Generalised knot groups distinguish the square and granny knots (with an appendix by David Savitt)

Given a knot K we may construct a group G_n(K) from the fundamental group of K by adjoining an nth root of the meridian that commutes with the corresponding longitude. These "generalised knot groups" were introduced independently by Wada and Kelly, and contain the fundamental group as a subgroup. The square knot SK and the granny knot GK are a well known example of a pair of distinct knots with isomorphic fundamental groups. We show that G_n(SK) and G_n(GK) are non-isomorphic for all n>1. This confirms a conjecture of Lin and Nelson, and shows that the isomorphism type of G_n(K), n>1, carries more information about K than the isomorphism type of the fundamental group. An appendix by David Savitt contains some results on representations of the trefoil group in PSL(2,p) that are needed for the proof.Comment: 25 pages, 5 figures, to appear in JKTR. v3: example of the target groups added; slight correction to the construction of the target groups; references updated; some changes to notation. v2: section 4.2 expanded to give overview of proo

Some factors influencing radiation of sound from flow interaction with edges of finite surfaces

Edges of surfaces which are exposed to unsteady flow cause both strictly acoustic effects and hydrodynamic effects, in the form of generation of new hydrodynamic sources in the immediate vicinity of the edge. An analytical model is presented which develops the explicit sound-generation role of the velocity and Mach number of the eddy convection past the edge, and the importance of relative scale lengths of the turbulence, as well as the relative intensity of pressure fluctuations. The Mach number (velocity) effects show that the important paramater is the convection Mach number of the eddies. The effects of turbulence scale lengths, isotropy, and spatial density (separation) are shown to be important in determining the level and spectrum of edge sound radiated for the edge dipole mechanism. Experimental data is presented which provides support for the dipole edge noise model in terms of Mach number (velocity) scaling, parametric dependence on flow field parameter, directivity, and edge diffraction effects

CCD Photometry of Delta Scuti stars 7 Aql and 8 Aql

As a continuation of the study of the Delta Scuti stars 7 Aql and 8 Aql; new CCD photometric data were acquired in 2007. We present a period analysis on these data that confirm the dominant modes detected in each star in the framework of the STEPHI XII campaign in 2003.Comment: 9 pages, 7 figures, 2 tables; Accepted for publication in Communications in Asteroseismology, Vol 153, 200

TiB_2 and ZrB_2 diffusion barriers in GaAs Ohmic contact technology

The transition metal diboride compounds, ZrB_2 and TiB_2, interposed between Ni/Ge/Au Ohmic contact metallization on n‐type GaAs wafers and an overlying thick Au contact layer, have been investigated to evaluate their effectiveness in stabilizing the Ohmic contact by limiting the in‐diffusion of Au. All of the metal layers were e‐beam deposited except the ZrB_2 which was rf‐diode sputtered. The barrier layer thicknesses were 50 and 100 nm for the TiB_2 and the ZrB_2, respectively. Postdeposition alloying of the contacts was performed at 400, 425, or 450 °C. Auger electron spectroscopy depth profiling of the resultant Ohmic contacts demonstrates that the barrier layers effectively preclude penetration of Au to the Ohmic contact structure. Specific contact resistivities for such contacts are in the low 10^(−7) Ω cm^2 range; although some degradation of the contact resistivity is observed after long term annealing, the values of resistivities do not exceed 1.5×10^(−6) Ω cm^2 after 92 h at 350 °C