The closest elastic tensor of arbitrary symmetry to an elasticity tensor of lower symmetry

The closest tensors of higher symmetry classes are derived in explicit form for a given elasticity tensor of arbitrary symmetry. The mathematical problem is to minimize the elastic length or distance between the given tensor and the closest elasticity tensor of the specified symmetry. Solutions are presented for three distance functions, with particular attention to the Riemannian and log-Euclidean distances. These yield solutions that are invariant under inversion, i.e., the same whether elastic stiffness or compliance are considered. The Frobenius distance function, which corresponds to common notions of Euclidean length, is not invariant although it is simple to apply using projection operators. A complete description of the Euclidean projection method is presented. The three metrics are considered at a level of detail far greater than heretofore, as we develop the general framework to best fit a given set of moduli onto higher elastic symmetries. The procedures for finding the closest elasticity tensor are illustrated by application to a set of 21 moduli with no underlying symmetry.Comment: 48 pages, 1 figur

‘It makes me feel alive’: the socio-motivational impact of drama and theatre on marginalised young people

An in-depth, longitudinal, idiographic study examined the impact of theatre and drama involvement on marginalised young people. Semi-structured interviews, at three separate time points over 2 years, were conducted with four young people (15–21 years of age) involved in a theatre project. Interpretative phenomenological analysis suggested that drama and theatre create space and support for the authentic self, and provide optimal conditions for promoting growth and resilience through voluntary engagement in a positive activity. In particular, the analysis highlighted the pivotal role of interpersonal relationships and a nurturing environment in re-engaging young people. Some participants’ accounts also suggested that drama provides a uniquely engaging and therapeutic way to reflect on, express and explore experiences. The results are discussed in relation to core psychological processes underpinning self-development and key directions for further research

Heat transfer in separated flows on the pressure side of turbine blades

Heat transfer in separated flows on the pressure side of a typical high lift turbine profile is numerically investigated by means of an in-house CFD code. The numerical code was first validated on attached flows in turbine blades. To obtain flow separation cases, the profile is subject to large negative incidences so that a separation bubble is obtained at the pressure side. The numerical results are compared to available experimental data for code validation. It is shown how local minima and maxima values of the heat transfer coefficient are related to the separation and reattachment points, where the velocity component perpendicular to the wall is shown to have a significant effect on the heat transfe

A ‘quiet revolution’? The impact of Training Schools on initial teacher training partnerships

This paper discusses the impact on initial teacher training of a new policy initiative in England: the introduction of Training Schools. First, the Training School project is set in context by exploring the evolution of a partnership approach to initial teacher training in England. Ways in which Training Schools represent a break with established practice are considered together with their implications for the dominant mode of partnership led by higher education institutions (HEIs). The capacity of Training Schools to achieve their own policy objectives is examined, especially their efficacy as a strategy for managing innovation and the dissemination of innovation. The paper ends by focusing on a particular Training School project which has adopted an unusual approach to its work and enquires whether this alternative approach could offer a more profitable way forward. During the course of the paper, five different models of partnership are considered: collaborative, complementary, HEI-led, school-led and partnership within a partnership

Dependence of Intramyocardial Pressure and Coronary Flow on Ventricular Loading and Contractility: A Model Study

The phasic coronary arterial inflow during the normal cardiac cycle has been explained with simple (waterfall, intramyocardial pump) models, emphasizing the role of ventricular pressure. To explain changes in isovolumic and low afterload beats, these models were extended with the effect of three-dimensional wall stress, nonlinear characteristics of the coronary bed, and extravascular fluid exchange. With the associated increase in the number of model parameters, a detailed parameter sensitivity analysis has become difficult. Therefore we investigated the primary relations between ventricular pressure and volume, wall stress, intramyocardial pressure and coronary blood flow, with a mathematical model with a limited number of parameters. The model replicates several experimental observations: the phasic character of coronary inflow is virtually independent of maximum ventricular pressure, the amplitude of the coronary flow signal varies about proportionally with cardiac contractility, and intramyocardial pressure in the ventricular wall may exceed ventricular pressure. A parameter sensitivity analysis shows that the normalized amplitude of coronary inflow is mainly determined by contractility, reflected in ventricular pressure and, at low ventricular volumes, radial wall stress. Normalized flow amplitude is less sensitive to myocardial coronary compliance and resistance, and to the relation between active fiber stress, time, and sarcomere shortening velocity

