimization algorithm with specific exchange moves between particles or trajectories. Tests on the 13- and 19- atom clusters show a significant improvement over the conventional basin-hopping method, the average search length being reduced by more than one order of magnitude. The method is applied to the more difficult case of the 38-atom cluster, for which the homogeneous clusters have a truncated octahedral shape. It is found that alloys of dissimilar elements (Ar--Xe) favor polytetrahedral geometries over octahedra due to the reduced strain penalty. Conversely, octahedra are even more stable in Kr--Xe alloys than in Kr_38 or Xe_38, and they show a core-surface phase separation behavior. These trends are indeed also observed and further analysed on the 55-atom cluster. Finally, we correlate the relative stability of cubic structures in these clusters to the glassforming character of the bulk mixtures.Comment: 14 pages, 8 figures, 5 tables PRB vol 70, in pres

An aeroacoustic investigation into the effect of self-oscillating trailing edge flaplets

The aeroacoustics of a NACA 0012 aerofoil with an array of self-oscillating flexible flaplets attached on the trailing edge has been investigated at low to moderate chord based Reynolds number (50,000 -- 350,000) and at geometric angles of attack from $\alpha_g = 0^\circ$ -- $20^\circ$. When the aerofoil is untripped, tonal peaks are observed on the baseline aerofoil. When the passive flaplets are attached to the pressure side of the aerofoil, the tonal peak is removed. If the flaplets are then placed on the suction side, the tonal peak is reduced, but not removed. It is therefore hypothesised that the flaplets on the pressure side modifies the laminar separation bubble situated on the pressure side of the aerofoil, a key mechanism for tonal noise. Throughout all cases, both tripped and untripped, a low frequency (0.1 kHz -- 0.6 kHz) noise reduction and a slight increase at higher frequencies (>2 kHz) is seen. This gives an average overall sound pressure level (OSPL) reduction of 1.5 -- 2 dB for the flaplets affixed to the pressure side. The cases where the tonal noise component is removed an OSPL reduction of up to 20 dB can be seen

Vortex Shedding and Modal Behavior of a Circular Cylinder Equipped with Flexible Flaps

When a cylinder is subject to a flow, vortices will be shed that can lead to strong tonal noise. The modification of the cylinder with soft, flexible flaps made of silicone rubber has been shown to affect the vortex shedding cycle in a way that the Strouhal number associated with the vortex shedding suddenly jumps to a higher value at a certain Reynolds number. In the present study, the effect of the flexible flaps on the vortex shedding is further examined by subsequently reducing the number of flaps and additionally shortening their length. Acoustic measurements and camera recordings of the flap motion, performed in an aeroacoustic wind tunnel, suggest that the sudden jump of the Reynolds number is caused by the movement of the outer flaps. A comparison with the eigenfrequencies obtained from a numerical modal analysis of the different flap rings revealed that the cause of the Strouhal number jump is most likely a lock-in of the natural vortex shedding cycle with the next higher eigenfrequency of the outer flaps

Population Annealing with Weighted Averages: A Monte Carlo Method for Rough Free Energy Landscapes

The population annealing algorithm introduced by Hukushima and Iba is described. Population annealing combines simulated annealing and Boltzmann weighted differential reproduction within a population of replicas to sample equilibrium states. Population annealing gives direct access to the free energy. It is shown that unbiased measurements of observables can be obtained by weighted averages over many runs with weight factors related to the free energy estimate from the run. Population annealing is well suited to parallelization and may be a useful alternative to parallel tempering for systems with rough free energy landscapes such as spin glasses. The method is demonstrated for spin glasses.Comment: 9 pages, 5 figures; version 2 has improved figure 5 and new titl