Geodesic knots in cusped hyperbolic 3-manifolds

We consider the existence of simple closed geodesics or "geodesic knots" in finite volume orientable hyperbolic 3-manifolds. Previous results show that at least one geodesic knot always exists [Bull. London Math. Soc. 31(1) (1999) 81-86], and that certain arithmetic manifolds contain infinitely many geodesic knots [J. Diff. Geom. 38 (1993) 545-558], [Experimental Mathematics 10(3) (2001) 419-436]. In this paper we show that all cusped orientable finite volume hyperbolic 3-manifolds contain infinitely many geodesic knots. Our proof is constructive, and the infinite family of geodesic knots produced approach a limiting infinite simple geodesic in the manifold.Comment: This is the version published by Algebraic & Geometric Topology on 19 November 200

Experimental investigation of transitional flow in a toroidal pipe

The flow instability and further transition to turbulence in a toroidal pipe (torus) with curvature (tube-to-coiling diameter) 0.049 is investigated experimentally. The flow inside the toroidal pipe is driven by a steel sphere fitted to the inner pipe diameter. The sphere is moved with constant azimuthal velocity from outside the torus by a moving magnet. The experiment is designed to investigate curved pipe flow by optical measurement techniques. Using stereoscopic particle image velocimetry, laser Doppler velocimetry and pressure drop measurements, the flow is measured for Reynolds numbers ranging from 1000 to 15000. Time- and space-resolved velocity fields are obtained and analysed. The steady axisymmetric basic flow is strongly influenced by centrifugal effects. On an increase of the Reynolds number we find a sequence of bifurcations. For Re=4075 a supercritical bifurcation to an oscillatory flow is found in which waves travel in the streamwise direction with a phase velocity slightly faster than the mean flow. The oscillatory flow is superseded by a presumably quasi-periodic flow at a further increase of the Reynolds number before turbulence sets in. The results are found to be compatible, in general, with earlier experimental and numerical investigations on transition to turbulence in helical and curved pipes. However, important aspects of the bifurcation scenario differ considerably

Three component laser Doppler measurements in an axisymmetric jet

A three-component laser Doppler anemometer (LDA) was used to acquire a detailed set of three-dimensional mean and fluctuating velocity measurements in a low-speed air jet entering a stagnant ambient, over the first 20 jet exit diameters along the jet trajectory. These data are physically consistent with previous measurements in axisymmetric jets. The relative difficulty of obtaining three-dimensional and two-dimensional LDA data is briefly discussed

Patterns of diversity, endemism and distribution of bees (Insecta: Hymenoptera: Anthophila) in southern Africa

AbstractFor southern Africa, patterns of bee diversity and endemism were studied with a special focus on South Africa and the Cape Floral Kingdom. Based on distribution records of 645 species incorporated in the “Southern African Bee Database” (SouthABees), the pattern of bee diversity was analysed on a 2°×2° grid. The resulting map shows a bicentric pattern, with highest species diversity located in the arid west and in the relatively moist east. The investigation of distribution patterns of 516 South African species identified twelve distribution types that largely coincide with patterns in the seasonality of precipitation: winter rainfall, early to mid summer rainfall, late to very late summer rainfall and rain all year. The largest number of bee species is associated with the winter rainfall area (46.3% of the fauna) and with the early to mid summer rainfall area (36.5% of the fauna). Consequently South Africa is a centre of bee diversity of global significance. The most important centres of endemism are the winter rainfall area in the west (27.3% of total fauna endemic) and the early to mid summer rainfall area (29.1% of total fauna endemic) in the east. The relationship between bee/plant diversity patterns and speciation is discussed

Subcritical versus supercritical transition to turbulence in curved pipes

Transition to turbulence in straight pipes occurs in spite of the linear stability of the laminar Hagen--Poiseuille flow if the amplitude of flow perturbations as well as the Reynolds number exceed a minimum threshold (subcritical transition). As the pipe curvature increases centrifugal effects become important, modifying the basic flow as well as the most unstable linear modes. If the curvature (tube-to-coiling diameter $d/D$) is sufficiently large a Hopf bifurcation (supercritical instability) is encountered before turbulence can be excited (subcritical instability). We trace the instability thresholds in the $Re-d/D$ parameter space in the range $0.01\leq\ d/D \leq0.1$ by means of laser-Doppler velocimetry and determine the point where the subcritical and supercritical instabilities meet. Two different experimental setups were used: a closed system where the pipe forms an axisymmetric torus and an open system employing a helical pipe. Implications for the measurement of friction factors in curved pipes are discussed

Regional Economic Issues: Determinants of Recession Duration and Determinants of New Firm Formation

Why are some regional economies able to outperform those of other regions? Using state-level data in two separate analyses, this thesis shows that industrial diversity is one potential answer. Industrial diversity is calculated using the Herfindahl index. In the first model, duration analysis on state recessions occurring between 1979 and 1996 indicates that an increase in industrial diversity is associated with shorter recessions. Other determinants of recession duration include unemployment, change in real income per capita, proportion of non-white workers, total population, and change in population growth. In the second model, regression analyses on 2001 firm formation rates show that higher levels of industrial diversity are associated with higher rates of new small firm formation. Other determinants of small firm formation include education, availability of financing, average size of existing establishments, and presence of environmental hazardous waste sites. Based on these results for industrial diversity, state policies aimed at increasing diversity appear to be justifiable

The Moment Problem for Continuous Positive Semidefinite Linear functionals

Let $\tau$ be a locally convex topology on the countable dimensional polynomial $\reals$-algebra \rx:=\reals[X_1,...,X_n]. Let $K$ be a closed subset of $\reals^n$, and let $M:=M_{\{g_1, ... g_s\}}$ be a finitely generated quadratic module in \rx. We investigate the following question: When is the cone \Pos(K) (of polynomials nonnegative on $K$) included in the closure of $M$? We give an interpretation of this inclusion with respect to representing continuous linear functionals by measures. We discuss several examples; we compute the closure of M=\sos with respect to weighted norm-$p$ topologies. We show that this closure coincides with the cone \Pos(K) where $K$ is a certain convex compact polyhedron.Comment: 14 page