Pulsation and Precession of the Resonant Swinging Spring

When the frequencies of the elastic and pendular oscillations of an elastic pendulum or swinging spring are in the ratio two-to-one, there is a regular exchange of energy between the two modes of oscillation. We refer to this phenomenon as pulsation. Between the horizontal excursions, or pulses, the spring undergoes a change of azimuth which we call the precession angle. The pulsation and stepwise precession are the characteristic features of the dynamics of the swinging spring. The modulation equations for the small-amplitude resonant motion of the system are the well-known three-wave equations. We use Hamiltonian reduction to determine a complete analytical solution. The amplitudes and phases are expressed in terms of both Weierstrass and Jacobi elliptic functions. The strength of the pulsation may be computed from the invariants of the equations. Several analytical formulas are found for the precession angle. We deduce simplified approximate expressions, in terms of elementary functions, for the pulsation amplitude and precession angle and demonstrate their high accuracy by numerical experiments. Thus, for given initial conditions, we can describe the envelope dynamics without solving the equations. Conversely, given the parameters which determine the envelope, we can specify initial conditions which, to a high level of accuracy, yield this envelope.Comment: 33 pages, 9 eps figure

Estimating the potential impacts of open access to research findings

Advances in information and communication technologies are disrupting traditional models of scholarly publishing, radically changing our capacity to reproduce, distribute, control, and publish information. The key question is whether there are new opportunities and new models for scholarly publishing that would better serve researchers and better communicate and disseminate research findings. Identifying access and efficiency limitations under the subscription publishing model, this paper explores the potential impacts of enhanced access to research outputs using a modified Solow-Swan model, which introduces ‘accessibility’ and ‘efficiency’ parameters into calculating returns to R&D. Indicative impact ranges are presented for Government, Higher Education and Australian Research Council R&D expenditures. We conclude that there may be substantial benefits to be gained from more open access to research findings

The symmetry of intersection numbers in group theory

For suitable subgroups of a finitely generated group, we define the intersection number of one subgroup with another subgroup and show that this number is symmetric. We also give an interpretation of this number.Comment: 19 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol2/paper2.abs.html . Includes erratum added to the original, published 19 Mar 199

Working wetlands: classifying wetland potential for agriculture

Wetlands / Ecology / Natural resources / Social aspects / Case studies / Zanzibar / Tanzania / Zimbabwe / Swaziland

Anisotropy of the Cosmic Microwave Background Radiation on Large and Medium Angular Scales

This grant has supported work at Brown University on measurements of the 2.7 K Cosmic Microwave Background Radiation (CMB). The goal has been to characterize the spatial variations in the temperature of the CMB in order to understand the formation of large-scale structure in the universe. We have concurrently pursued two measurements using millimeter-wave telescopes carried aloft by scientific balloons. Both systems operate over a range of wavelengths, chosen to allow spectral removal of foreground sources such as the atmosphere, Galaxy, etc. The angular resolution of approx. 25 arcminutes is near the angular scale at which the most structure is predicted by current models to be visible in the CMB angular power spectrum. The main goal is to determine the angular scale of this structure; in turn we can infer the density parameter, Omega, for the universe as well as other cosmological parameters, such as the Hubble constant

On the Universality of Mesoscience: Science of 'the in-between'

The universality of mesoscales, ranging between elemental particles and the universe, is discussed here by reviewing widely disparate fields and presenting four cases, at differing hierarchical levels, from chemistry, chemical engineering, meteorology, through to astronomy. An underpinning concept, "Compromise in competition", is highlighted between various dominant, but competing mechanisms, and is identified here to be the universal origin of complexity and diversity in such examples. We therefore advance this as a key underlying principle of an emerging science -- Mesoscience.Comment: 8 pages, 1 figur

Targeting Angiogenesis in Childhood Sarcomas

Angiogenesis and vasculogenesis constitute two processes in the formation of new blood vessels and are essential for progression of solid tumors. Consequently, targeting angiogenesis, and to a lesser extent vasculogenesis, has become a major focus in cancer drug development. Angiogenesis inhibitors are now being tested in pediatric populations whereas inhibitors of vasculogenesis are in an earlier stage of development. Despite the initial enthusiasm for targeting angiogenesis for treatment of cancer, clinical trials have shown only incremental increases in survival, and agents have been largely cytostatic rather than inducing tumor regressions. Consequently, the role of such therapeutic approaches in the context of curative intent for childhood sarcomas is less clear. Here we review the literature on blood vessel formation in sarcomas with a focus on pediatric sarcomas and developments in targeting angiogenesis for treatment of these rare cancers

IRS-1: Auditing the effectiveness of mTOR inhibitors

Rapamycin analogs that inhibit mTOR signaling have antitumor activity against certain lymphomas, but treatment of solid tumors has been less encouraging despite inhibition of mTOR function. Two recent papers give insight into the potential use of mTOR inhibitors. O'Reilly et al. provide evidence that poor tumor response to rapamycins is the result of relieving mTOR-mediated feedback inhibition of insulin receptor substrate 1, and activation of Akt-mediated survival. In the second paper, Kaper et al. address the impact of pathway activation on hypoxia-mediated downregulation of mTOR signaling, raising the possibility that rapalogs could selectively inhibit hypoxic cells