Calculation of the Stability Index in Parameter-Dependent Calculus of Variations Problems: Buckling of a Twisted Elastic Strut

We consider the problem of minimizing the energy of an inextensible elastic strut with length 1 subject to an imposed twist angle and force. In a standard calculus of variations approach, one first locates equilibria by solving the Euler--Lagrange ODE with boundary conditions at arclength values 0 and 1. Then one classifies each equilibrium by counting conjugate points, with local minima corresponding to equilibria with no conjugate points. These conjugate points are arclength values $\sigma \le 1$ at which a second ODE (the Jacobi equation) has a solution vanishing at $0$ and $\sigma$. Finding conjugate points normally involves the numerical solution of a set of initial value problems for the Jacobi equation. For problems involving a parameter $\lambda$, such as the force or twist angle in the elastic strut, this computation must be repeated for every value of $\lambda$ of interest. Here we present an alternative approach that takes advantage of the presence of a parameter $\lambda$. Rather than search for conjugate points $\sigma \le 1$ at a fixed value of $\lambda$, we search for a set of special parameter values $\lambda_m$ (with corresponding Jacobi solution \bfzeta^m) for which $\sigma=1$ is a conjugate point. We show that, under appropriate assumptions, the index of an equilibrium at any $\lambda$ equals the number of these \bfzeta^m for which \langle \bfzeta^m, \Op \bfzeta^m \rangle < 0, where \Op is the Jacobi differential operator at $\lambda$. This computation is particularly simple when $\lambda$ appears linearly in \Op. We apply this approach to the elastic strut, in which the force appears linearly in \Op, and, as a result, we locate the conjugate points for any twisted unbuckled rod configuration without resorting to numerical solution of differential equations. In addition, we numerically compute two-dimensional sheets of buckled equilibria (as the two parameters of force and twist are varied) via a coordinated family of one-dimensional parameter continuation computations. Conjugate points for these buckled equilibria are determined by numerical solution of the Jacobi ODE

Passive CO₂ removal in urban soils:evidence from brownfield sites

Management of urban brownfield land can contribute to significant removal of atmospheric CO2 through the development of soil carbonate minerals. However, the potential magnitude and stability of this carbon sink is poorly quantified as previous studies address a limited range of conditions and short durations. Furthermore, the suitability of carbonate-sequestering soils for construction has not been investigated. To address these issues we measured total inorganic carbon, permeability and ground strength in the top 20 cm of soil at 20 brownfield sites in northern England, between 2015 and 2017. Across all sites accumulation occurred at a rate of 1–16 t C ha−1 yr−1, as calcite (CaCO3), corresponding to removal of approximately 4–59 t CO2 ha−1 yr−1, with the highest rate in the first 15 years after demolition. C and O stable isotope analysis of calcite confirms the atmospheric origin of the measured inorganic carbon. Statistical modelling found that pH and the content of fine materials (combined silt and clay content) were the best predictors of the total inorganic carbon content of the samples. Measurement of permeability shows that sites with carbonated soils possess a similar risk of run-off or flooding to sandy soils. Soil strength, measured as in-situ bearing capacity, increased with carbonation. These results demonstrate that the management of urban brownfield land to retain fine material derived from concrete crushing on site following demolition will promote calcite precipitation in soils, and so offers an additional CO2 removal mechanism, with no detrimental effect on drainage and possible improvements in strength. Given the large area of brownfield land that is available for development, the contribution of this process to CO2 removal by urban soils needs to be recognised in CO2 mitigation policies

Development of rotorcraft interior. Noise control concepts. Phase 1: Definition study

A description of helicopter noise, diagnostic techniques for source and path identification, an interior noise prediction model, and a measurement program for model validation are provided

Restoration of eucalypt grassy woodland: effects of experimental interventions on ground-layer vegetation

We report on the effects of broad-scale restoration treatments on the ground layer of eucalypt grassy woodland in south-eastern Australia. The experiment was conducted in two conservation reserves from which livestock grazing had previously been removed. Changes in biomass, species diversity, ground-cover attributes and life-form were analysed over a 4-year period in relation to the following experimental interventions: (1) reduced kangaroo density, (2) addition of coarse woody debris and (3) fire (a single burn). Reducing kangaroo density doubled total biomass in one reserve, but no effects on exotic biomass, species counts or ground cover attributes were observed. Coarse woody debris also promoted biomass, particularly exotic annual forbs, as well as plant diversity in one of the reserves. The single burn reduced biomass, but changed little else. Overall, we found the main driver of change to be the favourable growth seasons that had followed a period of drought. This resulted in biomass increasing by 67%, (mostly owing to the growth of perennial native grasses), whereas overall native species counts increased by 18%, and exotic species declined by 20% over the 4-year observation period. Strategic management of grazing pressure, use of fire where biomass has accumulated and placement of coarse woody debris in areas of persistent erosion will contribute to improvements in soil and vegetation condition, and gains in biodiversity, in the future.Funding and in-kind logistic support for this project was provided by the ACT Government as part of an Australian Research Council Linkage Grant (LP0561817; LP110100126). Drafts of the manuscript were read by Saul Cunningham and Ben Macdonald

Sequestering atmospheric CO₂ inorganically:a solution for Malaysia's CO₂ emission

Malaysia is anticipating an increase of 68.86% in CO2 emission in 2020, compared with the 2000 baseline, reaching 285.73 million tonnes. A major contributor to Malaysia's CO2 emissions is coal-fired electricity power plants, responsible for 43.4% of the overall emissions. Malaysia's forest soil offers organic sequestration of 15 tonnes of CO2 ha(-1) year(-1). Unlike organic CO2 sequestration in soil, inorganic sequestration of CO2 through mineral carbonation, once formed, is considered as a permanent sink. Inorganic CO2 sequestration in Malaysia has not been extensively studied, and the country's potential for using the technique for atmospheric CO2 removal is undefined. In addition, Malaysia produces a significant amount of solid waste annually and, of that, demolition concrete waste, basalt quarry fine, and fly and bottom ashes are calcium-rich materials suitable for inorganic CO2 sequestration. This project introduces a potential solution for sequestering atmospheric CO2 inorganically for Malaysia. If lands associated to future developments in Malaysia are designed for inorganic CO2 sequestration using demolition concrete waste, basalt quarry fine, and fly and bottom ashes, 597,465 tonnes of CO2 can be captured annually adding a potential annual economic benefit of (sic)4,700,000.</p

Protocol for a longitudinal qualitative study: survivors of childhood critical illness exploring long-term psychosocial well-being and needs–The SCETCH Project

Life-threatening critical illness affects over a quarter of a million children and adolescents (0-18 years old) annually in the USA and the UK. Death from critical illness is rare; however, survivors and their families can be exposed to a complex array of negative physical, psychological and social problems. Currently, within the literature, there is a distinct paucity of child and adolescent survivor self-reports, thus limiting our understanding of how survivors perceive this adversity and subsequently cope and grow in the long-term following their critical illness. This study aims to explore and understand psychosocial well-being and needs of critical illness survivors, 6-20 months post paediatric intensive care admission