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

The Economic Impact of Enhanced Access to Research Findings

The environment in which research is being conducted and disseminated is undergoing profound change, with new technologies offering new opportunities, changing research practices demanding new capabilities, and increased focus on research performance. A key question facing us today is, are there new opportunities and new models for scholarly communication that could enhance the dissemination of research findings and, thereby, increase the returns to investment in R&D? Identifying access and efficiency limitations under the subscription-based publishing model that has dominated scientific publishing, this paper explores the potential impacts of enhanced access to research outputs. We develop a modified growth model, introducing access and efficiency into calculating the returns to R&D. Indicative impact ranges are presented for gross expenditure on R&D (GERD) and government expenditure on R&D (GovERD) for all OECD countries. We conclude that there may be substantial benefits to be gained from increased access to research findings, and our preliminary estimates suggest that this may be fertile ground for further policy relevant inquiry

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

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

The simulation of action disorganisation in complex activities of daily living

Action selection in everyday goal-directed tasks of moderate complexity is known to be subject to breakdown following extensive frontal brain injury. A model of action selection in such tasks is presented and used to explore three hypotheses concerning the origins of action disorganisation: that it is a consequence of reduced top-down excitation within a hierarchical action schema network coupled with increased bottom-up triggering of schemas from environmental sources, that it is a more general disturbance of schema activation modelled by excessive noise in the schema network, and that it results from a general disturbance of the triggering of schemas by object representations. Results suggest that the action disorganisation syndrome is best accounted for by a general disturbance to schema activation, while altering the balance between top-down and bottom-up activation provides an account of a related disorder - utilisation behaviour. It is further suggested that ideational apraxia (which may result from lesions to left temporoparietal areas and which has similar behavioural consequences to action disorganisation syndrome on tasks of moderate complexity) is a consequence of a generalised disturbance of the triggering of schemas by object representations. Several predictions regarding differences between action disorganisation syndrome and ideational apraxia that follow from this interpretation are detailed

Natural climate solutions

Our thanks for inputs by L. Almond, A. Baccini, A. Bowman, S. CookPatton, J. Evans, K. Holl, R. Lalasz, A. Nassikas, M. Spalding, M. Wolosin, and expert elicitation respondents. Our thanks for datasets developed by the Hansen lab and the NESCent grasslands working group (C. Lehmann, D. Griffith, T. M. Anderson, D. J. Beerling, W. Bond, E. Denton, E. Edwards, E. Forrestel, D. Fox, W. Hoffmann, R. Hyde, T. Kluyver, L. Mucina, B. Passey, S. Pau, J. Ratnam, N. Salamin, B. Santini, K. Simpson, M. Smith, B. Spriggs, C. Still, C. Strömberg, and C. P. Osborne). This study was made possible by funding from the Doris Duke Charitable Foundation. Woodbury was supported in part by USDA-NIFA Project 2011-67003-30205 Data deposition: A global spatial dataset of reforestation opportunities has been deposited on Zenodo (https://zenodo.org/record/883444). This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1710465114/-/DCSupplemental.Peer reviewedPublisher PD

Anomalous scaling and spin-charge separation in coupled chains

We use a bosonization approach to show that the three dimensional Coulomb interaction in coupled metallic chains leads to a Luttinger liquid for vanishing inter-chain hopping $t_{\bot}$, and to a Fermi liquid for any finite $t_{\bot}$. However, for small $t_{\bot} \neq 0$ the Greens-function satisfies a homogeneity relation with a non-trivial exponent $\gamma_{cb}$ in a large intermediate regime. Our results offer a simple explanation for the large values of $\gamma_{cb}$ inferred from recent photoemission data from quasi one-dimensional conductors and might have some relevance for the understanding of the unusual properties of the high-temperature superconductors.Comment: compressed and uuencoded ps-file, including the figures, accepted for publication in Phys. Rev. Lett

Non-Relativistic Fermions Coupled to Transverse Gauge-Fields: The Single-Particle Green's Function in Arbitrary Dimension

We use a bosonization approach to calculate the single-particle Green's function $G ( {\bf{r}} , \tau )$ of non-relativistic fermions coupled to transverse gauge-fields in arbitrary dimension $d$. We find that in $d>3$ transverse gauge-fields do not destroy the Fermi liquid, although for $d < 6$ the quasi-particle damping is anomalously large. For $d \rightarrow 3$ the quasi-particle residue vanishes as $Z \propto \exp [ - \frac{1}{2 \pi ( d-3)} (\frac{ \kappa}{mc } )^2 ]$, where $\kappa$ is the Thomas-Fermi wave-vector, $m$ is the mass of the electrons, and $c$ is the velocity of the gauge-particle. In $d=3$ the system is a Luttinger liquid, with anomalous dimension $\gamma_{\bot} = \frac{1}{6 \pi} ( \frac{ \kappa}{mc} )^2$. For $d < 3$ we find that $G ({\bf{r}} , 0 )$ decays exponentially at large distances.Comment: RevTex, no figures

Acceptability of alginate enriched bread and its effect on fat digestion in humans

Lifestyle interventions and physical activity remain the cornerstone of obesity management, as pharmacological therapies (orlistat) are associated with gastrointestinal (GI) side effects. Combining orlistat with fibers can reduce side effects, improving compliance. Therefore, a fiber that inhibits lipase without side effects could help treat obesity. The aims of the present work were to assess whether alginate enriched bread could inhibit fat digestion, and assess the acceptability of alginate bread and its effect on GI wellbeing. A double-blind, randomised, controlled cross-over pilot study (NCT03350958) assessed the impact of an alginate bread meal on; lipid content in ileal effluent and circulating triacylglycerol levels. This was compared against the same meal with non-enriched (control) bread. GI wellbeing and acceptability of alginate bread was compared to control bread through daily wellbeing questionnaires and food diaries (NCT03477981). Control bread followed by alginate bread were consumed for two weeks respectively. Consumption of alginate bread reduced circulating triacylglycerol compared to control (2% reduction in AUC) and significantly increased lipid content in ileal effluent (3.8 g ± 1.6 after 210 min). There were no significant changes to GI wellbeing when comparing alginate bread to control bread. A significant increase in the feeling of fullness occurred with alginate bread compared to baseline and the first week of control bread consumption. This study showed that sustained consumption of alginate enriched bread does not alter GI wellbeing and can decrease lipolysis, increasing lipid leaving the small intestine. Further studies are required to demonstrate that reduced fat digestion through the action of alginate can reduce fat mass or body weight