Building a Small Cinema: Resisting Neoliberal Colonization in Liverpool

In its stated aim of “creating cinemas not supermarkets,” the Small Cinema project voiced its alterity to the recent redevelopment of Liverpool’s city center and those of other former industrial cities throughout the Midlands and the north of the UK. These regeneration projects addressed the problem of a shrinking manufacturing base by replacing them with service industries, a move which has entailed the privatization of vast tracts of public space. Conversely, the building, functioning, and general praxis of the Small Cinema project suggests a mode of practice that more accurately fits within the paradigm of a collaborative commons than a capitalist marketplace. The project’s exemption from market criteria grants it the freedom to pursue public over private goods, thereby constituting a point of resistance to the ongoing neoliberalization of the city and changes to government policy that make it increasingly difficult for non-profit projects to exist. Historically speaking, cinemas have been accessible to the working class in a way that other artistic media have not. However, while the history of film as a tool for political subversion is well documented, less attention has been paid to the physical construction of independent cinematic space, its programming/running, and its potential as a node of resistance to neoliberal colonization. This paper uses the case study of the Small Cinema project in Liverpool as a means by which to understand how cinematic spaces can counteract the effects of policies that continue to have such a detrimental impact on the arts and education, as well as social health and well-being

Quantum dynamics of phase transitions in broken symmetry λϕ4\lambda \phi^4 field theory

We perform a detailed numerical investigation of the dynamics of broken symmetry $\lambda \phi^4$ field theory in 1+1 dimensions using a Schwinger-Dyson equation truncation scheme based on ignoring vertex corrections. In an earlier paper, we called this the bare vertex approximation (BVA). We assume the initial state is described by a Gaussian density matrix peaked around some non-zero value of $$, and characterized by a single particle Bose-Einstein distribution function at a given temperature. We compute the evolution of the system using three different approximations: Hartree, BVA and a related 2PI-1/N expansion, as a function of coupling strength and initial temperature. In the Hartree approximation, the static phase diagram shows that there is a first order phase transition for this system. As we change the initial starting temperature of the system, we find that the BVA relaxes to a new final temperature and exhibits a second order phase transition. We find that the average fields thermalize for arbitrary initial conditions in the BVA, unlike the behavior exhibited by the Hartree approximation, and we illustrate how$$ and $$depend on the initial temperature and on the coupling constant. We find that the 2PI-1/N expansion gives dramatically different results for$$.Comment: 28 pages, 21 figures; ver 2 -- additional comments on the nature of the phase transition in 1+1 dimension

Rpgrip1 is required for rod outer segment development and ciliary protein trafficking in zebrafish

The authors would like to thank the Royal Society of London, the National Eye Research Centre, the Visual Research Trust, Fight for Sight, the W.H. Ross Foundation, the Rosetrees Trust, and the Glasgow Children’s Hospital Charity for supporting this work. This work was also supported by the Deanship of Scientific Research at King Saud University for funding this research (Research Project) grant number ‘RGP – VPP – 219’.Mutations in the RPGR-interacting protein 1 (RPGRIP1) gene cause recessive Leber congenital amaurosis (LCA), juvenile retinitis pigmentosa (RP) and cone-rod dystrophy. RPGRIP1 interacts with other retinal disease-causing proteins and has been proposed to have a role in ciliary protein transport; however, its function remains elusive. Here, we describe a new zebrafish model carrying a nonsense mutation in the rpgrip1 gene. Rpgrip1homozygous mutants do not form rod outer segments and display mislocalization of rhodopsin, suggesting a role for RPGRIP1 in rhodopsin-bearing vesicle trafficking. Furthermore, Rab8, the key regulator of rhodopsin ciliary trafficking, was mislocalized in photoreceptor cells of rpgrip1 mutants. The degeneration of rod cells is early onset, followed by the death of cone cells. These phenotypes are similar to that observed in LCA and juvenile RP patients. Our data indicate RPGRIP1 is necessary for rod outer segment development through regulating ciliary protein trafficking. The rpgrip1 mutant zebrafish may provide a platform for developing therapeutic treatments for RP patients.Publisher PDFPeer reviewe