Likely equilibria of stochastic hyperelastic spherical shells and tubes

In large deformations, internally pressurised elastic spherical shells and tubes may undergo a limit-point, or inflation, instability manifested by a rapid transition in which their radii suddenly increase. The possible existence of such an instability depends on the material constitutive model. Here, we revisit this problem in the context of stochastic incompressible hyperelastic materials, and ask the question: what is the probability distribution of stable radially symmetric inflation, such that the internal pressure always increases as the radial stretch increases? For the classic elastic problem, involving isotropic incompressible materials, there is a critical parameter value that strictly separates the cases where inflation instability can occur or not. By contrast, for the stochastic problem, we show that the inherent variability of the probabilistic parameters implies that there is always competition between the two cases. To illustrate this, we draw on published experimental data for rubber, and derive the probability distribution of the corresponding random shear modulus to predict the inflation responses for a spherical shell and a cylindrical tube made of a material characterised by this parameter.Comment: arXiv admin note: text overlap with arXiv:1808.0126

Likely oscillatory motions of stochastic hyperelastic solids

Stochastic homogeneous hyperelastic solids are characterised by strain-energy densities where the parameters are random variables defined by probability density functions. These models allow for the propagation of uncertainties from input data to output quantities of interest. To investigate the effect of probabilistic parameters on predicted mechanical responses, we study radial oscillations of cylindrical and spherical shells of stochastic incompressible isotropic hyperelastic material, formulated as quasi-equilibrated motions where the system is in equilibrium at every time instant. Additionally, we study finite shear oscillations of a cuboid, which are not quasi-equilibrated. We find that, for hyperelastic bodies of stochastic neo-Hookean or Mooney-Rivlin material, the amplitude and period of the oscillations follow probability distributions that can be characterised. Further, for cylindrical tubes and spherical shells, when an impulse surface traction is applied, there is a parameter interval where the oscillatory and non-oscillatory motions compete, in the sense that both have a chance to occur with a given probability. We refer to the dynamic evolution of these elastic systems, which exhibit inherent uncertainties due to the material properties, as `likely oscillatory motions'

Generation and near-field imaging of Airy surface plasmons

We demonstrate experimentally the generation and near-field imaging of nondiffracting surface waves - plasmonic Airy beams, propagating on the surface of a gold metal film. The Airy plasmons are excited by an engineered nanoscale phase grating, and demonstrate significant beam bending over their propagation. We show that the observed Airy plasmons exhibit self-healing properties, suggesting novel applications in plasmonic circuitry and surface optical manipulation.Comment: 4 pages, 4 figure

Likely equilibria of the stochastic Rivlin cube

The problem of the Rivlin cube is to determine the stability of all homogeneous equilibria of an isotropic incompressible hyperelastic body under equitriaxial dead loads. Here, we consider the stochastic version of this problem where the elastic parameters are random variables following standard probability laws. Uncertainties in these parameters may arise, for example, from inherent data variation between different batches of homogeneous samples, or from different experimental tests. As for the purely elastic problem, we consider the following questions: what are the likely equilibria and how does their stability depend on the material constitutive law? In addition, for the stochastic model, the problem is to derive the probability distribution of deformations, given the variability of the parameters

A randomized controlled trial of training in Motivational Interviewing for child protection.

There has been interest in developing more evidence-based approaches to child and family social work in the UK in recent years. This study examines the impact of a skills development package of training and supervision in Motivational Interviewing (MI) on the skills of social workers and the engagement of parents through a randomized controlled trial. All workers in one local authority were randomly assigned to receive the package (n = 28) or control (n = 33). Families were then randomized to trained (n = 67) or untrained (n = 98) workers. Family meetings with the worker shortly after allocation were evaluated for MI skill. Research interviews gathered data including the WAI. Follow-up interviews 20 weeks later repeated the WAI, and other outcome measures including Goal Attainment Scaling (GAS) and rating of family life. Between group analysis found statistically significant difference in MI skills, though these were not substantial (2.49 in control, 2.91 MI trained, p = .049). There was no statistically significant difference between groups in any other outcome measures. The package of training and supervision did not create sufficient increase in MI skills to influence engagement or outcomes. Implications for understanding the relationship between skills, engagement and organizational change are discussed

Pragmatic Abilities of Children with Williams Syndrome: A Longitudinal Examination

Prior research has indicated that pragmatics is an area of particular weakness for individuals with Williams syndrome (WS). To further address this aspect of the WS social phenotype, we used an individual differences approach to consider both cross-sectional and longitudinal relations among different pragmatic abilities for 14 children with WS, taking into account individual differences in non-verbal reasoning abilities. We also considered the relations between pragmatic abilities and expressive vocabulary ability. Participants were tested at two time points: as 4-year-olds during a 30-min play session with their mothers (Time 1) and an average of 5.87 years later during a one-on-one conversation with a familiar researcher (Time 2). Children’s intellectual and expressive vocabulary abilities were assessed at both time points. Results indicated that the ability to verbally contribute information beyond what was required in response to a question (ExtendQ) was significantly related to the ability to verbally contribute new information in the absence of a question (ExtendS) both at age 4 years and during primary school. At age 4, both the ability to pair verbalizations with eye contact in triadic interactions (secondary intersubjectivity) and expressive vocabulary ability were related to both ExtendQ and ExtendS. Finally, both ExtendQ and the ability to pair verbalizations with eye contact (intersubjectivity) at age 4 years predicted ExtendQ at age 9–12 years. The theoretical implications of our findings and the importance of early pragmatic language intervention for children who have WS are discussed

American Pygmy Shrew, Sorex hoyi, Consumed by an Arctic Grayling, Thymallus arcticus

Arctic Grayling, Thymallus arcticus, are rarely reported to consume small mammals. We report an American Pygmy Shrew, Sorex hoyi, consumed by an Arctic Grayling caught in southern Yukon, Canada. This is the first record of an American Pygmy Shrew being consumed by an Arctic Grayling, and it confirms that Arctic Grayling will consume shrews (Sorex spp.) when they are available. We suspect that the body size of prey is a limiting factor in Arctic Grayling consuming small mammals, with some species of shrews being small enough for Arctic Grayling to consume