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

Radiolysis of Macromolecular Organic Material in Mars-Relevant Mineral Matrices

The fate of organic material on Mars after deposition is crucial to interpreting the source of these molecules. Previous work has addressed how various organic compounds at millimeter depths in sediments respond to ultraviolet radiation. In contrast, this study addressed how highenergy particle radiation (200MeV protons, simulating the effect of galactic cosmic rays and solar wind at depths of <45 cm) inuences organic macromolecules in sediments. Specically, we report the generation of organicacid radiolysis products after exposure to radiation doses equivalent to geological time scales (17 Myr). We found that formate and oxalate were produced from a variety of organic starting materials and mineral matrices. Unlike ultravioletdriven reactions that can invoke Fenton chemistry to produce organic acids, our work suggests that irradiation of semiconductor surfaces, such as TiO2 or possible clay minerals found on Mars, forms oxygen and hydroxyl radical species, which can break down macromolecules into organic acids. We also investigated the metastability of benzoate in multiple mineral matrices. Benzoate was added to samples prior to irradiation and persisted up to 500 kGys of exposure. Our ndings suggest that organic acids are likely a major component of organic material buried at depth on Mars

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

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

Computer program for calculating aerodynamic characteristics of upper-surface-blowing and over-wing-blowing configurations

The program is based on the inviscid wing-jet interaction theory of Lan and Campbell, and the jet entrainment theory of Lan. In the interaction theory, the flow perturbations are computed both inside and outside the jet, separately, and then matched on the jet surface to satisfy the jet boundary conditions. The jet Mach number is allowed to be different from the free stream value (Mach number nonuniformity). These jet boundary conditions require that the static pressure be continuous across the jet surface which must always remain as a stream surface. These conditions, as well as the wing-surface tangency condition, are satisified only in the linearized sense. The detailed formulation of these boundary conditions is based on the quasi-vortex-lattice method of Lan