Nonlinear Dirac Equations

We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincar\'e invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations

"Autism doesn't come with a manual, it comes with a parent who never gives up": A Family Resilience Perspective to Exploring the Views of Black and Minority Ethnic Parents of Children with Autism

This research sought to adopt a family resilience perspective to exploring the views of Black and Ethnic Minority (BME) parents of children with autism. Semi-structured interviews were carried out with ten parents with the aim to elicit what was meaningful to parents. The purpose of this research was to adopt a strength-based approach to investigate the views of BME parents of children with autism as they negotiate their way through the education system. The existing literature concentrates principally on a largely problemfocussed narrative around parents’ experiences of raising a child with autism. Therefore, the purpose of the study was to emphasise a family’s strengths and resources, using a family resilience framework to explore processes that enable families to thrive. The data was analysed using thematic analysis with themes emerging around family and relationships, values and beliefs and response to diagnosis. Overall, the findings illustrated a diverse range of experiences, values and beliefs that contributed to the resilience demonstrated by all the families. The main findings indicate overwhelming support for the positive aspects of raising a child with autism that are embedded with values and beliefs across individual, family and cultural contexts. The qualities of resilience demonstrated by families enabled them to function and remain optimistic in challenging situations. The research reflects implications for Educational Psychologists with respect to adopting culturally sensitive and strength-based approaches to working with families from diverse backgrounds. The qualitative paradigm has provided insight into understanding parents’ views and values on raising a child with autism, and their hopes for the future

Robust Control Synthesis for Gust Load Alleviation from Large Aeroelastic Models with Relaxation of Spatial Discretisation

This paper introduces a methodology for the design of gust load control systems directly from large aeroelastic models with relaxation of spatial discretisation. A convenient state-space representation of the vortex-panel unsteady aerodynamics suitable for control synthesis is presented. This allows a full understanding of the dynamics of the linearized vortex aeroelastic model and is suitable for control system design. Through the use of robust controllers, large reductions in loading could be achieved. Comparisons are also made between robust and classical control methods. It further demonstrates that controllers synthesized from models of coarse spatial discretizations and of an order of magnitude smaller in size were capable of rejecting disturbances on fully converged models, with performances comparable to expensive higher order controllers developed from full models

JointZone: users' view of an adaptive online learning resource for rheumatology

This paper describes an online learning resource for rheumatology that was designed for a wide constituency of users including primarily undergraduate medical students and health professionals. Although the online resources afford an informal learning environment, the site was pedagogically designed to comply with the general recommendations of the Standing Committee on Training and Education of EULAR (European League Against Rheumatism) for a rheumatology core curriculum. Any Internet user may freely browse the site content with optional registration providing access to adaptive features that personalize the user’s view, for example, providing a reading history and targeted support based on scores from completed case studies. The site has now been available since early 2003, and an online survey of site registrants indicates that well structured pedagogical materials that reflect a learners’ dominant ‘community of practice’ appear to be a successful aid to informal learning